Application and System Design of Elastomer Based Optofluidic Lenses

Application and System Design of Elastomer Based Optofluidic Lenses
Application and System Design of Elastomer Based Optofluidic Lenses
by
Nickolaos Savidis
_____________________
A Dissertation Submitted to the Faculty of the
COLLEGE OF OPTICAL SCIENCES
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2012
Copyright © Nickolaos Savidis 2012
2
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the dissertation
Prepared by Nickolaos Savidis
Entitled Application and System Design of Elastomer Based Optofluidic Lenses
And recommend that it be accepted as fulfilling the dissertation requirement for the
Degree of Doctor of Philosophy
_______________________________________________________________________
Date: 10/11/2012
James Schwiegerling
_______________________________________________________________________
Date: 10/11/2012
Nasser Peyghambarian
_______________________________________________________________________
Gholam Peyman
Date: 10/11/2012
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Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the
final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and recommend that it be
accepted as fulfilling the dissertation requirement.
________________________________________________ Date: 10/11/2012
Dissertation Director: James Schwiegerling
4
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the
University of Arizona and is deposited in the University Library to be made available to borrowers under
rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided that accurate
acknowledgment of source is made. Requests for permission for extended quotation from or reproduction
of this manuscript in whole or in part may be granted by the head of the major department or the Dean of
the Graduate College when in his or her judgment the proposed use of the material is in the interests of
scholarship. In all other instances, however, permission must be obtained from the copyright holder.
SIGNED: Nickolaos Savidis
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ACKNOWLEDGEMENTS
I would like to thank my advisor, Prof. Jim Schwiegerling, Prof. Nasser Peyghambarian
and Prof. Gholam Peyman for their guidance and support for this research, and the friendship
and understanding they have shown through the progress of our research
6
DEDICATION
To my family who have always offered support.
7
TABLE OF CONTENTS
LIST OF FIGURES .......................................................................................................... 11
LIST OF TABLES ............................................................................................................ 16
ABSTRACT ...................................................................................................................... 17
1.0 INTRODUCTION ...................................................................................................... 19
1.1 History of Optofluidic Lenses ................................................................................... 19
1.2 Optofluidic Lenses ................................................................................................... 21
1.3 Surface Profile Control of Pressure Actuated Fluidic Lenses ................................. 22
1.3.1 Shell Surface Profile .............................................................................................. 23
1.3.2 Spherical Surface Profile ...................................................................................... 24
1.3.3 Cylindrical Surface Profile ................................................................................... 25
2.0 HUMAN VISUAL SYSTEM .................................................................................... 28
2.1 Eye’s Anatomy......................................................................................................... 28
2.2 Eye’s Optical Properties .......................................................................................... 29
2.4 Spatial Acuity........................................................................................................... 32
3.0 ABERRATIONS AND ABBERATION CORRECTION......................................... 34
3.1 Circularly Symmetric Optical Systems and the Wavefront ..................................... 34
3.1.1 Defocus Aberration .............................................................................................. 36
3.1.2 Chromatic Aberration .......................................................................................... 37
3.1.3 Astigmatism Aberration ....................................................................................... 39
3.1.4 Spherical Aberration ............................................................................................. 40
3.2 Asymmetric Optical Systems, Zernike Fitting, and Ocular Aberrations ................. 41
3.2.1 Zernike Polynomials ............................................................................................. 41
3.2.2 Zernike Fitting and Ocular Aberrations ................................................................ 42
3.2.3 Factors Causing Ocular Aberrations ..................................................................... 45
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TABLE OF CONTENTS- Continued
3.2.4 Measuring Ocular Aberrations and Optical Measuring Devices ............................ 46
3.2.5 Light Source of Shack-Hartmann Wavefront Sensor ........................................... 49
3.2.6 Tradeoffs of the Shack-Hartmann Wavefront Sensor ........................................... 49
4.0 SPHERICAL FLUIDIC LENSES AND NON-MECHANICAL ZOOM ................. 52
4.1 Theory of Spherical Fluidic Lenses ......................................................................... 53
4.2 Fabrication of Elastomer Membrane ....................................................................... 55
4.3 Spherical Fluidic Lens One ...................................................................................... 56
4.4 Spherical Fluidic Lens Two ..................................................................................... 59
4.5 Zoom Lenses ............................................................................................................ 60
4.6 Theory: Variable Power Zoom System.................................................................... 61
4.7 Experiment: Zoom System Verification .................................................................. 64
4.8 Limitations of Fluidic Zoom System ....................................................................... 67
5.0 FLUIDIC ACHROMAT ............................................................................................ 69
5.1 Achromat One: Diffractive / Refractive Hybrid ...................................................... 70
5.1.2 Liquid Crystal Diffractive Lens ............................................................................ 72
5.1.3 Fluidic Refractive Lens ......................................................................................... 73
5.1.4 Test Methods and Results of the Hybrid Diffractive/Refractive Achromat ......... 75
5.2 Continuous Variable Achromat Fluidic Lens .......................................................... 89
5.2.1 Variable Focal Length Achromat Design ............................................................. 90
5.2.2 Testing Methods for Continuous Variable Focal Length Achromat .................... 93
6.0 WAVEFRONT CORRECTION OF THE FLUIDIC PHOROPTER AND
FLUIDIC AUTO-PHOROPTER ..................................................................................... 101
6.1 Fluidic Phoropter ..................................................................................................... 104
6.1.1 Wavefront Analysis of Defocus and Astigmatism Lenses ................................... 104
6.1.2 Wavefront Analysis of Fluidic Phoropter ............................................................. 107
6.2 Wavefront Analysis of the Fluidic Auto-Phoropter ................................................. 111
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TABLE OF CONTENTS- Continued
7.0 FLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: SYSTEM DESIGN ............ 113
7.1 Design of Fluidic Auto-Phoropter Prototype One ................................................... 114
7.1.1 Fluidic Auto-Phoropter Prototype One: Light Path from Source to Fluidic
Phoropter. ......................................................................................................................... 115
7.1.2 Fluidic Auto-Phoropter Prototype One: Light Path from Fluidic Phoropter
through the Eye Model..................................................................................................... 118
7.1.2.1 Fluid Selection for Fluidic Phoropter ................................................................ 119
7.1.2.2 Test Results with Fluidic Phoropter ................................................................... 123
7.1.3 Fluidic Auto-Phoropter Prototype One: Light Path Through Keplerian
Telescope ......................................................................................................................... 128
7.1.4 Fluidic Auto-Phoropter Prototype One: Light Path from Keplerian Telescope to
Shack - Hartmann Wavefront Sensor .............................................................................. 131
7.2 Fluidic Auto-Phoropter Prototype One: Alignment for Monocular Setup .............. 133
7.3 Fluidic Auto-Phoropter Prototype One: Binocular Alignment and Inter-Pupilary
Distance…........................................................................................................................ 135
8.0 FLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: MODELING ...................... 141
8.1 Lens Deign Model of Dynamic Range of Auto-Phoropter ...................................... 141
8.2 Illumination Model of Dynamic Range of Fluidic Auto-Phoropter ........................ 148
9.0 FLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: TESTING ........................... 158
9.1 Testing Approach: Measurements of Model Eye .................................................... 159
9.2 Testing Approach: Measuring Fluidic Phoropter .................................................... 166
9.2.1 Defocus Lens Filled with DI Water Fluid Volume Tested with Fluidic AutoPhoropter set for 3 mm and 6 mm Stop Sizes .................................................................. 169
9.2.2 Defocus Lens Filled with BK-7 Oil # 3 Tested with Fluidic Auto-Phoropter
for 3 mm and 6 mm Stop Sizes ........................................................................................ 174
9.2.3 Astigmatism Lens Filled with DI Water and Fluidic Auto-Phoropter set at a 3
mm Stop Size ................................................................................................................... 179
9.3 Nulling Error with the Fluidic Auto-Phoropter: Fluidic Phoropter Cancels Model
Eye Error .......................................................................................................................... 191
9.4 Limits of the Optical Design .................................................................................... 192
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TABLE OF CONTENTS- Continued
10.0 FLUIDIC AUTO-PHOROPTER: OFF-AXIS OPTICAL DESIGNS ..................... 198
10.1 Fluidic Auto-Phoropter with Traditional Off-Axis Optics .................................... 199
10.1.1 Design Setup of Fluidic Auto-Phoropter Prototype Two ................................... 201
10.1.2 Modeling and Testing of Fluidic Auto-Phoropter Prototype Two...................... 203
10.2 Nulling Error with Prototype Two Fluidic Auto-Phoropter .................................. 206
10.3 Limits of Optical Design ........................................................................................ 208
11.0 FLUIDIC AUTO-PHOROPTERS: OFF-AXIS OPTICAL DESIGNS WITH
HOLOGRAPHIC OPTICAL ELEMENTS ..................................................................... 215
11.1 Holography and Holographic Lenses ..................................................................... 217
11.2 Design of Fluidic Holographic Auto-Phoropter with Holographic Optical
Elements as Lenses .......................................................................................................... 219
11.3 Modeling of Fluidic Holographic Auto-Phoropter Prototype One ........................ 220
11.4 Design and Setup of the Fluidic Holographic Auto-Phoropter .............................. 222
11.5 Testing of Fluidic Holographic Auto-Phoropter .................................................... 224
11.6 Nulling Error with Fluidic Holographic Auto-Phoropter ...................................... 228
11.7 Limits of Holographic Optical Design ................................................................... 230
12.0 CONCLUSION AND FUTURE WORK ................................................................ 234
12.1 Wavefront Comparison of Freely Supported Edge vs. Clamped Edge Designs.... 235
12.2 Improving Fluidic Zoom with a Redesigned Terrestrial Keplerian Telescope...... 236
12.3 Progression of Fluidic Achromat ........................................................................... 237
12.4 Progression of the Fluidic Auto-Phoropter Systems .............................................. 237
12.5 Progression of Fluidic Holographic Auto-Phoropter ............................................. 240
12.6 Mobile Holographic Fluidic Auto-Phoropter......................................................... 243
REFERENCES ................................................................................................................ 247
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LIST OF FIGURES
Figure 1-1: Shell Membrane ........................................................................................... 23
Figure 1-2: Spherical Membrane .................................................................................... 24
Figure 2-1: Eye Profile.................................................................................................... 28
Figure 2-2: The Arizona Eye Model ............................................................................... 30
Figure 2-3: Optical and Visual Axis ............................................................................... 31
Figure 2-4: Visual Acuity ............................................................................................... 33
Figure 3-1: Optical Coordinate System .......................................................................... 35
Figure 3-2: Defocus Aberration ...................................................................................... 37
Figure 3-3: Chromatic Aberration of the Marginal Ray ................................................. 38
Figure 3-4: Chromatic Aberration of the Chief Ray ....................................................... 39
Figure 3-5: Astigmatism Aberration ............................................................................... 40
Figure 3-6: Spherical Aberration .................................................................................... 41
Figure 3-7: Shack-Hartmann Wavefront Sensing ........................................................... 47
Figure 3-8: Shack-Hartmann Spot Displacement ........................................................... 48
Figure 3-9: Shack-Hartmann Dynamic Range vs. Sensitivity ........................................ 50
Figure 4-1: Fluidic Lens 1............................................................................................... 56
Figure 4-2: Zoom Control of Fluidic Lens 1 .................................................................. 58
Figure 4-3: Fluidic Lens 2............................................................................................... 59
Figure 4-4: Zoom Control of Fluidic Lens 2 .................................................................. 60
Figure 4-5: Zoom System ............................................................................................... 62
Figure 4-6: Zoom System Setup ..................................................................................... 64
Figure 4-7: Zoom Magnification of Letter Chart ............................................................ 65
Figure 4-8: Experimental vs. Theoretical Zoom Magnifying Power .............................. 66
Figure 5-1: Diffractive / Refractive Hybrid Design ........................................................ 71
Figure 5-2: Achromat Test Setup.................................................................................... 79
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LIST OF FIGURES - Continued
Figure 5-3: Diffractive Spot’s Per Wavelength .............................................................. 84
Figure 5-4: Fluidic Achromat Focal Length ................................................................... 85
Figure 5-5: Discrete Diffractive / Refractive Focal Length Achromat Results .............. 88
Figure 5-6: Dual Fluidic Achromatic Lens Design ......................................................... 91
Figure 5-7: Dual Chamber Fluidic Achromat ................................................................. 92
Figure 5-8: Coupled Single Chamber Achromatic Design ............................................. 92
Figure 5-9: Dual Achromat Testing Design.................................................................... 93
Figure 5-10: ZEMAX Model of a 80 mm Focal Length Achromat Design ................... 96
Figure 5-11: ZEMAX Model of a 400 mm Focal Length Achromat Design ................. 96
Figure 5-12: ZEMAX Model of a - 100 mm Focal Length Achromat Design ............... 99
Figure 5-13: ZEMAX Model of a - 60 mm Focal Length Achromat Design ................. 99
Figure 6-1: Fluidic Phoropter Compared to Standard Phoropter .................................... 103
Figure 6-2: Wavefront Measurement of Defocus Lens .................................................. 105
Figure 6-3: Wavefront Measurement of Astigmatism Lens ........................................... 107
Figure 6-4: Fluidic Phoropter Orientation ...................................................................... 108
Figure 7-1: Targets at Multiple Planes for Focusing Through Fluidic Auto-Phoropter . 113
Figure 7-2: Layout of Optofluidic Auto-Phoropter Prototype One ................................ 115
Figure 7-3: Specifications of Fiber Coupled SLD .......................................................... 116
Figure 7-4: Circuit Used to Drive the SLD’s .................................................................. 117
Figure 7-5: Defocus Lens Power Profile ........................................................................ 124
Figure 7-6: Double Astigmatic Fluidic Lens Power Profile ........................................... 125
Figure 7-7: Imaging Results of Model Eye through Fluidic Phoropter .......................... 126
Figure 7-8: Modeling Myopia and Hyperopia ................................................................ 127
Figure 7-9: Design of Optofluidic Auto-Phoropter Prototype One ................................ 128
Figure 7-10: Folding Mirror Analysis............................................................................. 131
Figure 7-11: Line of Sight of User .................................................................................. 132
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LIST OF FIGURES - Continued
Figure 7-12: Alignment of Monocular Fluidic Auto-Phoropter Prototype One ............. 133
Figure 7-13: Base Setup of the Binocular Fluidic Auto-Phoropter ................................ 137
Figure 7-14: Machined Adapters for Inter-pupilary Distance of Binocular Fluidic
Auto-Phoropter ................................................................................................................ 138
Figure 7-15: Spots of Alignment Beam at 15 Feet Away of Binocular Fluidic AutoPhoropter .......................................................................................................................... 140
Figure 7-16: User Position in a Fully Aligned Binocular Fluidic Auto-Phoropter......... 140
Figure 8-1: ZEMAX Layout of Monocular Setup of Auto-Phoropter ............................ 142
Figure 8-2: Model of Image Plane of Shack-Hartmann Wavefront Sensor in ZEMAX 144
Figure 8-3: Dynamic Range Limits of Auto-Phoropter ................................................. 148
Figure 8-4: FRED Model of Binocular Fluidic Auto-Phoropter .................................... 149
Figure 8-5: Model of Image Plane of Shack-Hartmann Wavefront Sensor in FRED .... 150
Figure 8-6: Power Range of Defocus Lens of Fluidic Phoropter ................................... 151
Figure 8-7: Power Variation of Defocus Fluidic Lens in FRED of Fluidic AutoPhoropter .......................................................................................................................... 154
Figure 8-8: Defocus Lens Power Variation and Effects on Fluidic Auto-Phoropter ...... 155
Figure 8-9: Astigmatism Lens One Power Variation and Effects on Fluidic AutoPhoropter .......................................................................................................................... 156
Figure 8-10: Astigmatism Lens Two Power Variation and Effects on Fluidic AutoPhoropter .......................................................................................................................... 157
Figure 8-11: Defocus and Astigmatism Lens Two Power Variation and Effects on
Fluidic Auto-Phoropter .................................................................................................... 157
Figure 9-1: Step 2: Testing Auto-Phoropter with Eye Model ........................................ 160
Figure 9-2: Unfolded Eye Model .................................................................................... 161
Figure 9-3: Model Eye Power vs. Defocus Wavefront Relative to Pupil Size ............... 165
Figure 9-4: Defocus Measurements through our Auto-Phoropter System ..................... 166
Figure 9-5: Step 3: Testing Auto-Phoropter with Fluidic Phoropter .............................. 167
Figure 9-6: Wavefront Measurements with DI water and 3 mm Stop for Defocus Lens171
Figure 9-7: Wavefront Measurements with DI water and 6 mm Stop for Defocus Lens172
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LIST OF FIGURES - Continued
Figure 9-8: Refraction Terms with DI Water and 3 mm Stop for Defocus Lens ........... 173
Figure 9-9: Refraction Terms with DI Water and 6 mm Stop for Defocus Lens ........... 174
Figure 9-10: Wavefront Measurements with BK-7 Oil and 3 mm Stop for Defocus
Lens .................................................................................................................................. 176
Figure 9-11: Wavefront Measurements with BK-7 Oil and 6 mm Stop for Defocus
Lens .................................................................................................................................. 177
Figure 9-12: Refractive Terms with BK-7 Oil and 3 mm Stop for Defocus Lens .......... 178
Figure 9-13: Refractive Terms with BK-7 Oil and 6 mm Stop for Defocus Lens.......... 178
Figure 9-14: Fluidic Valve Control System .................................................................... 180
Figure 9-15: Fluidic Phoropter Combination .................................................................. 181
Figure 9-16: Wavefront Measurements with DI Water and 3 mm Stop for Astigmatism
Lens One .......................................................................................................................... 182
Figure 9-17: Wavefront Measurements with DI Water and 3 mm Stop for Astigmatism
Lens Two ......................................................................................................................... 183
Figure 9-18: Axis Term for Astigmatism Lens One with DI Water and 3 mm Stop for
Fluidic Auto- Phoropter ................................................................................................... 185
Figure 9-19: Axis Term for Astigmatism Lens Two with DI Water and 3 mm Stop for
Fluidic Auto- Phoropter ................................................................................................... 186
Figure 9-20: Cylinder and Sphere Term for Astigmatism Lens One with DI Water
and 3 mm Stop for Fluidic Auto-Phoropter ..................................................................... 187
Figure 9-21: Cylinder and Sphere Term for Astigmatism Lens Two with DI Water
and 3 mm Stop for Fluidic Auto-Phoropter .................................................................... 188
Figure 9-22: Astigmatic Mapping of Auto-Phoropter System ....................................... 191
Figure 9-23: Nulled Defocus Error with Eye Model at 1 D and -1 D Defocus of
Fluidic Phoropter ............................................................................................................. 192
Figure 9-24: Line of Sight Limit of Fluidic Auto-Phoropter .......................................... 195
Figure 9-25: Line of Sight Limit of Off-Axis Fluidic Auto- Phoropter ......................... 196
Figure 10-1: Fluidic Auto-Phoropter Prototype Two ..................................................... 200
Figure 10-2: Testing Fluidic Auto-Phoropter Prototype Two ........................................ 202
Figure 10-3: Mobile Fluidic Auto-Phoropter Prototype Two ........................................ 203
15
LIST OF FIGURES - Continued
Figure 10-4: Comparing Wavefront Error of Prototypes One and Two Relative to
Defocus Power of the Model Eye .................................................................................... 205
Figure 10-5: Wavefront Error of Prototype Two Relative to Defocus Power of the
Model Eye ........................................................................................................................ 206
Figure 10-6: Nulling Power Error with Fluidic Auto-Phoropter Prototype Two ........... 207
Figure 10-7: Nulling Power Observed for Fluidic Auto-Phoropter Prototype Two
from Shack-Hartmann Wavefront Sensor ........................................................................ 208
Figure 10-8: Modified Fluidic Auto-Phoropter Prototype Two ..................................... 211
Figure 10-9: Fluidic Auto-Phoropter Prototype Three ................................................... 213
Figure 10-10: Image of Fluidic Auto-Phoropter Prototype Three .................................. 214
Figure 11-1: Fluidic Holographic Auto-Phoropter ........................................................ 220
Figure 11-2: Fluidic Holographic Auto-Phoropter ZEMAX Model............................... 221
Figure 11-3: Fluidic Holographic Auto-Phoropter Power Range ................................... 222
Figure 11-4: Testing Fluidic Holographic Auto-Phoropter ............................................ 224
Figure 11-5: Comparing Wavefront Error of Prototypes Two and HOE Designs
Relative Defocus Power of the Model Eye ...................................................................... 226
Figure 11-6: Wavefront Error of Prototype Two Relative to Defocus Power of the
Model Eye ....................................................................................................................... 228
Figure 11-7: Nulling Power Error with Holographic Fluidic Auto-Phoropter ............... 229
Figure 11-8: Image Plane of Holographic Fluidic Auto-Phoropter ................................ 230
Figure 11-9: Polarization Controlled Holographic Fluidic Auto-Phoropter Design ...... 232
Figure 12-1: Terrestrial Keplerian Telescope in Zoom System ...................................... 237
Figure 12-2: Advanced Holographic Fluidic Auto-Phoropter with Pupil Imaging ........ 242
Figure 12-3: 4F Advanced Holographic Fluidic Auto-Phoropter with Pupil Imaging ... 243
Figure 12-4: Binocular Advanced 4F Holographic Fluidic Auto-Phoropter without
Pupil Imaging ................................................................................................................... 245
Figure 12-5: Mobile Binocular Helmet with Two Advanced 4F Holographic Fluidic
Auto-Phoropter Designs................................................................................................... 246
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LIST OF TABLES
Table 3-1: Ocular Aberrations ........................................................................................ 44
Table 4-1: Zoom Magnification ...................................................................................... 66
Table 5-1: Achromat Lookup Table ............................................................................... 76
Table 5-2: Diffractive Lens A ......................................................................................... 83
Table 5-3: Diffractive Lens B ......................................................................................... 84
Table 5-4: Analysis of Fluidic Lens Radius of Curvature .............................................. 94
Table 5-5: Radius of Curvature for Achromitization of Two Fluids .............................. 98
Table 7-1: Fluid Compatibility with Auto-Phoropter Material....................................... 121
Table 7-2: Fluid Optical and Chemical Properties ......................................................... 121
Table 8-1: Power Shift of Auto-Phoropter System Due to Variation in Corneal Radii . 146
Table 8-2: Empirical Measurements of Defocus Lens and Radii of Curvature .............. 152
Table 9-1: Results of Auto-Phoropter with Eye Model .................................................. 163
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ABSTRACT
Adaptive optic technology has revolutionized real time correction of wavefront
aberrations. Optofluidic based applied optic devices have offered an opportunity to produce
flexible refractive lenses in the correction of wavefronts. Fluidic lenses have superiority relative
to their solid lens counterparts in their capabilities of producing tunable optical systems, that
when synchronized, can produce real time variable systems with no moving parts. We have
developed optofluidic fluidic lenses for applications of applied optical devices, as well as
ophthalmic optic devices. The first half of this dissertation discusses the production of fluidic
lenses as optical devices. In addition, the design and testing of various fluidic systems made
with these components are evaluated. We begin with the creation of spherical or defocus singlet
fluidic lenses. We then produced zoom optical systems with no moving parts by synchronizing
combinations of these fluidic spherical lenses. The variable power zoom system incorporates two
singlet fluidic lenses that are synchronized. The coupled device has no moving parts and has
produced a magnification range of 0.1 x to 10 x or a 20 x magnification range. The chapter after
fluidic zoom technology focuses on producing achromatic lens designs. We offer an analysis of
a hybrid diffractive and refractive achromat that offers discrete achromatized variable focal
lengths.
In addition, we offer a design of a fully optofluidic based achromatic lens. By
synchronizing the two membrane surfaces of the fluidic achromat we develop a design for a
fluidic achromatic lens.
The second half of this dissertation discusses the production of optofluidic technology in
ophthalmic applications. We begin with an introduction to an optofluidic phoropter system. A
fluidic phoropter is designed through the combination of a defocus lens with two cylindrical
fluidic lenses that are orientated 45° relative to each other. Here we discuss the designs of the
18
fluidic cylindrical lens coupled with a previously discussed defocus singlet lens. We then couple
this optofluidic phoropter with relay optics and Shack-Hartmann wavefront sensing technology
to produce an auto-phoropter device. The auto-phoropter system combines a refractometer
designed Shack-Hartmann wavefront sensor with the compact refractive fluidic lens phoropter.
This combination allows for the identification and control of ophthalmic cylinder, cylinder axis,
as well as refractive error. The closed loop system of the fluidic phoropter with refractometer
enables for the creation of our see-through auto-phoropter system. The design and testing of
several generations of transmissive see-through auto-phoropter devices are presented in this
section.
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1.0 INTRODUCTION
The field of optofluidics was initially coined in the 1980’s through developments in the
field of micro-electronics [1, 2].
At the time, massive technological breakthroughs in
nanotechnology brought micro-electronics into the field of optics.
Fast and small fluid
controlled mechanisms made on-chip optical devices realizable. Currently, optofluidics has
progressed to encapsulate all optical devices which apply fluid or fluid control, where fluid
encapsulates liquids and gases [3]. With this broad definition, optofluidics has been found in the
fields of imaging, medical devices, bioengineering, metrology, display technologies, data storage
and optical communication.
Due to the diversity of optofluidics, the field can be categorized in a couple of broadly
engulfing sub-fields. There has been an evolution of optofluidics in two primary directions: 1)
Photonics and 2) Applied Optics. Optofluidic based photonic devices have found application in
sensing, switching, waveguides, tweezing, plasmonics, resonators, photonic crystals, material
research, amongst other branches.
Optofluidic based applied optic devices have found
application in imaging, lenses, microlenses, plasmonics, and material research.
Optofluidic technologies have grown across a wide variety of fields due to their ease in
producing highly controlled, wide dynamic range, high resolution, and smooth interfacing
capabilities. We have found that these advantages offered by optofluidic lenses relative to solid
lenses are desirable. Our primary focus of this dissertation is on the development of optofluidic
lenses and their applications in system devices. We will describe the optofluidic lenses
developed and the devices we applied towards imaging, medical devices, and bioengineering.
1.1 History of Optofluidic Lenses
20
The origins of fluid controlled optical devices have a longer history in the field of lenses.
In the late 18th century Robert Blair achieved aberration correction by trapping fluid in two glass
pieces. The control mechanism was to alter the concentration of fluid which enabled the device
to then alter the index of refraction. In turn these static lenses were capable of correcting
aberration through fluid volume control. This optofluidic device is the first documented fluid
based optical lens [4].
The first optofluidic lens with a flexible surface was invented in the late 19th century
through, to the author’s knowledge, the oldest patent filed on the subject matter [5]. The patent,
which was filed in 1890 and accepted in 1893, offered a pressure controlled mechanism to alter
the curvature of a refracting or reflecting surface. This lens was described to offer transmission
in radiant energy on both sides of the lens. Each side of the lens was composed of elastic
material such as elastic plates or membranes.
Optofluidic lenses in the field of ophthalmic optics progressed further in 1918 with the
proposition of fluid based spectacles [6].
This patent was focused on producing multifocal
lenses by altering the amount of fluid in a central chamber. Screws on the side of the glasses
would be adjusted to alter the amount of transmissive fluid in the line of sight of the user. These
glasses were proposed to correct for defocus through the control of the focal power of the
optofluidic lenses. Two decades later a patent was filed in 1938 and accepted in 1942 to produce
a variable cylinder fluidic lens to correct for astigmatism [7]. This optofluidic lens was proposed
to have a flat transparent side and a flexible membrane side. Cylinder was produced by bending
the transmissive membrane in one direction. A relatively stiff material was required to flex the
membrane in one dimension, limiting this proposed design.
21
A modern pressure actuated optofluidic lens was proposed in a patent filed in 1941 from
Bausch and Lomb [8]. The motivation was to correct for spherical aberration and also for
chromatic aberration.
Fluid inserted into one or more chambers were placed between a
transparent elastic diaphragm and a rigid transparent surface. Pressure actuation deformed the
surface membrane into a continuous shape that corrected for spherical aberration. Multiple fluid
chambers with varying index of refraction allowed for the creation of chromatically corrected
optofluidic lenses. This proposed patent focused on the properties of the fluids. In addition to
the transparency of the material, they suggested control on the index of refraction and fluid
reactivity to system mechanisms. This lens structure is still a major approach utilized today in
membrane actuated optofluidic lenses.
1.2 Optofluidic Lenses
The patent from B&L in 1941 was an introduction to the modern pressure controlled
optofluidic lenses built with widely tunable membranes. Progress in the field continued into the
1980’s in both theory and design [9, 10, 11]. As is in the early B & L patent, large aperture
fluidic lenses are composed of a rigid chamber with an elastic polymer based wall. The polymer
wall flexes as pressure is applied into the chamber.
There are two types of optofluidic lens: liquid lenses and pneumatic lenses [3]. Liquid
based optofluidic lenses contain fluid within the rigid structure, where the fluid is either a liquid
or a gas. Here is where the author’s definition slight differs with a more commonly used term in
the field.
We call optofluidic liquid lenses fluidic lenses rather than liquid lenses for a
fundamental reason. The designed lenses pressure mechanism is applicable to either a gas or
liquid. The term liquid lens implies a limitation to this optofluidic technology and neglects the
22
possibility of gas-based optofluidic lenses. For this reason we select to call fluid chamber
optofluidic lenses fluidic lenses from here forth.
The functionality of the fluidic lenses has a flexible surface. The polymer membrane
deforms to compensate for a pressure differential as fluid is injected or withdrawn within the
active chamber. Pneumatic based optofluidic lenses do not contain any fluid and are based on
varying the polymer shape to produce focusing power [12]. Both optofluidic lenses operate
through the application of pressure on an elastomer surface.
The difference in controlling optical power lies in the approach of producing power
variation. Optical power tuning in pneumatic optofluidic lenses is achieved through optical
pathlength variation across the elastomer’s clear aperture, as the lens is one continuous elastomer
material. In fluidic lenses, optical power tuning is achieved by controlling the bending profile of
the elastomer membrane, which is microns thick, and the index variation between the contained
fluid and material external to the lens. When the elastomer membrane is thin it is observed as
negligible, allowing for the fluidic lens power to be modeled directly by the indexes stated above
and the surface curvature. The fluidic lens can produce a wide range of powers as certain
elastomers offer high flexibility but often times do not produce large clear apertures. One can
increase clear apertures of fluidic lenses through control of the surface profile.
1.3 Surface Profile Control of Pressure Actuated Fluidic Lenses
Pressure actuated fluidic lenses produce a bending to the thin elastomer membrane. As
we know, index variation and surface curvature defines the power control of the fluidic lens.
Through the control of the opto-mechanical structure of the optofluidic element, we are able to
produce various spherical and cylindrical lenses by controlling the surface profile of the
23
membranes. We first begin with the surface profile characterization of an optofluidic lens that
produces a circularly symmetric optical element and then that of a cylinder lens. In this section
we will characterize the geometric representations of the surface profiles.
There are two
approaches in characterizing the geometry of a circularly designed flexed membrane surface: that
of a shell geometry [13, 14] or that of a sphere geometry [15, 16].
1.3.1 Shell Surface Profile
Figure 1-1 Shell Membrane: This is a typical membrane where the clear aperture applies the
entire active area of the membrane with multiple radii of curvature. [3]
Shell geometry is a fair representation of an optofluidic liquid lens that actively applies
the majority of the elastomer surface in the clear aperture of the optical element. If r o is the
semi-diameter of the clear aperture as is observed from Figure 1-1, there is a variation in the
radius of curvature of the membrane as one progresses from the central active area to the
peripheral active area. The periphery is clamped down to maintain a chamber structure. This
causes the curvature u(r) to vary along the surface profile. It is desirable to develop an optomechanical design that produces one continuous surface profile. Hence, we would be able to
define a continuous radius of curvature and model the optofluidic liquid lenses with a single
continuous radius of curvature from a single geometry.
24
1.3.2 Spherical Surface Profile
There are two approaches used to design a liquid lens where we can estimate the surface
profile with a spherical geometry. One approach is to control the clear aperture area of the lens.
If one were to apply just the central active area of the optofluidic liquid lens as the clear aperture,
it would be observed as approximately a continuous spherical surface. The periphery will still
have a radius that is discontinuous, but relative to the active clear aperture area, the device
observes a continuous radius of curvature. A second approach in producing an optofluidic liquid
lens with a spherical geometry is to design the opto-mechanics of the structure so the lenses
would be tightly suspended on the periphery, similar to a drum. By creating a drum suspension
there is continuous pressure surrounding the periphery of the clear aperture through the center.
We have applied both approaches in the development of our two spherical fluidic lenses that are
modeled by this spherical geometry.
Figure 1-2 Spherical Membrane: This is a typical membrane where the clear aperture applies
the active area of the membrane with a single continuous radius of curvature [16].
Figure 1-2 defines a spherical membrane with a diameter d, a sag h, and a radius of
curvature rc. We are capable of extracting the radius of curvature of the spherical surface through
the simple relationship of knowing the optical power of the optofluidic liquid lens [16].
25
1-1
The index of refraction of the fluid nfluid and the external surroundings nexternal must be
known. One can measure the focal location and optical power of the lens. One can derive the
sag of the fluidic lens from information of the radius of curvature and diameter of the clear
aperture.
1-2
We were able to determine the sag and radius of curvature of the volume from the
structure of the fluidic lens and the power at the focal position. The determination of the amount
of fluidic volume required to alter the curvature of the lens is further expanded from the top two
equations [16]. Fluidic volume (V) is determined by
1-3
From the equation of optical power of an interfacing surface and the assumption of a
spherically symmetric surface, we were able to map the correlation of the radius of curvature,
sag, change in fluid volume and optical power produced by any fluidic lens.
1.3.3 Cylindrical Surface Profile
A cylindrical profile is achievable by destroying the circular symmetry of the fluidic lens.
The fluidic lens must be developed through a rectangular suspension with reflective mirror
26
symmetry. This is achievable by opto-mechanically designing the optofluidic liquid lens so that
the membrane has a rectangular frame. The active area of the cylinder lens is designed such that
the restrained rectangular frame is much larger than the clear aperture of the liquid lens.
Through the examination of the freely constrained beam deflection we are able to map
this cylindrical surface profile [17]. The relative length of the long side and short side of the
rectangular frame define the performance of the cylindrical profile. We are able to replicate that
of a freely constrained beam when constraining the frame so that the longer side is significantly
longer than the shorter side. Beam deflection for a freely constrained surface profile is mapped
by [18]:
1-4
Where  is the displacement at the center of the beam, q is the pressure, E is the Young’s
Modulus, I is the shape factor, which depends on the cross sectional profile of the beam, l is the
length, c is the thickness, and  is the Poisson ratio. This produces a cross sectional profile that
is effectively a x 2 term and a x 4 term. This term is similar to the circular lens cross sectional
profile.
We can achieve control of larger deflections where the curvature becomes more parabolic
by properly modeling the rectangular restraints. The separation between the edge restraints
defines the mirror symmetry. If we analyze the cross sectional profile from the long side of the
frame to the opposite side of the frame, across the short side of the rectangle, we see that the
highest magnitude of deflection is at the center and is zero at the edges. The clear aperture,
27
however, is located at the center of the rectangular frame. The clear aperture is designed as a
360o window that does not reach the edge of the frame. Therefore, at no period of inserting or
withdrawing fluid is the deflection magnitude zero unless there is zero power variation in the
clear aperture region.
The size of the clear aperture relative to the rectangular frame allows for the cylindrical
profile to be achieved. If we define the shortest side from the center to the edge as our zero
point, we can rotate in the clear aperture by 45o to the edge of the rectangular frame. The short
side by our starting point has the highest slope as the magnitude of the deflection monotonically
decreases from the center across our horizontal profile. As we rotate towards the edge of the
rectangular frame our curvature lowers until we hit that 45 o angle. At this 45o location we have
hit the lowest curvature as it is the longest distance from the center of the membrane to the
corner of the frame. By limiting the active area of the membrane to the central portion of the
constraint, we are able to treat the four corners as single low curvatures to the edges. Edge
effects that produce higher order aberrations are negligible as their effects are not observed in the
central active area of the fluidic lenses clear aperture. Depending on the optical design, there
will be small amounts of residual spherical power with the cylinder profile. This is correctible
with the proper optical designs as we will further discuss in this dissertation.
28
2.0 HUMAN VISUAL SYSTEM
The properties of the human visual system (HVS) are essential in the understanding and
correction of observed ocular aberrations with fluidic lenses. Fluidic lenses will be shown to
correct for defocus and astigmatism measured in various optical auto-phoropter designs. We will
also discuss approaches in the correction of trefoil and spherical aberration through the use of
fluidic technology. Thus, this section is dedicated to analyzing the eyes properties in the support
of these fluidic based elastomer designs.
2.1 Eye’s Anatomy
Figure 2-1 Eye Profile: Eye’s side profile [19].
Light propagates into the eye through the cornea, a durable transparent membrane that
produces two thirds of the optical power at a fixed focus location by refraction. The crystalline
lens offers the additional third of optical power by focusing light onto the retina. In-between the
cornea and the crystalline lens is the iris, where a clear aperture at the center of the iris is known
29
as the pupil. Traditionally, the combination of the crystalline lens and the cornea focus light onto
the retina, but if an individual is suffering from Myopia (nearsightedness) or Hyperopia
(farsightedness), then corrective eye wear is necessary to focus the propagating light onto the
retina. Retinas are composed of photoreceptors and ganglia that convert the retinal image into
neural signals that are then transmitted by means of the optic nerve to the brain. The brain
inverts the image and combines the optical information of both eyes to produce stereoscopic
imagery.
2.2 Eye’s Optical Properties
A fundamental property for an optical detector is the wavelength detection range. The
HVS includes wavelength detection from approximately 400 to 780 nm. The crystalline lens
absorbs light for wavelengths below 400 nm. On the opposite side of the visual spectrum, longer
wavelength reflection is primarily seen at the cornea with additional reflections at the crystalline
lens. Thus, in addition to controlling the optical power, the cornea and crystalline lens limit the
HVS’s detection range.
The iris, which is situated between the cornea and crystalline lens, is the aperture stop of
the eye. Depending on the surrounding lighting conditions, the iris relaxes or contracts in order
to control the pupil size, adjusting the stop size. Pupil sizes vary between 2 – 8 mm, where 8
mm is necessary for extremely dim lighting conditions. The image of the iris in object space is
known as the eye’s entrance pupil. Entrance pupil positions vary relative to the iris, depending
on the eye model utilized to determine the separation between optical elements. A model known
as the Arizona Eye model, as is shown in Figure 2.2 below, is a sophisticated design established
to calculate on and off axis aberrations, which is extensively applied in the clinical field [19].
30
This Arizona Eye Model is utilized to determine that the entrance pupil location relative to the
eyes center of rotation is approximately10 mm.
Figure 2-2 The Arizona Eye Model: The fundamental guidelines on applying the Arizona Eye
Model [19].
For a rotationally symmetric optical system the entrance pupil diameter is traditionally
symmetric about the optical axis. The lens’ center of curvature defines the optical axis for these
rotationally symmetric optical elements. However, it is fundamentally difficult to classify the
eye’s optical axis due to the lack of rotational symmetry. Field dependent on-axis aberrations,
such as astigmatism, illustrate the eye’s asymmetry, whereas symmetric systems have zero field
dependence on-axis. Consequently, a technique was necessary to identify the optical axis for this
asymmetric system. The optical axis is thus defined as the least gradient slope of the cornea’s
surface [19].
The visual axis, which defines the gazing direction, is not the optical axis. These two
axes overlap only when an individual stares through the cornea’s center to an infinite distance.
31
To account for gaze direction, the visual axis is defined as the axis where the ray propagates
from the fixation point to the front nodal point and then from the rear nodal point to the fovea.
Figure 2-3 Optical and Visual Axis: An image defining the optical and visual axis [19].
Nodal points define points in an optical system with unit angular magnification [20]. If
the nodal points were overlapping, then the visual axis is continuous from the fixation point to
the fovea. However, the nodal points do not overlap, where the visual axis is translated along the
optical axis, allowing for the same angular subtend with 1:1 magnification. Hence, the visual
axis has the properties of a light ray passing from the location of fixation to the fovea through the
nodal points.
Also due to a lack of symmetry, a variation in the eye’s rotational field of view exists,
where the center of the field of view is relative to the eye’s line of sight. Line of sight is defined
as the ray path onto the fovea from a fixed location through the pupil’s center, known as the
chief ray. Four fields of view were determined relative to the eye’s line of sight: 1) 60o nasally,
as in the direction of the nose, 2) 100o temporally, directed toward the outside of the head, 3) 60o
superiorly, directed above the head, and 4) 70o inferiorly directed below the head.
For a
stationary eye, the horizontal field of view is 160 o and the vertical field of view is 130o, which is
deduced by summing the respective fields of view. An overlap between the left and right eyes
permits 120o of stereoscopic vision, the region of the HVS where depth perception produces
32
stereoscopic imaging. As the eyes move and rotate, the field of view shifts with a maximum eye
rotation between 25o to 30o [21].
2.3 Spatial Acuity
Eye movements evolved as a means to produce a detailed scene; therefore, scanning
occurs to shift the scene onto the macula, where a high percentage of the photoreceptors are
located. The highest observed resolution is seen from the macula due to the concentration of red,
blue and green cones. Each specific cone, also identified as long, middle, and short, detects the
light of their specified wavelength region. Color vision is produced when the brain combines
data from these three cones.
Cone receptors are intended for day vision due to their low light sensitivity.
Cones
provide high spatial resolution, with the packing of the red and green cones possessing the
highest density. Progressing away from the eyes’ line of sight, there is a reduction in cones as
well as an increase in ganglia and rods, rods being the eye’s second type of photoreceptors. In
addition to the reduction in the amount of cones, these photoreceptors become larger and less
receptive to temporal resolution. The main focal area, the fovea, requires smaller movements to
produce finer detailed images, while larger movements are necessary for the peripheral in order
to gather information due to the rods low temporal and spatial resolution. Additionally, the
decrease of cones in the peripheral produces a sharp drop in resolution.
Rods are football shaped receptors situated primarily in the macula’s periphery. These
receptors have high sensitivity to light, gathering single photons in pitch dark conditions, even at
night. Rods work well with dim lighting and offer the HVS a dynamic range that no man-made
detector has replicated. A lower acuity in the periphery exists since the rods have a low
resolution and the presence of ganglia. Ganglia are the cells that transmit the signal to the optical
33
nerves, and have a ratio of thousands of cells to a few photoreceptors in the periphery compared
to half a dozen cones per ganglia in the fovea. Decreased resolution arises in the periphery due
to an increased ratio of ganglia to photoreceptors, which poses a greater effect than the decrease
in the amount of cones. Hence, there is lower peripheral data resolution, much larger angular
subtended angles than the one arc minute resolution found at the fovea’s center. The fovea’s
high concentration of cones closer to the center of gaze produces a region of high resolution
known as the area of interest (AOI). A natural exponential drop-off in spatial foveal acuity
arises when progressing away from the AOI.
Figure 2-4 Visual Acuity: The eye’s acuity over a visual field in logarithmic and real scales [22].
34
3.0 ABBERATIONS and ABERRATION CORRECTION
A capability of optofluidic lens technology, as well as many adaptive optic technologies,
is to correct for specific aberrations observed in propagating light and thus it is significant to
analyze the optical properties of a wavefront. In addition to the correction of the wavefront, one
must measure the aberrations of the wavefront in real time. We offer an objective evaluation of
aberrations, as well as an evaluation of aberrations within the human visual system, that enables
us to analyze our experimental setups. In the determination of the accuracy and reliability of
aberration control within fluidic lenses, we must first establish an understanding for both
circularly symmetric and circularly asymmetric optical systems, such as that observed within the
uncorrected eye. Lastly, we will discuss generic measuring approaches and the application of
Shack-Hartmann sensing in wavefront correction.
3.1 Circularly Symmetric Optical Systems and the Wavefront
Our assessment of aberrations will begin with a description of aberrations in a circularly
symmetric optical system. The wavefront completely describes the image forming properties of
any optical system. This ideal wavefront can be referenced as spherical waves focusing to a
point with no optical path difference from any sampled location. Aberrations are developed
when there is a shift from this perfect sphere due to various shaped optical elements in the
propagating wave’s path. The aberrated wavefront becomes a sum of the spherical wavefront
and the localized wavefront error. Under ideal conditions light in an optical system converges to
a focal point where the size is defined by a diffraction-limited spot or Airy disk. Aberrations are
observed in the image plane when the energy distribution of the focused spot becomes larger
than the diffraction-limited Airy disk in a real optical system.
Mathematical expansions
35
physically describe how the wavefront would be observed relative to a paraxial image plane with
differing aberrations.
For a rotationally symmetric optical system, the coordinate system
becomes a function of the normalized pupil coordinates xp, yp and the normalized image height H
[20]. A wavefront expansion is developed to describe the aberrations through these two
coordinate planes in the determination of ray positioning relative to the referenced image plane.
Figure 3-1 Optical Coordinate System: Normalized pupil coordinates and a diagram of
wavefront aberrations [20].
The wavefront expansion below is a power series expansion for the wavefront aberrations
of a rotationally symmetric optical system, where the expansion terms are
and H
.
The coefficient subscripts represent the powers of each respective polynomial term:
.
W= W020 + W111H
W222
+ W040
+ W220
+ W131H
+
+ W311
3-1
The coordinate terms are called primary or first-order aberrations and third-order, or
Seidel aberrations for a circularly symmetric optical system. The wavefront terms represent the
36
different aberrations: defocus, tilt, spherical, coma, astigmatism, field curvature, and distortion
aberrations, respectively [22].
Additionally, higher order aberrations exist beyond the third-
order which are higher terms of the series expansion. Due to the lack of rotational symmetry
found in the eye, the field aberrations found in eq. 3-1 can also appear on axis. Furthermore,
additional aberrations such as trefoil and tetrafoil are found in the eye as well. Many books have
been written on optical imaging and aberrations for both ray geometrical and wave diffraction
optics. The following subsections offer an overview description of the aberrations that fluidic
lens technology can compensate and correct for.
3.1.1 Defocus Aberration
Defocus, W020, is a monochromatic pseudo-aberration as it is caused when we adjust the
focus position. The real wavefront has a parabolic shape with a differing radius of curvature
relative to the exit pupil. As one translates across the optical axis the adjustment of focal
position enables us to compensate for higher order even aberrations relative to our reference
point. There is no field dependence for this aberration. In the human eye specifically, the light
properly focuses at the retina (Emmetropia), in front of the retina (Myopia) or behind the retina
(Hyperopia). The latter two scenarios result in a reduction of sharpness and contrast of the image
at the retinal plane where the cones and rods are located. Corrective eye wear compensates for
these conditions to bring the focusing light to the retinal plane.
37
z
ey
R
Image /
Retinal
Plane
Figure 3-2 Defocus Aberration: The real and aberrated wavefronts for defocus are both
spherically parabolic approximations with differing radii of curvature.
3.1.2 Chromatic Aberration
Refractive index of a given material, whether solid, liquid or gas, depends on the
wavelength of light propagating through it. The amount of dispersion that is observed from a
given material varies by wavelength and can be quantified into a value known as an Abbe
number. The dispersive variation across the wavelength range causes the focal location to vary
along the optical axis by wavelength. It is found that the shorter wavelengths with higher energy
focus closer to a positive lens and the longer wavelengths focus further along the optical axis.
Traditionally, chromatic aberration is defined from blue to red, which is relative to the human
visual spectrum. This chromatic focal length variation along the optical axis is known as axial or
longitudinal chromatic aberration (W020).
As is observed in Figure 3-3, axial aberration creates an image blur relative to focal
position of the axial aberration. If one chooses to place a plane at a given image location, various
amounts of blur is observable in size between the blue and red wavelengths. This blur size due
to the axial variation in focus perpendicular to the optical axis is known as transverse axial
chromatic aberration TACH [20]. Both axial or longitudinal chromatic aberration and transverse
38
axial chromatic aberration are a description of the dispersion caused by wavelength dependence
in the spreading of the marginal ray
TACH
z
W020
Figure 3-3 Chromatic Aberration of the Marginal Ray: Chromatic aberration is observed in a
lens as the marginal ray spreads relative to focal length. A blue ray focuses before a red ray,
producing longitudinal or axial chromatic aberration  W020 and transverse axial chromatic
aberration TACH.
A third chromatic aberration exists that describes the dispersion of the chief ray known as
lateral or transverse chromatic aberration (W111).
It is noted that transverse chromatic
aberration is not transverse axial chromatic aberration as we are describing dispersion created by
two different rays of light. To alleviate confusion, we will refer to the spreading of the chief ray
as lateral chromatic aberration rather than transverse chromatic aberration.
Lateral chromatic
aberration occurs when there is a radial or angular displacement along the image plane. The
displacement of the chief ray is a function of wavelength variation passing through a lens system,
where the edge behaves as a prism rather than a lens, causing the chief ray to spread.
39
W111
Stop
Image
Plane
z
Figure 3-4 Chromatic Aberration of the Chief Ray: Chromatic aberration is observed in a lens
as the chief ray spreads relative to the image plane. A blue ray focuses below and a red ray above
the central green ray, producing lateral or transverse chromatic aberration  W111.
3.1.3 Astigmatism Aberration
Astigmatism, W222, is a monochromatic aberration in which the unequal curvature along
differing meridians of the lens prevents light rays from focusing clearly at one point on the image
plane. Astigmatism may be illustrated by extending the focused image along the curved image
plane or Petzval surface relative to the flat image plane. The tangential rays lose their axial
symmetry as the object point traverses off axis. However, the sagittal rays emanating from the
same object point remain axially symmetric and come to a focus at the flat image plane. The
difference in focal positions of the tangential and sagittal rays is the cause of astigmatism. The
image point is observed as straight lines at the tangential and sagittal focal locations where the
line points are orthogonal to one another. In locations between theses focal planes the image
point appears to be elliptical or oblate, as there is a combination of focusing power. The amount
of astigmatism in a lens is a function of the power and shape of the lens and its distance from the
aperture or diaphragm [23]. In the eye, the lack of rotational symmetry can introduce astigmatism
40
on axis. In this case, one or more of the ocular surfaces is toroidal in shape introducing the
difference in curvature along orthogonal meridians.
Figure 3-5 Astigmatism Aberration: Astigmatism aberration illustrates the variation of focal
position between the Tangential and Sagittal planes [22].
3.1.4 Spherical Aberration
Spherical aberration, W040, is a monochromatic aberration caused by the refraction
through a spherical surface. Spherical aberration is the variation of focus with aperture size. Rays
that are close to the optical axis focus close to the paraxial image plane or paraxial focus. As the
ray height increases, the marginal focus moves farther away from the paraxial image plane. The
distance from the marginal focus to the paraxial focus is called longitudinal spherical aberration.
The distance at paraxial focus from the center to the edge of half the blur size is identified as the
transverse spherical aberration. The location with the smallest blur is observed at the circle of
least confusion.
Spherical aberration can be measured by tracing a paraxial ray and a
trigonometric ray from the same axial object point to determine their final intercept distances.
The same amount of spherical aberration is present on and off axis [23].
41
Marginal
Focus
Circle of Least
Confusion
Spot size at
image plane
or paraxial
focus
Transverse
Spherical
Aberration
Caustic
Longitudinal
Spherical
Aberration
Figure 3-6 Spherical Aberration: An illustration of the primary features of a spherically
aberrated system.
3.2 Asymmetric Optical Systems, Zernike Fitting, and Ocular Aberrations
In optics, there are numerous examples of non-rotationally symmetric or asymmetric
optical systems. Optical lenses such as progressive lenses or cylindrical lenses which produce
toroid or biconics surfaces are examples of asymmetric lenses. When an optical engineer works
with square apertures, birefringence, gratings, or wedges they are producing asymmetric optical
systems. Atmospheric turbulence or optical misalignment of mounts or manufacturing errors can
also produce asymmetric optical systems. Imaging systems such as the Scheimpflug camera or
the eye are also examples of imaging systems that are rotationally asymmetric.
3.2.1 Zernike Polynomials
It is necessary to generalize aberrations to non-rotational symmetric systems, achievable
through the use of Zernike polynomials. We can further our series expansion that was stated
above to a power series which enables us to assess asymmetric optical systems in addition to
rotationally symmetric optical systems. There are several advantages in fitting an optical system
to Zernike polynomials. Zernike polynomials are orthogonal over a unit circle. As a majority of
42
optical systems have circular pupils it is advantageous to apply a weighted sum of power series
terms that match the pupil coordinates of our optical function. We can therefore establish a data
fitting set that represents a series of wave aberrations. Each term of the polynomial expansion is
independent of the other expansion terms as they are mutually orthogonal. This enables for the
representation of each aberration independently. Additionally, each of the Zernike terms is
continuous, so one can produce a continuous derivative of the function. This allows for the
representation of smoothly varying surfaces and also for the identification of discontinuities in
the function [24]. The Zernike polynomials form a complete set, meaning they can represent
arbitrarily complex continuous surfaces given enough terms. It must be noted that Zernike
fitting is a significant issue in the replication of real trends. With too few terms, discontinuities
are observed which may cause loss of significant information. When too many additional terms
are inserted then the function may also fit noise into the data. The most optimal fit would be to
represent numerous data points with as few terms as possible [24].
3.2.2 Zernike Fitting and Ocular Aberrations
There are over half a dozen various Zernike polynomial schemes that exist.
A
standardized approach in the treatment of Zernike polynomials for ocular aberrations is defined
in polar coordinates [25]. There are two standard schemes that are applied for ocular aberrations:
1) a double indexing and 2) a single indexing scheme. These standard Zernike sets are often
used to fit the wavefront error of ocular aberrations. We will represent the Zernike polynomials
using the double indexing scheme.
There are different ways to group the total ocular aberrations based on the Zernike terms.
A common separation for the vision community is in the separation of the ocular aberration
43
terms into lower order and higher order ocular aberrations. The lower order or second order
ocular aberrations, defocus and astigmatism, are the refractive errors in the eye that can be
corrected by spectacles, contact lenses or with laser refractive surgery. The term second order
comes from the fact that defocus and astigmatism are the coefficients of the second order radial
Zernike terms. The lower order ocular aberrations are the most significant aberrations that
require correction. The majority of higher order ocular aberrations were thought to be negligible
relative to lower order ocular aberrations. It has been found that there are a few higher order
ocular aberrations of significance. There is a second grouping for higher order ocular aberrations
that emphasizes these relative aberrations individually.
These higher order aberrations are
spherical aberration, coma, trefoil, fourth order astigmatism and tetrafoil or the third and fourth
radial Zernike orders. An additional separation is to divide the aberrations in groups of the same
radial Zernike orders. The higher order aberrations are then separated into third, fourth, fifth,
and sixth order aberrations.
44
Aberrations
Defocus and
Astigmatism
Lower
Order
Zernike Coefficients
Higher Order
Aberrations
Spherical
Coma
Individual
Aberrations
Higher
Order
Trefoil
Fourth Order
Astigmatism
Quadrafoil
Third Order
Grouped by
Radial
Zernike
Order
Fourth Order
Astigmatism
Fifth Order
Sixth Order
Table 3-1 Ocular Aberrations: Describes the various Zernike terms and groups them relative to
defined vision terms.
There are several ways of extracting and calculating aberrations from Zernike
coefficients. The two most common approaches are to either compare the root-sum-squared
(RSS) or the root-mean-squared (RMS) of the coefficients a m,n [26]:
Root-Sum-Squared:
3-1
Root-Mean-Squared:
3-2
45
The RSS corresponds to the wavefront error caused by these terms, where the first piston term
Z0,0 is excluded from the calculation This term is constant over the entire circle where no
variance exists.
The RMS equals the RSS divided by the square root of the number of
coefficients n. These terms are image quality metrics for aberration extraction. It is significant
to recognize which approach is applied for aberration identification.
3.2.3 Factors Causing Ocular Aberrations
It is necessary to understand causes of the ocular aberrations within the eye in order to
apply corrective fluidic lens technology to compensate for the ocular error. Image quality at the
retinal plane has a high dependence on these ocular aberrations. Therefore, it is significant to
identify the location and causes of ocular aberrations.
It is shown that aberrations vary on an individual basis [27] and that room lighting, which
affects pupil size, varies the aberrations [28]. Saccadic movements and tear film slightly adjust
the aberration readings with the rapid movement of the eye [29]. Additionally, the shape of the
retinal plane, which is our image plane, may induce aberrations due to variations in eccentricity
[30].
There are, however, two additional factors that cause ocular aberrations to vary
dramatically.
The ocular elements that produce the highest amount of variation in ocular
aberration are the crystalline lens and the cornea. These are the two ocular elements that produce
the focusing power onto the retinal plane. As one accommodates to focus at various object
planes, the curvature of their cornea and crystalline lens adjusts. This causes a variation in focus
power and hence a variation in ocular aberrations [31]. As one ages the dynamic range of the
crystalline lens reduces and intraocular lenses (IOL’s) may be required for optical corrections.
Aging is found to be a significant fact in the reduction of image quality and increase in
46
aberrations [32, 33, 34, 35, 36]. Lastly, aberrations vary as the eye adjusts relative to room
illumination or other external lighting conditions. The iris or system stop varies relative to
scotopic or well lit conditions, thus adjusting the pupil sizes. The pupil size is a significant
factor in variation of ocular aberrations [37, 38, 39, 40].
3.2.4 Measuring Ocular Aberrations and Optical Devices
Our auto-phoropter designs take advantage of wavefront sensing technology coupled with
fluidic lens technology. This offers the capability of ocular aberration measurement and
correction in real time. As this dissertation’s focuses on the application of optofluidic lens
technology and the testing of these systems, we require measurement approaches that measure
the wavefront. To correct optical errors with fluidic lenses, a wavefront sensing mechanism is
required. The identification of the ocular aberrations is necessary to compensate the wavefront
in real time with optofluidic technologies.
There are many wavefront sensing techniques that can measure aberrations. There are
direct and indirect wavefront sensing approaches. Direct wavefront sensing approaches measure
the wavefront directly, while indirect wavefront sensing approaches indirectly measure signals of
the information related to the wavefront. Indirect wavefront sensing includes but is not limited
to image sharpness, phase diversity, and phase retrieval. Direct wavefront measuring can be
achieved through wave optics such as lateral shearing interferometry or geometrical optical
measurements such as that of Shack-Hartmann wavefront sensing. Shack-Hartmann wavefront
sensing is the wavefront sensing technique that is applied to aberration identification and
correction for our systems.
47
A Shack-Hartmann wavefront sensor is a modification of the Hartmann screen test [41,
42, 43, 44]. The sensor applies a lenslet array rather than a screen with apertures [42]. A
propagating wavefront is divided into discrete points by the lenslet arrays sub-aperture lenses.
Each lens of the lenslet array focuses part of the wavefront onto the image plane as a spot, where
the centroid of the spot is set as a marker. If a plane wave impinges on the surface of the
lenslets, the light focuses directly behind each individual lens on axis. The light forms focused
spots which are observed as dots and are of a grid pattern in two dimensions. If there is
uncollimated light, or aberrated light, the light from each lenslet no longer focuses directly
behind each point. The spot is displaced, where the displacement of each focal position offers
data that can be extracted for wavefront measurements. The discrete data points are properly
summed and fitted to produce continuous information on the observed aberrations.
Plane
Wave
Lenticular
Array
Wavefront
Lenticular
Array
aberrated
unaberrated
Figure 3-7 Shack-Hartmann Wavefront Sensing: Focus spot patterns created in the focal
plane of the lenslet array illustrate how the plane wave focuses light on axis while the aberrated
shows displacement.
There is a systematic approach in achieving measurable results with a Shack-Hartmann
wavefront sensor. The first step is to apply a perfect plane wave to calibrate the sensor. The
uniform grid pattern will have the same pitch separation between focused points as that of the
pitch of the lenslet array. The next step is to test a system and see where the spots have moved
48
according to the aberrations. The spot displacement for each spot is then measured in the x and y
dimension (xij,yij).
Figure 3-8 Shack-Hartmann Spot Displacement: Identification of the displacement of the
centroid relative to the on-axis collimated wavefront in the y dimension for lens i p,jp of the
lenslet array. This analysis is also performed in the x-dimension.
Here, we examine the position of the spot of the aberrated beam entering a single lens
relative to the position of the spot for the collimated unaberrated beam that is on-axis. The lens
is localized at pixel coordinates (i p,jp) when on axis, where we locate the center position of a
single lens in the lenslet array. Here, we show a displacement in the y dimensions so that the
centroid location is displaced to (ip,jp+y). We can identify the slope of the wavefront for each
lenslet by analyzing the displacement relative to the focal length in the y dimension, where a
similar expression holds for the x derivative.
3-3
49
As we know the geometric displacement, we convert the spot displacements into sets of
slopes
in both dimensions. At this point one can integrate the slope data to extract
the wavefront shape, W. There are several ways to integrate the term back, where one of the
more common approaches is to use least squares method for the discrete function to find the
coefficients anm. Often times, there is a loss of information from terms with constant shifts such
as tilt and piston terms. This approach allows for the Shack Hartmann technology to quickly
extract wavefront information of a conjugate plane relative to the lenslet array. It is desired to
conjugate the exit pupil of the tested system with the lenslet array through relay optics in order to
achieve accurate wavefront measurements of a pupil plane.
3.2.5 Light Source of the Shack-Hartmann Wavefront Sensor
The Shack-Hartmann does not require a temporally coherent light source to achieve
results. The operation wavelength is therefore significant depending on the application. In vision
research, a wavelength that is not in the visible range but can still pass through the ocular
elements is preferred for the application of a Shack-Hartmann wavefront sensor. In early vision
application, it was found that a light source in the visible caused a discomfort for patients. At a
design wavelength of 780 to 800 nm the light source is at the edge of the visible spectrum,
allowing for light to transmit to the retina while no longer providing a target or discomfort to the
user.
When calibrated at this wavelength the Shack-Hartmann wavefront sensor is also
applicable as a measurement device with fluidic lenses.
3.2.6 Tradeoffs of the Shack-Hartmann Wavefront Sensor
There are advantages and disadvantages of any detection system.
Shack-Hartmann
wavefront sensors are relatively simple setups to produce. There is however a major assumption
50
that allows for the sensor to function. One must assume that the wavefront that is imaged must
be slowly varying over the lenslet aperture such that the wavefront appears as a tilted plane wave
at the image plane from a given lens. The pitch between the lenslets defines not only the width of
the lenses but also defines the relative shape that is measurable for a given spatial frequency. We
are capable of producing a piecewise continuous set of facetted plane waves that impinge on the
lenslet surface when assuming each section of the wave is represented by small plane waves.
The limitation that develops with such a system is the measurement of a wavefront with a large
curve. The spot of the plane wave entering a single lens may overlap with a spot entering from a
neighboring lens. The dynamic range of the Shack-Hartmann wavefront sensor is defined as the
maximum slope change that the sensor can observe.
Figure 3-9 Shack-Hartmann Dynamic Range vs. Sensitivity: Here we illustrate the fact that
longer focal lengths have a higher sensitive but worse dynamic range relative to short focal
length lenslets in the array.
This illustration shows that as we decrease the focal length of the lenslet array we can
increase the dynamic range. This seems as an advantageous result, but there is a tradeoff in the
sensitivity of the sensor. The sensitivity describes the smallest change in slope variation that is
51
detected by the sensor. Therefore, the tradeoff is between having the capability of measuring
higher slope angles and the sampling of smaller features within the wavefront. Determining the
proper focal length and pitch relative to the pixel size of the detector varies with application and
must be determined by the user.
52
4.0 SPHERICAL FLUIDIC LENSES and NON-MECHANICAL ZOOM
We can begin to explore fluidic optic designs and applications, now that we have
established the concepts of fluidic lenses and a wavefront measurement approach for these
fluidic lenses.
As was described in section 1.3.2, there are two approaches in producing
spherical profile shapes, which are both utilized in this work. Our spherical or defocus fluidic
lens one produces spherical profiles by taking advantage of a large membrane locked to a frame,
giving a freely supported edge design. The active clear aperture area is much smaller than the
membrane shape, producing a defocus fluidic lens with no moving parts. Spherical lens two
produces the spherical shape by suspension control of the frame or clamped edge design. The
clear aperture active area applies a larger proportion of the membrane surface with this lens
structure.
Fluidic lenses are adaptive refractive lenses where their optical power is adjustable.
From a geometric standpoint, fluidic lenses offer more degrees of freedom relative to static
lenses by varying the system focal length through focal position control of the individual fluidic
lenses rather than varying the separation between static lenses. There are also fewer physical
limitations with fluidic lenses in addition to the lower probability of optical misalignment. Zoom
lens designs for optical power variation with no moving parts are achievable through active
optics such as fluidic lenses. Active optics allow for optical elements to achieve optical power
variation in either refractive or reflective configurations.
Fluidic lenses provide tunable optical power through form control of a surface
membrane. Fluidic lenses have been achieved through different driving approaches: electrowetting [45, 46], mechanical-wetting [47], chemical driving [48, 49], thermal driving [50, 51],
radiation pressure [52] and pressure controlled elastic expansion [53, 54, 55]. Our research
53
focuses on the application of controlled elastic expansion of fluidic lenses. Various fluidic lens
designs within our group have produced rotationally symmetric lenses, as well as cylinder lenses
in sequence, which will be discussed in chapter 6 [15]. Further advanced technologies within
our work have coupled fluidic lenses with variable diffractive lenses to produce a hybrid
achromat design, which will be discussed in chapter 5 [56]. As fluidic lens technology has
matured, multi-lens zoom systems and aberration correction systems have been analyzed [57, 58,
59].
Furthermore, zoom lens systems with two small aperture fluidic lenses applying piezo-
electric actuation have been developed [60]. Our work expands on the concept of applying
pressure-controlled fluidic lenses in the development of zoom lenses.
We have developed a variable power zoom system with no moving parts, which
incorporates both spherical lens one and spherical lens two. The designed system applies two
single chamber plano-convex fluid singlets, each with their own distinct design, as well as a
conventional refractive lens. We combine the two fluid elements to form a variable power
telescope, while the fixed lens enables image formation. In this configuration, the image plane
location is fixed. By synchronizing the powers of the two fluidic lenses, we produce a varying
magnification zoom system. The design of each lens and the coupled system is analyzed. The
coupled device experimentally produced a magnification range of 0.1 x to 10 x zoom or a 20 x
zoom magnification range with no moving parts.
Furthermore, we expand on optical
performance and capabilities of our system with fluidic lenses relative to traditional zoom lenses.
4.1 Theory of Spherical Fluidic Lenses
Our spherical lenses take advantage of pretension membranes locked into metal frames.
Both designs attempt to produce evenly distributed pressure around the periphery of the
membrane. This even force load allows for us to estimate the opto-mechanical designs as a
54
uniformly loaded circular plate with freely supported edges [17]. At small deflections the
following equation is applied to map the deflection properties of our circularly symmetric lenses
[61, 62]:
4-1
Where r is the radial distance from the center, z is the membrane deflection defined at zero in the
center, p is the pressure, R is the radial location at the edge of the lens, D is flexural stiffness,
which is a constant for a uniform thickness and material membrane, and  is the Poisson Ratio of
the elastomer material. This equation functions as the solution for the freely supported structure
and is a fair representation of spherical fluidic lens one for small deflection mappings.
Fluidic lens two has a clamped edge design rather than a freely supported design. Under
these conditions the derivative of the deflection term relative to its derivative of radial distance is
zero. This makes the deflection properties for a small deflection equal
4-2
Ultimately we apply equations 4-1 and 4-2 to determine the membrane shape by
identifying the deflection z through its relative radial distance dependence for this circularly
symmetric structure. The radial profile of the membrane shape is determined by the amount of
deflection as we progress from the center. As one can see, if we were located at the center of the
55
membrane r = 0 and thus the deflection equals zero. We progress from this center point to
identify correlation of the radial positions r to each z deflection point. The deflection maps to a
continuous radius of curvature shape for the membrane profile.
There is a variation on a constant term between the results of fluidic lens one and fluidic
lens two for the defocus term with r2 dependence. The elastomer that is chosen for these projects
is polydimethylsiloxane (PDMS), which has a Poisson ratio  of approximately 0.5. Hence,
there is a scaling difference of 2.333 for our r2 defocus term of the freely supported fluidic lens 1
compared to the clamped fluidic lens 2 with small deflections.
There is a similar relationship for that of large deflections to that of small deflections [61,
63]. Large deflections are classified as deflections three times larger than the thickness of the
membrane. Through the combination of large deflections and built-in stress a group was able to
identify a scaling factor for large deflections through a continuation of thin plate theory [63].
Therefore, the small deflection equations are applied when the membrane flexes with deflections
below three times the thickness of the membrane. The large deflection equations are applicable
beyond this limit. The membrane dynamics are active once a high enough tension is introduced
through deflection and preload [64].
4.2 Fabrication of Elastomer Membrane
The variable surface membrane material deflected is composed of PDMS, as was
previously mentioned. Our designed deformable membrane layers are moldable clear optical
elastomers with uniform thickness. PDMS was chosen as the membrane material offers high
optical transparency for the visible wavelengths and highly controllable elastic properties [65].
Fabrication of the PDMS membrane within a clean room begins with a PDMS mixture of
56
Sylgard 184 [66]. The mixture is composed of a 10:1 ratio of PDMS to curing agent, which is
deposited into circular molds within a glass optical flat with better than 5 of surface variation.
The membrane is then stirred in a vacuum chamber to remove air bubbles within the PDMS
solution. The PDMS is then baked at 140o C for 45 minutes to complete the curing process. The
membrane layers are removed with nylon tweezers, trimmed and clamped tightly into custom
made chambers. We have designed these elastic membranes to range between 100 – 300 m in
thickness. Note that thicker membranes offer higher control at lower powers [67]. Both fluidic
lenses use the PDMS membranes as their flexible surface, but the fluid capacity varies between
designs. The variation in the design defines the dynamic range that each of these lenses can
achieve.
4.3 Spherical Fluidic Lens One
Figure 4-1 Fluidic Lens 1: Here is an image of the fabricated, machined and assembled fluidic
lens 1.
As was previously described, each refractive fluidic lens is a plano-convex singlet. The
plano side of each lens has an optical flat while the optically clear fluid is sealed within a flexible
57
membrane on the opposing side. There is a predetermined amount of fluid inserted into each
lens. The curvature of the membrane surface is altered through the hydrostatic pressure in the
fluidic-filled lens cavity. By properly designing the optical lens there is an even distribution and
a continuous radius of curvature in the active optical area, which reduces undesired third order
aberrations. The fluid control within the active area is achieved with syringes controlling the
amount of fluid within the active chamber area. During preparation, fluid is inserted in excess
within the chamber as to induce a vacuum pressure to evacuate air. The air would be treated as a
second index within the clear aperture if not evacuated, resulting in a drastic alteration of desired
lens properties. The change of only the membrane curvature with pumped fluid allows for
control of the exiting focal length within our fluidic lenses.
Fluidic lens 1 was designed with a flat glass surface face of 12.5 mm on the plano side
and a clear aperture diameter of 10 mm. A circularly shaped opto-mechanical wedge protrudes
beyond the rim of the housing to produce a rotationally symmetric base for the fluidic chamber.
The membrane is secured onto the top housing with a retainer ring. Physically, the fluidic lens is
capable of achieving both positive and negative focal lengths. The amount of fluid infused or
withdrawn from the lens cavity was designed for the maximization of positive power as we were
developing a Keplerian-type telescope which requires two positive focal lengths lenses.
Similarly, we could have chosen to produce a Galilean telescope if we adjusted the amount of
fluid within a single fluidic lens chamber to produce negative focal lengths. The selected fluid is
infused through a tube from pump controlled syringes to a fluidic fitting connected to the
chamber. The syringe infusion or withdrawal of fluid alters the radius of curvature of the
membrane and hence the optical power of each fluidic lens.
58
We have created a test bed to measure the optical power of the fluidic lenses. A
collimated laser beam is shone through the fluidic lens. The back focal distance of the lens is
measured as a function of fluid volume. By systematically varying the amount of fluid in the
chamber, we can relate the lens focal length to fluid volume.
Lens 1: Syringe
Position Vs. Power
405
355
305
255
205
155
105
55
Power (Diopters)
Focal Length (mm)
Lens 1: Syring Position
Vs. Focal Length
0
200
400
600
800
Syringe Position (l)
1000
20
15
10
5
0
0
500
1000
Syringe Position (l)
Figure 4-2 Zoom Control of Fluidic Lens 1: We observe the variation of focal length on the left
and the change in power on the right as fluid is evacuated from the syringe connected to fluidic
lens 1.
The plots in Figure 4-2 illustrate the characterization of fluidic lens 1 and the dynamic
focal range of our lens. De-ionized (DI) water was placed in the chamber and syringe to
characterize the fluidic lenses focal range for both fluidic lenses. DI water has an Abbe number
of 55.74 and an index of refraction of 1.34 [68]. Figure 4-2a specifically characterizes the focal
length range of fluidic lens 1. The syringe position describes the amount of fluid contained
within the syringe. At 0 l all of the fluid in the syringe is in the lens chamber and the highest
radius of curvature observed for the membrane of fluidic lens 1. In this position, fluidic lens 1
has a focal length of 55 mm. When the plunger is fully withdrawn, 1 ml of fluid is removed
from the lens chamber, corresponding to a focal length of over 400 mm.
59
Figure 4-2b identifies the power range that this fluidic plano-convex lens is capable of
reaching. We find that fluidic lens 1 has a dynamic range of 15 Diopters with a 1 ml syringe. If
we opted to apply a 2 ml syringe instead of a 1 ml syringe the dynamic range of fluid lens 1
would be -17 Diopters to 17 Diopters, assuming the same amount of initial fluid was deposited
within the active chamber. Our desire for this Keplerian telescope was to maintain positive
lenses and thus a 1 ml syringe was most desirable.
4.4 Spherical Fluidic Lens Two
Figure 4-3 Fluidic Lens 2: Here is an image of the fabricated, machined and assembled fluidic
lens 2.
Fluidic lens 2 varies in membrane suspension and tension design as this is a clamped
edge design. The membrane is compressed between two pre-tensioners, which maintain small
amounts of stress on the membrane. These pre-tensioners support the tensioners by applying
pressure on the membrane side of the chamber. The pre-tensioners are aligned and connected
onto the base of the fluidic lens. A force is applied from the tensioner that locks the base and
pre-tensioners together to the tensioner. The base of the fluidic lens possesses an optical flat
60
which again defines the plano side of fluid lens 2. Again we have designed a holder for a 12.5
mm flat optical window and the clear aperture of the second fluidic lens is 10 mm. This
assembly produces tighter tension for fluidic lens 2 relative to fluidic lens 1, which results in a
greater dynamic range for fluidic lens 2. There again is a port that connects the fluid chamber to
a syringe pump. Similarly to fluidic lens 1, fluidic lens 2 can produce lens powers that are either
positive or negative. We identified the focal length and power range of fluidic lens 2 with our
testing apparatus and DI water.
Lens 2: Syring Position
Vs. Focal Length
Lens 2: Syringe Position
Vs. Power
50
250.000
Power (Diopters)
Focal Length (mm)
300.000
200.000
150.000
100.000
50.000
0.000
40
30
20
10
0
0
50
100
Syringe Position (l)
0
50
100
150
Syringe Position (l)
Figure 4-4. Zoom Control of Fluidic Lens 2: We observe the variation of focal length on the
left and the change in power on the right as fluid is evacuated from the syringe connected to
fluidic lens 2.
The plots in Figure 4-4 show the characterization of fluidic lens 2 and the dynamic focal
range of our lens with a syringe that applies 150 L of fluid. De-ionized (DI) water is again
used in the chamber. The shortest radius of curvature observed for the membrane of fluidic lens
2 at 0 L provided a focal length of 25 mm.
4.5 Zoom Lenses
61
We have designed two fluidic lenses whose elestemer membrane produce spherical
profiles. Zoom lenses are often found in imaging systems and are applied within numerous
fields of optics. Zoom lenses are devices that maintain focus at a defined image plane while
altering the systems optical power. Traditional zoom systems apply physical motion between
optical elements to alter the systems optical power through mechanical motion. Mechanical
motion of optical elements is often cumbersome, expensive, and optical misalignment can occur
due to complex cam mechanics required to drive the individual lenses [22]. Optical lenses with
fixed focal lengths limit the dynamic design of zoom optical systems.
We have designed, modeled, and fabricated two separate fluidic lenses with widely
tunable zoom capabilities and larger apertures than previous designs. Here, we demonstrate a
zoom system with two refractive fluidic lenses that require no translation of the optical elements.
Specifically, the fluidic lenses form a Keplerian Telescope with variable angular magnification,
combined with a static lens to enable imaging.
4.6 Theory: Variable Power Zoom System
Traditional zoom systems control optical power by adjusting lens positions. Complex
zoom systems apply multiple lens groups that move independently to sustain a fixed image
plane. The two lens zoom system is the most basic zoom system with a defined focal length and
back focal distance. The separations of the two optical elements, as well as the distance between
the rear element and the image plane are adjusted to maintain a fixed image location, while the
total system focal length is varied. A second option in controlling the systems optical zoom
power develops by adjusting the optical power of each refractive lens rather than adjusting the
position of the optics. Variable power lenses differ from traditional zoom lenses, which depend
on mechanically moving optics to adjust focus. Fluidic lenses offer the capability of controlling
62
individual element focal lengths, while eliminating the need to adjust lens positions. Variable
power zoom systems are achievable when synchronizing two or more fluidic lenses. Our primary
focus is in the production of a zoom system consisting of a Keplerian telescope and a fixed
power lens for zoom imaging.
Fluid
Lens 2
Fluid
Lens 1
0
1
2
n1
Fixed
Lens
CCD
3
n2
f2
f1
L
Figure 4-5 Zoom System: Schematic of an afocal system with two plano-convex fluidic optical
elements coupled with a fixed lens as a relay to produce a zoom lens system.
Figure 4-5 illustrates the configuration of our design. Each of the fluidic lenses offers a
single active surface which varies in power. Surface one (1) is the variable power surface for
the first fluidic lens and surface two (2) is the variable power surface for the second fluidic
lens. Surfaces zero and three are fixed plates that offer no optical power as our fluidic lenses are
both plano-convex. The thicknesses of the fluidic lenses does not affect the lens power when
we vary the amount of fluid within the chambers as each fluidic lens has a surface of zero
optical power. We therefore treat surface 1 and surface 2 as thin lens representations of each
liquid lens. If we opted to take advantage of both optical surfaces per fluidic lens, rather than
applying a plano-convex lens within a single optic, we would have to characterize the optical
effects on the separation of the two surface vertices relative to each other to measure the power
exiting each fluidic lens. The final element in Figure 4-5 is a static lens that takes the collimated
63
light emerging from the second fluidic lens element and focuses it onto a fixed image plane. In
this manner, if the first two elements maintain an afocal configuration, then the final element
will ensure the location of the image plane remains fixed.
Consider the net power of the first two elements of Figure 4-5. In general, the net power
of two thin lenses in free space is given by
4-3
where sys is the power of the optical system, fsys is the focal length of the optical system, 1 and
f1 are the power and focal length of surface one from the first fluidic lens respectively, 2 and f2
are the power and focal length of surface two from the second fluidic refractive lens
respectively, and L is the length between the first fluidic lens and the second fluidic lens. Our
zoom system seeks to keepsys = 0 so that the final static element focuses the emerging
collimated light onto the image sensor. To maintain the afocal relationship of the first two
elements, the separation between the fluidic elements must satisfy L=f 1+f2. Each of our fluidic
lenses can vary independently in focal length by controlling the fluid pressure within each lens
chamber. We are thus able to produce a Keplerian telescope with the first two elements by
synchronizing the focal length of the fluid lenses so that the sum of the focal lengths always
equals the separation of the two optical elements. The third element then will convert the
collimated light emerging from the telescope and form an image at its rear focal point. As the
relative focal lengths of the first two elements are varied in sync, the magnification of the entire
system changes, but the image location remains fixed.
64
4.7 Experiment: Zoom System Verification
Fixed
Lens
BeamSplitter
Liquid
Lens
Liquid
Lens
BeamSplitter
Collimating
Lens
Eye Chart
CCD
Laser
BeamSplitter
Mirror
Figure 4-6 Zoom System Setup: Above we display the physical setup of the experiement. A
laser system was designed to varify the focal location of each of the fluidic lenses seperatly. A
letter chart is placed at a distance while being imaged to our ccd camera through our zoom
system.
The setup shown in Figure 4-6 was used to verify the properties of our proposed system.
The fluidic lens telescope is placed between two fixed lenses. An inverted letter chart is placed
at the front focal point of the first fixed lens. This illuminated letter chart is then projected
through the telescopic system and through a second fixed lens which focuses light onto a CCD
array. The variation in power of the coupled fluidic lenses produces variable magnification as is
observed on the CCD. An additional off axis green laser source was added into the active optical
65
design to analyze the focal positions of the fluidic lenses. The exact focal position was measured
and compared to the expected focal locations of each of the fluidic lenses. We synchronized the
two fluidic lenses to gain the desired change in magnification. To increase the dynamic range of
the experiment we applied fluidic lens 1 as our objective lens and fluidic lens 2 as our eyepiece
for half of the experiment. We then switched the positions allowing for fluidic lens 2 to become
the objective lens and fluidic lens 1 to become the eyepiece.
This produced a wider
magnification range as is observed in Figure 4-7. Table 4-1 summarizes the configuration for the
various magnification levels.
10.0x
8.5x
7.0x
3.5x
2.5x
0.0x
0.65x
0.4x
0.3x
0.25x
0.1x
Figure 4-7 Zoom Magnification of a Letter Chart: Experiemental results achieved by varying
the two fluidic lenses as a zoom system. The magnification values shown are approxamate
magnifications that were achieved. The exact theoretical and experiemental values are observed
in the chart below. Chart illumination was adjusted as vignetting varied between the two fluidic
lenses.
66
Sample
1
2
3
4
5
6
7
8
9
10
11
L1
(mm)
340
300
285
265
225
180
107.5
82.5
47.5
40
32.5
L2
(mm)
35
75
90
110
150
180
267.5
292.5
327.5
335
342.5
mTheory mExperimental
0.10294 0.10959
0.25
0.26027
0.31579 0.31507
0.41509 0.41096
0.66667 0.65753
1.00
1.00
2.48837 2.46575
3.54545 3.53425
6.89474 6.80822
8.375
8.43836
10.5385 10.65909
% Error
6.46
4.11
-0.23
-0.99
-1.37
0
-0.91
-0.32
-1.25
.76
1.14
Table 4-1 Zoom Magnification: This table shows the experimental magnification of the 11
images shown in figure 4-7. We compare the experiemental results to the theoretical results by
analyzing the observed percent error.
Magnification Power Variation
Zoom Magnification
10
8
6
Theoretical
Magnification
4
Experimental
Magnification
2
0
35
85
135
185
235
Lens 1 Focal Length (mm)
285
335
Figure 4-8 Experimental vs Theoretical Zoom Magnifying Power: Twenty sample points
were measured to produce the continuous experimental magnification compared to the
theoretical magnification for the zoom system.
Figure 4-8 shows a plot of the theoretical and achieved magnification. The measurement
of the theoretical magnification was determined from the focal lengths of each of the fluidic
67
lenses. We specifically picked the letter E from the second to bottom line on the letter chart.
The experiemental magnification was assessed through an analysis of the image height at each
magnified configuration relative to the image height of the telescope set at 1:1 imaging. We then
analyzed the variation of error between the theoretical magnification and the expected
magnification. Theoretically we expected a dynamic range from 0.07 x to 14 x, but were not
able to achieve this range experiementally. The achievable dynamic range of our system was
from 0.12 x to 10.5 x, offering a change of magnification of approximately 20 x.
4.8 Limitations of Fluidic Zoom System
The two limiting factors for our zoom optical system are vigneting and aberrations. The
limitations on magnifying came from the size of our fluidic lenses. The two lenses offer a clear
apperature of 10 mm. These clear aperatures block off axis ray bundles from reaching our CCD
array. The angular subtend of our off axis ray bundles increases as we increase the radius of
curvature, power, of the fluidic lenses. This vignetting effect decreases the systems optical
throughput, requiring an increased amount of illumination at the object plane.
After a
magnification of 3 x we inserted a second light source to increase the etendue off the reflected
surface of the object plane. We found that the size of the letter E at approximately 8.5 x
magnification no longer fit in the active area of the CCD. In order to attain accurate results for
10 x magnification, analysis of the center line to base line of the magnified image E was
compared to the center line to base line of the letter E when the telescope is set to 1:1 imaging. In
addition, the light loss beyond 10 x was significant, even with both light sources illuminating the
object plane at maximum power, causing poor imaging conditions that limited magnification.
Aberrations were also observed to limit the image quality of the letters. We found that as
we altered the amount of fluid in the synchronized fluidic lenses the letter chart drifted up and
68
down. We found that a slight amount of tilt caused our image plane to slightly move, but was
negligable as the results remained on the ccd plane. There was also observed distortion as we
observed a slight waviness in the outputted letter lines. Also, a negligible amount of astigmatism
can be observed from a slight rotation of the letter lines when comparing the 0.1 x thru to the 10
x magnification. Results were achievable as the aberrations were not dominant enough to
destroy resolvability of the letter lines.
We have demonstrated a zoom imaging system that consists of two variable pressure
controlled liquid lenses. We used two refractive fluidic lenses to produce zoom power in a
Keplerian telescope setup. A static lens in combination with the fluidic Keplerian telescope
stabilized the image plane at the CCD array. The fluidic lenses provided continuous variation in
focal power, which enabled us to produce zoom magnifications between 0.1 x to 10 x with
results that nearly matched the theoretical values.
The full range in magnification we
experimentally produced a 20 x variation in magnification. This zoom imaging system has no
moving parts and offers potential in the stabilization of static refractive zoom systems.
69
5.0
FLUIDIC ACHROMATS
A traditional achromatic lens or achromat corrects for primary chromatic aberration by
matching the focal points of a red and a blue wavelength. The dispersion is reduced over the
visible spectrum, however residual secondary chromatic aberration remains at the green
wavelength. Achromatic doublets consist of a crown glass and a flint. The crown glass has a
positive focal length with low dispersion while the flint has a negative power with high
dispersion. The combination of these two glass disparities is designed to match the red and blue
wavelengths to a common focus along the optical axis (z-axis) to eliminate primary chromatic
aberration.
As we have shown in the previous chapter, fluidic lenses are a very powerful tool for
systems design. In this chapter, we will describe two designs with fluidic technology that
enables for us to correct for chromatic aberration. The first design describes the combination of
a variable lens with our fluidic lens 1. Fluidic lens 1 applies the freely supported edge design in
the creation of our achromatic design. We have previously discussed fluidic lens 1 and so this
section will discuss the facilitation of the lens and its combination to a syringe actuation system.
We will also illustrate the diffractive / refractive achromat with discrete focal lengths of
correction [56]. The second design is the creation of a dual chamber clamped edge design fluidic
achromat. There are two chamber controlled by syringe actuation. When the two surfaces are
synched, one can produce the proper achromatization at continuous wavelengths. By reverse
engineering data from ZEMAX we determined how to produce an achromat with two known
liquid materials. We have designed this achromat in SolidWorks and will explain a structural
approach in achieving achromatization with this design.
70
5.1
Achromat One: Diffractive / Refractive Hybrid
We demonstrate a variable focal length achromatic lens that consists of a flat liquid
crystal diffractive lens and a pressure-controlled fluidic refractive lens. The diffractive lens is
composed of a flat binary Fresnel zone structure and a thin liquid crystal layer, producing high
efficiency and millisecond switching times while applying a low ac voltage input. The focusing
power of the diffractive lens is adjusted by electrically modifying the sub-zones and reestablishing phase wrapping points. The refractive lens includes a fluid chamber with a flat glass
surface and an opposing elastic polydimethylsiloxane (PDMS) membrane surface. Inserting fluid
volume through a pump system into the clear aperture region alters the membrane curvature and
adjusts the refractive lens’ focal position. Primary chromatic aberration is remarkably reduced
through the coupling of the fluidic and diffractive lenses at selected focal lengths.
It is known that diffractive lenses have strong chromatic aberration [69]. We have
previously reported on designing and demonstrating adjustable focus diffractive lenses using
liquid crystal as the variable index medium [70, 71]. In this paper, we present an adjustable
liquid crystal diffractive lens and an adjustable pressure-controlled fluidic lens that in
combination (Figure 5-1) minimizes primary chromatic aberration. Previously, discrete tunable
liquid crystal diffractive lenses [70, 71, 72, 73, 74], continuous tunable liquid crystal refractive
lenses [75, 76, 77], and continuous tunable fluidic lenses [78, 79, 67] with variable focal lengths
were demonstrated individually. At each focal location chromatic aberration is observable when
uncorrected. Chromatic aberration is greater in elements with larger dispersion, such as
diffractive lenses, and becomes more significant for materials with lower Abbe numbers.
Diffractive and holographic lenses have been proposed to replace the traditional achromatic
doublets for fixed focal length designs [69, 80]. More recently, a useful hybrid variable focal
71
length fluidic/diffractive lens was demonstrated; however, the diffractive component applies a
fixed focal length [81]. We have extended this work to include a variable focal length diffractive
component. In effect, we have created a variable achromatic doublet with no moving parts.
Figure 5-1 Diffractive / Refractive Hybrid Design: Schematic of the hybrid liquid crystal
diffractive lens and fluidic lens.
Diffractive lenses have an Abbe number much smaller than their refractive counterparts
[69]. The Abbe number of a diffractive lens is unique in that it is equal to -3.45, solely dependent
upon the specified Fraunhofer d, F, C wavelengths, as given by Vdiffractive = λd / (λF - λC) [69, 80].
The focal length of a Fresnel zone-based diffractive lens is given by f = r12 / (2 λ) where r1 is the
radius of the first Fresnel zone and λ is the wavelength of the incident light [69]. Therefore, the
focal length at any other wavelength λ, in nm, can be scaled by the design wavelength according
to f (λ) = (555/ λ) fd where fd is the design focal length at 555 nm.
An approach must be established to correlate the diffractive lens with the refractive lens.
For certain focal lengths of the diffractive lens, fd , we may choose the focal lengths and Abbe
number of the fluidic lens such that they satisfy the achromat equation: ff Vf - 3.45 fd = 0, where ff
and Vf are the focal length and Abbe number of the fluidic lens, respectively. Refractive lenses
have an Abbe number that is related to the indices of refraction as specified by the Fraunhofer d,
C, F lines where Vfluidic = (nd - 1) / (nF – nC). By knowing the focal length of the diffractive lens
and the Abbe numbers of the refractive and diffractive lenses, one is able to determine the focal
length range of the fluidic lens required to achieve an achromat. Table 5-1 identifies which focal
72
length ranges are necessary for a variable fluidic lens to produce an achromat with diffractive
lenses ranging between 67 mm and 1000 mm focal lengths at specified Abbe numbers of the
refractive lens. Optical glasses have an Abbe range between 25 and 65 [20], however using
optical fluids increases this range of achievable Abbe numbers. Once the focal lengths are
determined to identify what is necessary to match the diffractive lenses, the proper Abbe number
and hence fluid may be chosen to achieve this goal.
5.1.2. Liquid Crystal Diffractive Lens
We began by designing diffractive elements with known focal lengths and Abbe
numbers.
We developed two variable focal length diffractive lenses.
Diffractive lens A
possesses a design focal length of 1000 mm at λ=555 nm with a clear aperture of 10 mm and
eight binary phase quantization that results in a maximum diffraction efficiency of 94.9% in
theory. Diffractive lens B possesses a design focal length of 400 mm at λ=555 nm with a clear
aperture of 6 mm and twelve levels of binary phase quantization that results in a maximum
diffraction efficiency of 97.7% in theory. By properly shunting the electrodes, the diffractive lens
A can provide focal lengths of 1000 mm, 500 mm, and 250 mm, and the diffractive lens B can
provide 400 mm, 200 mm, 133 mm, 100 mm, and 67 mm focal lengths [80, 81].
Desired phase profiles are achieved by shifting the effective refractive index of a nematic
liquid crystal. The nematic liquid crystal is sandwiched between a flat Fresnel zone electrode
substrate and a ground reference substrate, where both substrates contain a transparent and
conductive Indium-Tin-Oxide (ITO) layer. To maintain the electrical isolation between the
electrodes in the diffractive lens A, the odd-numbered and even-numbered electrodes are formed
in two separate layers with an insulating layer of SiO2 in between [81]. For the diffractive lens B,
one-micron gaps are implemented as isolators between the electrodes that reduce the fabrication
73
steps [80]. The electrodes (or subzones) of the same counting index within each of the Fresnel
zones are connected to bus bars through bias made in the insulating layer of SiO2.
Fabrication of our diffractive lenses involves a few steps of deposition, lithography and
etching. Ion beam sputtering was the deposition method used to produce uniform films of around
150 nm thick. Then photo-lithography was carried out using a diluted S-1805 photoresist (from
Rohm and Hoss) and Karl-Suss MA6 mask aligner. The patterns were then etched using the
appropriate acids/etchants for each layer. After the micro-fabrication process, both the patterned
electrodes and the reference substrates are spin-coated with a nylon alignment layer. The
substrates are then baked at 115 °C, buffed unidirectionally, and put together in the anti-parallel
geometry to provide a homogeneous molecular orientation for the liquid crystal. Glass fiber
spacers are used in the cell assembly. The lens cell is filled with the liquid crystal (E7 from
Merck) via the capillary action at a temperature above the clearing point (60°C) and cooled
slowly to the room temperature. Finally, the cell is sealed and connected to drive electronics
through a set of thin stranded wires.
Two resistive circuits with eight and twelve potentiometers drive the diffractive lenses.
The resistances and the input voltage, hence the driving electric field across different Fresnel
subzones, are adjusted to introduce the appropriate phase shift for the maximum diffraction
efficiency. The voltages are applied simultaneously and are monotonically increasing from the
first to the last subzone. The focal lengths are electronically switchable to fractions of the
maximum design focal length in milliseconds. It is also possible to achieve negative focal
lengths by reversing the order in which the voltages are applied to the diffractive lenses, thus
reversing the slope of the phase profile. [80, 81]
5.1.3 Fluidic Refractive Lens
74
The refractive lens is the freely supported edge fluidic lens 1. The refractive lens is a
plano-convex singlet with a predetermined amount of fluid inserted into the lens chamber.
During preparation, fluid is inserted in excess within the chamber as to induce a vacuum pressure
to evacuate air. If the air is not evacuated then it is treated as a second index within the clear
aperture, resulting in a drastic alteration of desired lens properties. Only the membrane curvature
changes when fluid is pumped into the chamber since the frame is metal and the opposing side is
transparent glass.
The chamber is a metal frame which the membrane locks into, possessing a clear aperture
within the center and flanges on its periphery. Control of the lens’ output shape is achieved by
controlling the clear aperture’s optomechanical shape, where this clear aperture has a circular
shape as to produce a rotationally symmetric fluidic lens. There is a retainer ring that has equal
and opposite flanges relative to the metal frame. Through pressure, the membrane is applied
onto the flat metal frame and the retainer ring locks the membrane onto the frame. This flat
frame is then aligned and squeezed into a two part assembly, creating the singlet chamber. The
chamber is then mounted onto a frame that has openings to place onto a rail. The chamber
posses a single fluidic fitting that connects the fluid chamber to a syringe.
A syringe is placed into a pump system that alters the fluid output, permitting for control
of the fluidic lens’ radius of curvature and focal length. The applied pump controllers operate at
a maximum of 0.0125 ml / sec, an operation rate of 50 µl in 4 seconds. This corresponds to a
focal shift of approximately 10 mm per 50 µl evacuation when there is high lens curvature, and a
shift of approximately 50 to 100 mm per 50 µl evacuation.
The boundary between high
curvature and low curvature varies with the designed focal length. With our fluidic chamber,
which was designed for an 80 mm base focal length with methanol, an evacuation of 150 µl
75
defines our barrier between low curvature and high curvature. It is observed in Figure 5-4 as the
approximate location in which the slope varies in the relative amount of fluid evacuated. Due to
drastic fluid removal effects at flatter curvatures, it was opted to decrease the amount of fluid
inserted or removed at higher radii of curvature. A plano-convex lens is developed over this
region and only positive focal lengths are selectively outputted.
5.1.4. Test Methods and Results of the Hybrid Diffractive / Refractive Achromat
It is non-trivial to place the proper fluid into the chamber when compensating for the
diffractive lens. Identifying the proper fluid came from a four step process. Firstly, one must
identify the membrane’s radius of curvature range.
This allows for one to physically
characterize the limitations of the fluidic lens. Also, by identifying the radius of curvature with a
known fluid, it is possible to quantify the focal length range of any fluid by knowing the new
fluid’s index of refraction. Once one knows the achievable radii of curvature and focal lengths
of the fluidic lens, it is necessary to specify the focal lengths needed to compensate for the
diffractive lens. For our experimental setup, we have already specified the Abbe number of the
diffractive lenses and also the focal lengths achievable by our diffractive lenses. Table 5-1 took
these values into consideration and found the focal length solutions of fluids at a wide scope of
Abbe values. Therefore, we match the physical focal length range of the fluidic lens to a
reasonable Abbe number so that a high percentage of achromatic doublets are achievable. The
final step is to identify a fluid with the proper index of refraction and Abbe number as was
previously assessed. It is also important that the fluid found is non-reactive or absorptive with
the membrane that one is applying. Through this approach we satisfy the achromat equation: f1
V1 + f2 V2 = 0, where V is the Abbe number.
76
Diffractive lens
powers and focal
lengths
Needed fg
if Vf =5
Needed fg
if Vf =10
Needed fg
if Vf
=13.66
Needed fg
if Vf =15
Needed fg
if Vf =20
1 D (1000 mm)
690.00
345.00
252.56
230.00
172.50
2.0 D (500 mm)
345.00
172.50
126.28
115.00
86.25
2.5 D (400 mm)
276.00
138.00
101.02
92.00
69.00
4.0 D (250 mm)
172.50
86.25
63.14
57.50
43.13
5.0 D (200 mm)
138.00
69.00
50.51
46.00
34.50
7.5 D (133.33 mm)
92.00
46.00
33.67
30.67
23.00
10 D (100 mm)
69.00
34.50
25.26
23.00
17.25
15 D (66.66 mm)
46.00
23.00
16.84
15.33
11.50
20 D (50 mm)
34.50
17.25
12.63
11.50
8.63
25 D (40 mm)
27.60
13.80
10.10
9.20
6.90
30 D (33.333 mm)
23.00
11.50
8.42
7.67
5.75
35 D (28.57 mm)
19.71
9.86
7.22
6.57
4.93
40 D (25 mm)
17.25
8.63
6.31
5.75
4.31
50 D (20 mm)
13.80
6.90
5.05
4.60
3.45
60 D (16.66 mm)
11.50
5.75
4.21
3.83
2.87
Needed fg
if Vf =25
Needed fg
if Vf =30
Needed fg
if Vf =35
Needed fg
if Vf =40
Needed fg
if Vf =45
1 D (1000 mm)
138.00
115.00
98.57
86.25
76.67
2.0 D (500 mm)
69.00
57.50
49.29
43.13
38.33
2.5 D (400 mm)
55.20
46.00
39.43
34.50
30.67
4.0 D (250 mm)
34.50
28.75
24.64
21.56
19.17
5.0 D (200 mm)
27.60
23.00
19.71
17.25
15.33
77
7.5 D (133.33 mm)
18.40
15.33
13.14
11.50
10.22
10 D (100 mm)
13.80
11.50
9.86
8.63
7.67
15 D (66.66 mm)
9.20
7.67
6.57
5.75
5.11
20 D (50 mm)
6.90
5.75
4.93
4.31
3.83
25 D (40 mm)
5.52
4.60
3.94
3.45
3.07
30 D (33.333 mm)
4.60
3.83
3.29
2.87
2.56
35 D (28.57 mm)
3.94
3.29
2.82
2.46
2.19
40 D (25 mm)
3.45
2.88
2.46
2.16
1.92
50 D (20 mm)
2.76
2.30
1.97
1.73
1.53
60 D (16.66 mm)
2.30
1.92
1.64
1.44
1.28
Needed fg
if Vf =50
Needed fg
if Vf =55
Needed fg
if Vf =60
Needed fg
if Vf =65
Needed fg
if Vf =70
1 D (1000 mm)
69.00
62.73
57.50
53.08
49.29
2.0 D (500 mm)
34.50
31.36
28.75
26.54
28.75
2.5 D (400 mm)
27.60
25.09
23.00
21.23
19.71
4.0 D (250 mm)
17.25
15.68
14.38
13.27
12.32
5.0 D (200 mm)
13.80
12.55
11.50
10.62
9.86
7.5 D (133.33 mm)
9.20
8.36
7.67
7.08
6.57
10 D (100 mm)
6.90
6.27
5.75
5.31
4.93
15 D (66.66 mm)
4.60
4.18
3.83
3.54
3.29
20 D (50 mm)
3.45
3.14
2.88
2.65
2.46
25 D (40 mm)
2.76
2.51
2.30
2.12
1.97
30 D (33.333 mm)
2.30
2.09
1.92
1.77
1.64
35 D (28.57 mm)
1.97
1.79
1.64
1.52
1.41
78
40 D (25 mm)
1.73
1.57
1.44
1.33
1.23
50 D (20 mm)
1.38
1.25
1.15
1.06
0.99
60 D (16.66 mm)
1.15
1.05
0.96
0.88
0.82
Table 5-1 Achromat Lookup Table: Values needed for fluidic lens focal lengths fg (in mm) at
different fluid Abbe number values and given diffractive lens focal lengths at the design
wavelength of 555 nm.
De-ionized (DI) water was first used to characterize the fluidic lens’ radius of curvature
range. DI water has an Abbe number of 55.74 and the indices of refraction are known for a wide
scope of wavelength ranges [68]. The focal lengths of the DI water fluidic lens were first
measured using red (HeNe 633 nm), green (HeNe 543 nm), and blue (Argon 488 nm) lasers with
the previously described pump controls. All three laser beams were aligned to the optical axis.
The combination of the lasers allows to either individually test the lenses with specific
wavelengths or to concurrently test multiple wavelengths as shown in Figure 5-2. The dichroic
mirrors have specified bands in which they reflect and transmit. We found the proper dichroic
mirrors to pass the previous wavelengths while reflecting the incoming perpendicular laser
wavelengths. By mixing the lasers or adding an aperture stop, we varied the desired input
wavelengths. We then used a single beam expander using an achromatic objective lens and
another achromatic collimating lens to collimate the three beams in this single optical axis. A
color CCD camera on a rail was employed to find the best focus spot. The spots were not of a
perfect sphere since there was a slight amount of astigmatism observed at the focal spot. This is
caused by a slight distribution in tension around the flanges and it is observed more drastically at
longer focal lengths.
Color CCD
Camera
Fluidic Lens
B
Liquid Crystal
Diffractive Lens
G
Polarizer
R
Achromatic
Beam Expander
79
Figure 5-2 Achromat Test Setup: Three laser beams aligned and collimated to measure the
focal lengths of the diffractive and fluidic lens by a color CCD camera on a rail.
As was previously stated we applied DI water, with known indices of refraction per
wavelength, in identifying the fluidic lenses radius of curvature range. For a given amount of
fluid in the lens, we measured the focal length at each of the three test wavelengths. The radius
of curvature, r, of the lens surface was calculated using Ф= 1/f = (nair - nDI)/r, where  is the
surface power and nair and nDI are the indices of refraction for air and DI water per index,
respectively. It is noted that with the defined coordinate system the radius of curvatures are
negative values as the vertex to the center propagates to the left; however, we are stating the
values as definitions of magnitude as to alleviate the constraint of a coordinate system. The index
of refraction for air is approximately one at all wavelengths and the index of refraction of DI
water is known at each wavelength [68]. The focal length, f, of each measurement was equal to
the back focal distance of the fluidic lens using the thin lens approximation. Each radius of
curvature was calculated at red, green, and blue wavelengths and averaged to determine a single
radius of curvature per fluid volume. The experiment was repeated as we increased the fluid
volume in the lens by increments of 50µL.
To define the workable range for the fluidic lens we quantified the repeatability of
outputting the radius of curvature. It was found that the average radius of curvature per fluid
volume between the three wavelengths varied in accuracy of 0.02% to 0.88% for a radius of
80
curvature from 20 to 100 mm. For DI water this corresponded to a focal length range of 60 mm
to 300 mm. To clarify, a radius of curvature with an accuracy of 0.02% means that our lens
accuracy for a radius of curvature at 20 mm was at 20 mm +/- .004 mm or with an accuracy of
0.88% the radius of curvature outputted at 20 mm +/- .176 mm. Similarly the radius of curvature
range for our larger 100 mm varied from 100 mm +/- .02 mm to 100 mm +/- .88 mm
respectively. It was found that the smaller radii of curvature actually observed a lower amount
of inaccuracy.
As we increase the amount of fluid we are reducing the lenses radius of
curvature. This suggests that our caustic is not as long and more of the rays are focused in one
location. What is occurring is that with a smaller radius of curvature we have almost no effect
by the frame which allows for the shape of the membrane to be controlled by the fluid with
almost no dependence on the optomechanical structure. With this higher control the smaller the
radius of curvature the higher control of aberrations is observed.
We broke up the accuracy of the radius of curvature into two additional sections. The
radius of curvature between 100 to 200 mm had outputted an accuracy between 1 and 2 %, which
for DI water is a focal length range of 300 to 600 mm. Focal lengths from 600 to 900 mm
produced an accuracy on the radius of curvature between 2 and 5% of the expected focal length.
Our goal was to apply a highly accurate fluidic lens to couple with the diffractive lens as to
diminish in accuracies related to the control of the fluidic lens. These two additional sections
had high accuracy and repeatability but were not the best results since they had larger radius of
curvatures. Therefore, we defined the highly accurate radius of curvature range between 20 to
100 mm as the fluidic lenses functional range while attempting to determine the best fluid to
work with in producing the final achromatic design.
81
The two most significant fluid characteristics for this experiment, as was observed from
the achromat equation, were the fluids focal length and Abbe number. The focal length is
dictated by the radius of curvature of the fluidic lens and the index of refraction of the fluid. In
the previous paragraph we experimentally assessed the fluidic lenses controlled radius of
curvature range to be between 20 to 100 mm with high accuracy. The fluids index of refraction
can vary the focal length, but the range would increase or decrease the focal range slightly. This
is observable by evaluating Ф= 1/f = (nair-nFL)/r once more, where now nFL is the new fluids
index of refraction rather than DI water. We observe that our only alteration to the equation is
the applied fluids index of refraction. If we find a fluid with a larger index of refraction than the
tested DI water, then focal lengths shorter than 60 mm are achievable. As most indices of
refraction for glass range between 1.3 and 2.5, a reasonable approximation is that a majority of
optical fluids operate within this index range. It is safe to approximate that the calculated focal
length range of DI water of 60 mm to 300 mm can be decreased by at least 10 mm to 50 mm or
higher. We are not stating that the focal length cannot be further decreased, but rather we are
defining a reasonable index of refraction range as to not constrain the fluids when attempting to
find the proper Abbe number to produce a functional diffractive / refractive achromatic lens.
With the focal length range approximated it was necessary to determine the proper fluid
Abbe number to achromatize the focal lengths of the diffractive lens. On the left hand side of
Table 5-1 are the diffractive lens values that would be required to be achromatized. Table 5-1
identifies which focal lengths are needed from the fluidic lens for each Abbe number to achieve
achromitization with these designed diffractive lens powers. Our approximation showed that our
fluidic lens will achieve focal lengths in the relative area of 50 mm or higher. Our experimental
DI water has an Abbe number of 55. It is seen within the table that DI water would only
82
achromatize the 1 D Diffractive lens with our fluidic lens, due to the constraints on the lenses
radius of curvature.
A fluid with an Abbe number of 15 would achromatize four of the
diffractive lens’ focal lengths and an Abbe number of 10 would achromatize five focal lengths
above 50 mm. Theoretically, a fluid with an Abbe number of 5, as observed from Table 5-1,
would produce approximately all possible achromatic combinations from either diffractive lens
developed here, since the greatest Diopter range achieved by the diffractive lenses is 15 D.
Finding a fluid with a known index of refraction to achieve a focal length as low as 50 mm and a
characterized Abbe numbers from 5 to 15 will offer the capability of illustrating a variable focal
length achromat with discrete focal lengths of achromatization.
Methanol (Methyl alcohol) was chosen as the fluid for the fluidic lens due to its high
dispersion value and non-reactivity with the PDMS membrane. Methanol has an Abbe number of
13.66 which achromatizes 5 of the diffractive lens focal lengths as is observed in Table 5-1 and
is widely available as it is a cleaning agent. The desired focal length range to achromatize all of
the diffractive lenses focal locations with the fluidic lens would be from 16.8 to 101.0 mm when
coupled with diffractive lens B and from 63.14 to 252.6 mm when coupled with diffractive lens
A. As was previously stated, the diffractive lens A provides focal lengths of 1000, 500, and 250
mm, and the diffractive lens B provides 400, 200, 133, 100, and 67 mm focal lengths. As seen
from Table 5-1, all three possible focal lengths of the diffractive lens A, and two out of five focal
lengths of the diffractive lens B (400 and 200) can be achromatized. Using Table 5-1, we identify
the focal lengths of the fluidic lens for every focal length of the diffractive lens. Results of the
two combined focal lengths develops a predicted achromatic focal length at green wavelength
through Фexpected = Фdiffractive + Фfluidic and fexpected = 1/ Фexpected. The five expected achromatic
83
focal lengths, fexpected, for green must be achieved through the experimental setup for the
achromat to work properly.
Focal lengths of the diffractive and fluidic lenses were first measured separately using the
red (HeNe 633 nm), green (HeNe 543 nm), and blue (Argon 488 nm) lasers. We used a linear
polarizer with the diffractive lens to account for the polarization effects of the nematic liquid
crystal. We can remove the polarizer so the lens works with any randomly polarized light if we
add another liquid crystal diffractive lens with an orthogonal buffing direction to the first
diffractive lens. As expected, the red light comes into focus first for the diffractive lens since it
has negative dispersion. The test results for the two diffractive lenses are shown in Table 5-2
and 5-3. The experimental and theoretical values of focal lengths at the aforementioned three test
wavelengths are presented in Table 5-2 (diffractive lens A) and Table 5-3 (diffractive lens B).
The design wavelength for both lenses is λ = 555 nm, and the design focal lengths (1000 mm for
lens A and 250 mm for lens B) as well as additional observed focal lengths developed when
these lenses were shunted as is presented at the design wavelength. The focal lengths at the three
test wavelengths are calculated using the diffractive lens formula discussed in the introduction, f
(λ) = (555/ λ) fd where fd is the design focal length at 555 nm.
Wavelength
(nm)
633
f (555nm) = 1000
mm
Data
Theory
870
876.8
f (555nm) = 500
mm
Data
Theory
435
438.4
f (555nm) = 250
mm
Data
Theory
217
219.2
543
1015
1022.1
505
511.1
252
255.5
488
1125
1137.3
560
568.6
281
284.3
Table 5-2 Diffractive Lens A: Measured and calculated focal lengths at the three test
wavelengths.
84
Wavelength
(nm)
f (555nm) =
400
f (555nm) =
200
f (555nm) =
133
f (555nm) =
100
f (555nm) =
67
Data Theory Data Theory Data Theory Data Theory Data Theory
633
543
488
348
405
447
350.7
408.5
454.9
174
202
225
175.3
204.2
227.5
116
135
152
116.9
136.1
151.6
88
102
114
87.7
102.1
113.7
59
69
76
58.4
68.1
75.8
Table 5-3 Diffractive Lens B: Measured and calculated focal lengths at the three test
wavelengths.
As an example, the images of three of the focal spots of the diffractive lens B are shown
in Figure 5-3. This was for the case when the diffractive lens B was shunted from a 12-level lens
to a 4-level lens in order to produce the focal length of 133 mm (at the design wavelength of 555
nm) which is one-third of the design focal length of 400 mm [70]. The focus spots were all
nearly round and sharp, with some background scattered light due to lowering of the diffraction
efficiency especially at shorter focal lengths.
Figure 5-3 Diffractive Spot’s Per Wavelength: Sample images of the best focus spots for the
diffractive lens B when it is set to the focal length of 133 mm at the green wavelength.
The fluidic lens illustrates a nonlinear response as fluid is withdrawn. As the membrane
reaches higher radii, the membrane becomes flatter. The sensitivity to the amount of fluid
increases within this range since a smaller amount of fluid varies the curvature. The measured
85
values of the fluidic lenses focal length for the three wavelengths are depicted in Figure 5-4 in
terms of the amount of fluid injected in the lens.
Focal Length (mm)
140
130
120
110
633 nm
100
543 nm
90
488 nm
80
0
100
200
300
Amount of Methanol Evacuated from Chamber
(L)
Figure 5-4 Fluidic Achromat Focal Length: Chromatic dispersion of the variable focal planoconvex lens alone applying methanol at the three test wavelengths when set for 80 mm focal
length and higher.
The final step in producing the variable focal length achromat is the combination of the
liquid crystal diffractive lens with the pressure controlled methanol fluidic lens. After adjusting
the focal lengths of each lens to the appropriate values dictated by the achromat equation we
measured the overall focal length of the hybrid lens at the red, green, and blue wavelengths. The
experiment verified that the focus spots of the red and blue wavelengths coincided very closely.
Figure 5-5 (a-e) depict the focal spots for the red and the blue wavelengths as the focal lengths of
the diffractive and the fluidic lenses are varied according to the achromat equation. In Figure 5-5
(a-c) diffractive lens A, and in Figure 5-5 (d, e) diffractive lens B was combined with the fluidic
lens. The other three focal lengths from the diffractive lens B could not be used for this
experiment because of the limited minimum achievable focal length of the fluidic lens in its
current form. As the focal length is decreased, the spot size and aberrations are reduced as
86
expected; however, the background scattered light is slightly increased. This is caused by the
reduction in diffraction efficiency at the shorter focal lengths as the number of binary phase
levels decreases due to the electrode shunting [70, 71]. The issue of low diffraction efficiency
can be overcome by designing diffractive lenses with higher number of binary phase levels
which results in smaller electrode sizes if the design optical power and aperture size are kept
constant. This will require a more advanced micro-fabrication technique. On the other hand, the
fluidic lens showed nearly round and sharp focus spots at short focal lengths when the curvature
of the membrane was high, but at long focal lengths as the membrane became flatter
considerable aberrations started to show up, of which astigmatism and coma were more
pronounced as evident from Figure 5-5 (a), (b).
Figure 5-5 (f) shows the values of the overall focal length of the hybrid diffractive/fluidic
lens for the green, blue and red test wavelengths. As expected, the green light comes to focus
first and then the red and blue lights will come into focus near the same plane. The measured
focal lengths of the hybrid lens closely matched with the expected focal length values seen from
Figure 5-5 (f). Although our hybrid diffractive/refractive lens has the advantage of being multifocal and non-mechanical compared to the traditional lenses, its current optical qualities are
slightly inferior to the conventional lenses because of the few available focal lengths of our
liquid crystal diffractive lenses in their current form and low diffraction efficiencies at shorter
focal lengths, as well as physical limitations of our fluidic lens in its current form including small
fluid pump, limited aperture size, and significant aberrations at longer focal lengths when the
membrane’s curvature is decreased. The chromatic aberration was significantly reduced but not
completely at this time corrected due to the current limitations which can be overcome by
improving the fabrication.
87
The clear aperture of our liquid crystal diffractive lenses is limited by the photolithography capabilities, number of binary phase levels, and diffraction efficiency, whereas the
fluidic lens is aperture limited by the pressure control of the mechanical flanges on the
periphery. If the aperture becomes too large then we cannot produce an even distribution of
pressure holding down the membrane, inducing uncontrollable aberrations. The function radius
of curvature of the fluidic lens is limited by the tensile strength of the designed membrane. Using
a broad-band positive photoresist (S1805) and Karl-Suss MA6 contact printer operating around iline (365 nm), we were able to achieve one micron feature sizes. Employing more advanced
fabrication tools smaller features can be made and the design aperture can be increased. This is
due to the facts that the Fresnel zones get narrower as moving away from center and as the
number of binary phase levels or the design optical power is increased. Diffraction efficiency can
also become a limiting factor if the zone widths become comparable to the liquid crystal
thickness or the inter-electrode gaps (in case of one-layer electrode design) [70, 82].
Diffractive lens A has a maximum design aperture of 10 mm, 8 phase levels, 1 D
minimum optical power, no inter-electrode gaps (odd and even electrodes interleaved into two
layers), about 8-micron narrowest electrode, and about 7-micron thick liquid crystal. Diffractive
lens B has a maximum design aperture of 6 mm, 12 phase levels, and 2.5 Diopter minimum
optical power with one micron inter-electrode gaps (one-layer electrode design), about 5-micron
narrowest electrode, and about 4-micron thick liquid crystal. To increase the diffraction
efficiency liquid crystal thickness can further be decreased by using smaller glass fiber spacer
beads during assembly. However, the minimum thickness in order to achieve at least 2π phase
retardation is (λ ΔΦmax) / (2π Δnmax) = λ / Δnmax = 0.633 / 0.225 = 2.8 micron.
88
(a)
(b)
(d)
(c)
(e)
(f)
Figure 5-5 (a-e) Discrete Diffractive / Refractive Focal Length Achromat Results: Focal
spots when the diffractive and fluidic lenses are combined to produce the best focus for the red
and the blue lights. The focal length values at the green wavelength are: (a) f diffractive = 1000 mm,
ffluidic = 252 mm; (b) fdiffractive = 500 mm, ffluidic = 126 mm; (c) fdiffractive = 250 mm, ffluidic = 63 mm;
(d) fdiffractive = 400 mm, ffluidic = 101 mm; (e) fdiffractive = 200 mm, ffluidic = 51 mm; (f) overall focal
length of the hybrid system for the green, red and blue wavelengths.
89
In conclusion, we have demonstrated a variable focal length achromatic lens that consists
of a variable liquid crystal diffractive lens and a variable pressure-controlled fluidic lens. We
used two diffractive lenses that produce multiple discrete focal lengths with an Abbe number of 3.45. The fluidic lens can provide a more continuous variation, and its focal lengths are chosen
such that they minimize the dispersion of the diffractive lens. We chose Methanol for the fluidic
lens due to its high dispersion properties. Then we combined the fluidic lens and one diffractive
lens at a time to minimize the dispersion between the red and blue wavelengths. The lenses
showed acceptable optical properties and the test results were close to the theoretical predictions.
This adjustable hybrid lens has no moving parts and would be useful for compact color imaging
applications, and medical and ophthalmic imaging devices.
5.2 Continuous Variable Focal Length Achromatic Fluidic Lenses
The previous design produced achromatization for specific foci.
A more advanced
achromatic lens would be to produce any focal length that one is interested in with a continuous
variable focal length achromat.
We propose the development of a variable focal length
achromat. The achromat design is composed of two individual variable lenses, one with a
crown-like oil fluid and the other with a flint-like oil fluid, which are combined to correct for
chromatic aberration. The fluidic lenses have two elastic membranes, one for each chamber.
Fluid pressure causes the membranes to change shape and alter the optical power of light passing
through it. By adjusting the fluidic pressure of the two chambers in sync with each other we can
produce exact achromatized focal lengths.
As was stated earlier, an achromat corrects for longitudinal chromatic aberration through
the combination of a positive dispersive crown glass and a negative dispersive flint glass, where
90
the high dispersion and low power of the flint lens counter balances the dispersion of a higher
power crown lens. Crown and flint glasses typically have an Abbe number above and below 55
respectively for standard glasses. As we shown in the previous section, fluids offer Abbe
numbers that can vary from high dispersive =5 to low dispersive Abbe numbers of =100. The
flint and crown lenses balance the dispersion and focal lengths in order to match the focal
position between designed blue and red wavelengths, where the primary dispersion is therefore
corrected for.
5.2.1 Variable Focal Length Achromatic Design
Our fluidic achromat is developed in much the same way. Each chamber has a crown-like
or flint-like fluid instead of a solid glass material. Similarly, the crown-like and flint-like fluids
are separated, with the crown-like fluid having a lower dispersion. To be used in refractive
applications, the control of dispersion, index, transparency within the visible, toxicity, volatility,
and transition factors are all significant in the production of the proper fluids. Any fluid
including, but not limited to, optical immersion fluids, laser fluids, inter connect fluids, or any
other optical fluid’s can be applied into these chambers. As long as the optical fluid does not
react with the metal frame, any optical fluid is applicable.
91
Figure 5-6 Dual Fluidic Achromatic Lens Design: The SolidWorks design of our two fluidic
chamber system.
Figure 5-6 shows an embodiment of our design with a double fluidic chamber, which
functionally acts like a doublet design.
Our design is symmetric about the center so the
chambers on either side are symmetric. Each chamber has a protective glass window so that our
membranes would not collect dust. If we were to pass light through the window, the light passes
through the window. The next structure is a pressure based tensioner. There are two pretensioners in which the membranes are compressed in between and locked into. The pretensioners are locked down onto the central frame. The tensioner which has the window locked
onto it is then secured onto the pre-tensioners and locked in. The tensioner applies pressure onto
the membrane so that it locks the membrane down in a clamped edge design. The achromatic
base connects the same symmetric design on either side of the frame. This allows for us to
produce a doublet designed achromatic chamber.
92
Figure 5-7 Dual Chamber Fluidic Achromat: Here is a current image of our double chamber
fluidic lens.
A second approach that we have proposed in developing an achromatic lens is in the
coupling of two singularly controlled plano-convex singlet fluidic lenses.
By altering the
curvature of each fluidic device in sync with each other we are able to control the power exiting
each single surface.
Figure 5-8 Coupled Single Chamber Achromatic Design: This shows a combination in
concept of two fluidic lenses coupled together.
93
5.2.2 Test Methods for Continuous Variable Focal Length Achromatic
One of the most significant factors in producing an achromatized lens is in the fluid
selection.
A couple of optical features that are important are the index of refraction and
dispersion value. Again, we take advantage of f1 1 + f2 2 = 0 to produce an achromatic lens.
The fluids selected determine the amount of dispersion or Abbe numbers 1 and 2 that satisfy
the equation. Knowing the focal length range of each of the lenses allows for us to know f 1 and
f2. As was previously described, we can determine the radius of curvature of each radius of
curvature surface through our testing apparatus.
Our testing apparatus is similar to the hybrid system except now we only test fluidic
lenses.
The combination of the various lasers allows for us to either individually test
wavelengths for the fluidic lens or to concurrently test wavelengths. The dichroic mirrors have
specified bands in which they reflect and so we found the proper dichroic mirrors to pass the
previous wavelengths while reflecting the following lasers wavelength. By mixing the lasers or
adding a stop we can vary the output of the lasers.
B
G
R
Shack-Hartmann Sensor
Achromatic Fluidic Lens
Shield
Collimating Lens / Expander
Mirror
Mirror
Dichroic
Mirror
Dichroic
Mirror
Figure 5-9 Dual Achromat Testing Design: Here is the generic setup which we are attempting
to test the achromatic fluidic lens.
94
We mentioned two possible designs of dual fluidic lenses where one has two singlet
fluidic lenses coupled together and the second had a single double chamber fluidics as our
achromat designs. The two singlet design offers an easier testing approach. We can apply laser
light through various pressure volumes on each individual lens and identify where that individual
lens focuses. We can then identify the radius of curvature from the determined focal lengths.
The radius of curvature will be significant information in the synchronization of the two lenses.
As an example we show the radius of curvature of fluidic lens one as was determined through
this testing approach with DI water.
Table 5-4 Analysis of Fluidic Lens Radius of Curvature: From our testing apparatus we have
determined the radius of curvature of fluid lens 1.
The above table shows an example of us determining the radius of curvature from the
three wavelengths that we were testing with. For each fluid extraction we applied multiple tests
per laser wavelength. A significant factor is in determining a fluid that is stable and transparent
in the visible wavelengths. A stable fluid with no evaporation rate allows for us to verify that the
95
repeatability of our fluidic lens technology is accurate. This test was for a proof of concept and
so we applied DI water for testing purposes. Hence, with a stable fluid volume and knowledge
of the index of refraction of fluid and air we were able to determine the radius of curvature of the
lens per fluid volume:
The above equation determines the radius of curvature per wavelength as the index of
refraction varies for all materials per wavelength. We then averaged out the three radii of
curvature to determine the average radius of curvature per fluid volume. The three radius of
curvature values were approximately the same value. This measuring approach can be applied to
the achromat design by first measuring a single surface with fluid inserted.
After the
measurements are complete, one must zero out the power of the first lens before inserting fluid
for the second chamber. The second chamber can then be measured with the first lens chamber
nulled out. From this approach one can determine the radii of curvature of a dual chamber
system.
An approach in producing a continuous achromat can be achieved by determining what
the radii of curvature must be for achromatization per system focal length. We mentioned
several times syncing the two surfaces allows for achromatization and we have been focusing on
the radius of curvature identification of our achromat. By knowing the radii of curvature of each
surface we can determine where the focal length of each fluids lens would be with a determined
fluid that has a known index of refraction and Abbe number. We have begun experimenting
with four fluids where two have crown like properties and two have flint like properties.
96
Figure 5-10 ZEMAX Model of an Achromat Design with 80 mm Focal Length: Here we
show the radii of curvature necessary from each of the fluidic lens surfaces to achieve an
achromatic lens that is diffraction limited at 80 mm focal length.
Figure 5-11 ZEMAX Model of an Achromat Design with 400 mm Focal Length: Here we
show the radii of curvature necessary from each of the fluidic lens surfaces to achieve an
achromatic lens that is diffraction limited at 400 mm focal length.
We can determine the radii of curvature needed from our fluidic lens chamber through
modeling in optical design software such as ZEMAX. We place a desired focal length that we
would like to optimize in ZEMAX with our two fluids. Again it is significant to know the index
97
of refraction of the fluid at a designed wavelength and also the Abbe number for that fluid. We
set the two fluidic lens surfaces as variable and then optimize for aberration correction. We now
know what radius of curvature is desired from our fluidic lenses for an achromatic lens with a
given focal length. Above we show an example of a given crown with two different flint fluids.
The focal shift is shown to be more of the traditional curved shape in the longer focal lengths in
comparison of Figures 5-10 and 5-11. We also see that as the focal length for the achromat is
longer, it is easier to produce a diffraction limited achromatic lens as is seen in Figure 5-11. In
Figure 5-10, we have an achromatic focal length of 80 mm that reaches the edge of the
diffraction limit, where the black circle identifies the diffraction limit. The focal length shift per
wavelength has more of a skewed focal length variation on the shorter achromatic focal lengths
as seen in Figure 5-10. We can use ZEMAX to fully map the necessary radii of curvature for the
two surfaces so that our achromat is continuous.
98
Focal Length
Radius 1
Radius 2
Focal Length
Radius 1
Radius 2
(mm)
(mm)
(mm)
(mm)
(mm)
(mm)
80
18.15
34.11
170
38.43
76.55
90
20.10
37.72
180
40.751
81.53
100
22.27
42.13
190
43.08
86.51
110
24.53
46.86
200
45.40
91.49
120
26.82
51.73
210
47.72
96.48
130
29.14
56.66
220
50.04
101.46
140
31.46
61.62
230
52.37
106.44
150
33.78
66.59
240
54.69
111.42
160
36.10
71.57
250
57.01
116.40
Table 5-5 Table of Fluidic Lens Radius of Curvature for Achromatization of Two Fluids:
We have determined two fluids to map the radii of curvature for each fluidic lens chamber. This
enables us to produce an achromatic lens at a given focal length.
These charts coupled with the known radii of curvature per fluid volume enables us to
produce a computer controlled achromatic lens that is continuous with variable focal lengths.
We can further illustrate that this fluidic lens technology is applicable in the production of
negative focal length chromates in addition to positive focal length chromates. We have chosen
two more fluids that allow for us to produce negative focal lengths. Here we show two positions
of -60 mm focal length and -100 mm focal lengths chromates. We choose -60 mm to show that
it is possible to design the achromat so that it is not necessarily diffraction limited but that the
aberration is slightly larger than this scenario, making these shorter focal lengths also realizable.
99
Figure 5-12 ZEMAX Model of an Achromat Design with -100 mm Focal Length: Here we
show the radii of curvature necessary from each of the fluidic lens surfaces to achieve an
achromatic lens that is diffraction limited at -100 mm focal length.
Figure 5-13 ZEMAX Model of an Achromat Design with -60 mm Focal Length: Here we
show the radii of curvature necessary from each of the fluidic lens surfaces to achieve an
achromatic lens that is diffraction limited at -60 mm focal length.
We can produce tables to identify the radius of curvature for more than these specific
fluids and are not limited by these specific fluids. Hence, we choose the two optical fluids to
produce the achromat, we identify the radius we need to produce a focal length, and then we
100
output that achromatic focal length. Once these fluids are inserted into the chambers, the fluidic
chromates becomes functional. By syncing the proper curvature between the front membrane
and the rear membrane an achromat is produced.
The radii of curvature are mapped to the amount of fluid volume withdrawn or inserted
into the fluidic lens. We can replicate the results of these various achromatic designs by setting a
look up table to a given focal length for a couple of our fluids. We can then adjust the
achromatic focal length according to the desires of the user. Thus, we have created a digital
achromatic lens through optofluidic technology.
101
6.0
WAVEFRONT CORRECTION OF THE FLUIDIC PHOROPTER
AND FLUDIIC AUTO-PHOROPTER
We have discussed applications of optofluidic designs of zoom optical systems and
achromatic correction mechanisms. Microscopes and other imaging systems are achievable with
no moving parts through optofluidic adaptive optic technology.
Adaptive optics finds its
application in many accommodating designs, but also in wavefront correcting systems.
Wavefront correction can be found in a broad array of fields from astronomy to vision science.
Wavefront technology has made vision correction and retinal imaging realizable in real time
correction of ocular aberrations.
Wavefront sensing technology identifies the aberrations that exist in an optical system
such as the eye and adaptive optic technology corrects for the measured wavefront. The ShackHartmann wavefront sensor has made measuring of ocular aberrations realizable. The concept of
applying the Shack-Hartmann wavefront sensor for ocular measurements of the wavefront was
first achieved at the University of Heidelberg in the early 1990’s [83]. Adaptive correction of
the eye progressed further through automation and the advancement of adaptive optic technology
[84].
The first closed-looped adaptive optic technology that coupled the Shack-Hartmann
wavefront sensing technology with adaptive optic technology was that of the reflective
deformable mirror. This technology has found application in multiple areas of vision science
such as ocular correction, retinal imaging, refraction correction, eye tracking and disease
identification [84, 85, 86]. Our interest is in the application of the measurement and correction
of ocular aberrations in real time. Through real time measurements, one is able to identify and
measure a patient’s accommodation, and the eye’s dynamic range. Also in real time, one can
102
extract a user’s prescription for various focal locations and output the results in an objective
manner. This streamlines the subjective eye exam to an automated objective testing device.
Phoropters are used to estimate and correct for the second order defocus and astigmatism
aberrations of the eye. Subjects are systematically asked to compare varying amounts of
correction to iteratively determine their ideal correction. An optofluidic phoropter, which is an
adaptive optic phoropter, takes the entire phoropter system and compresses it into a group of
fluidic lenses. This grouping of fluidic lenses enables for the correction of ocular second order
aberrations. Furthermore, advances in fluidic lens technology may lead to systems that can
correct higher order aberrations as well.
It is necessary for wavefront technology to couple the adaptive optic technology to
produce a correction in real time. A fluidic auto-phoropter discussed here takes advantage of the
closed-loop technology to measure and correct the low order aberrations in the human eye. Autophoropters have been produced when coupling Shack-Hartmann wavefront sensors with the
adaptive optic technology of either a deformable mirror [84] or liquid crystal technology [87].
Deformable mirror technology is often times expensive and bulky and requires large relay
systems to work. Also, scaling is required to match the pupil size of the deformable mirror with
the pupil size of the human eye. The adaptive optic liquid crystal auto-phoropter has limitations
in that it is strongly wavelength dependent, has high noise limitations, and also the system is
bulky [88]. There has been an expansion on adaptive optics and optofluidic technology in the
field of ophthalmology [17, 89, 90, 91, 92]. We have designed optofluidic auto-phoropter
systems with the focus on producing a cheap, compact, mobile, and quick device that at the same
time achieves the goal of identifying a prescription in real time.
103
Figure 6-1 Fluidic Phoropter Compared to Standard Phoropter: The motivation is the have
our fluidic phoropter on the left completely replaces the standard phoropter system on the right.
Our fluidic auto-phoropter combines a Shack-Hartmann wavefront sensor with a compact
and inexpensive refractive fluidic phoropter. Our system has an open-view design, where the
user observes real objects at various image depths. Furthermore, the elements are transmissive,
allowing for a more compact design when compared to reflective systems. The goal is to
develop an adaptive binocular see-through auto-phoropter that automatically measures a patient’s
spherical and cylindrical error, nulling this error with a stack of sphero-cylindirical fluidic lenses.
We expand on see-through auto-phoropter systems, rather than reflective systems, to offer a
natural scene for the user. This will offer more accurate readings on the user’s prescription at
various object distances. The measurements from the Shack Hartmann wavefront sensor directly
identify an individual’s wavefront slope. The wavefront slope directly offers information for
astigmatism and defocus aberrations, in addition to higher order ocular aberrations. This slope
information in turn drives pump mechanisms for the fluidic lenses.
This chapter focuses on the wavefront theory of how the adaptive optical fluidic
phoropter functions and how the auto-phoropter functions. We begin with an organization of the
optofluidic phoropter, or fluidic phoropter, as was discussed in the dissertation by Randal Marks
of “Fluidic Astigmatic and Spherical Lenses for Ophthalmic Applications” [17].
The
104
predecessor of this dissertation was focused on design and testing of the optofluidic phoropter.
We will describe the theory that enables this fluidic phoropter to compensate for the vision error
of a user. The end of the chapter is focused on the wavefront correction of auto-phoropter
designs.
6.1 Fluidic Phoropter
Traditional phoropter systems primarily focus on correction of the lower order
aberrations of astigmatism and defocus. Therefore, it is necessary to produce sphero-cylinder
correction for a standard fluidic auto-phoropter design. In chapter 1 section 3, we focused on the
fundamental theory of membrane shape control through deflection of our fluidic lenses. This
theory identified the type of deflection that was necessary to reproduce specific lens types. We
had found that we were able to replicate a spherical lens, which we will call a defocus lens. We
also produced a sphero-cylinder lens by fabricating a pair of lenses with a rectangular framed
membrane. We had found that if the rectangle was infinite in one direction then we would have
pure cylinder, but since we needed a clear aperture active area we would require a lens that
produces sphero-cylinder results. The additional spherical power induced by these lenses will
need to be compensated by the defocus lens.
6.1.1 Wavefront Analysis of Defocus and Astigmatism Lenses
We can identify the aberrations that are exhibited by each of these lenses through the
measurement of a Shack-Hartmann wavefront sensor.
105
Figure 6-2 Wavefront Measurement of Defocus Lens:
astigmatism in the
term [17].
The defocus lens shows residual
As was mentioned, we find that our defocus lens has residual astigmatism error. This
residual error is caused by the clamping approach of our membrane to the frame at the screw
locations. It is observed that this defocus lens exhibits a high control of defocus and low
amounts of residual astigmatism aberration. Each one of the colors on the wavefront scale
measures the wavefront at different settings in fluid volume ranging from -3 to +3 Diopters. The
higher order aberrations are measured to be negligible beyond the astigmatism measurement of
either
or
. Even when we focus within 0.5 m of RMS of the wavefront measurement,
the primary observed aberrations are the second order radial Zernike’s. The third order radial
Zernike’s are the next highest terms with less than 0.1 m RMS for up to 3 Diopters of power.
Therefore, the third order radial Zernike’s are observed to be negligible relative to the
functionality of the fluidic lens.
106
A similar observation is made when analyzing the astigmatism lenses.
anticipated, there was an observation of sphero-cylinder aberrations.
As was
The higher order
aberrations measured through the cylinder lens is even smaller then the higher order residual
aberrations observed in the defocus lens. There is less than 0.1 m RMS Error observed from
these higher terms. The cylinder lens is primarily dominated by astigmatism and has less
defocus aberration. Once the astigmatism lens reaches + 3 D of astigmatism we find that there is
an increase in residual astigmatism in the opposite orientation. This residual astigmatism is
below a quarter of a Diopter; however, it is not negligible like the additional higher order terms.
The additional residual astigmatism in the opposite orientation is due to the relative orientation
of the two fluidic lenses to the wavefront sensor. The two astigmatism lenses are orientated at
45o relative to each other, but are also orientated relative to the lenslet array of the ShackHartmann wavefront sensor. Residual astigmatism error in the opposite astigmatic Zernike term
is produced with a slight misalignment of the astigmatism lenses relative to the Shack-Hartmann
wavefront sensor.
measurements.
This assembly error must be taken into account while producing
107
Figure 6-3 Wavefront Measurement of Astigmatism Lens: The astigmatism lens has the
anticipated defocus aberration in addition to a residual aberration of the additional second order
Zernike astigmatism term of the opposite orientation [17].
6.1.2 Wavefront Analysis of Fluidic Phoropter
We are able to correct for given amounts of astigmatism and defocus by compensating
for aberrations with a stack of two cylinder lenses and a defocus lens, our fluidic phoropter. It is
advantageous that the cylinder and defocus lenses produce negligible aberrations for all terms
except our second order Zernike polynomial terms of astigmatism and defocus.
108
Double
Astigmatic
Lens
Defocus
Lens
Figure 6-4 Fluidic Phoropter Orientation: Here we show a mechanical model view of
phoropter with a defocus lens and two astigmatic lenses that are oriented 45o to each other [17].
The fluidic phoropter produces power and cylinder correction at any angle. The designed
system is a compilation of two astigmatism lenses oriented 45 o relative to each other and a
defocus lens. Ideally, the defocus lens would only produce power variation and each astigmatism
lens would produce a defocus and astigmatism term. By orientating the two astigmatism lenses
45o relative to each other, we can correct for any orientation of astigmatism error in addition to
power error.
6-1
6-2
109
6-3
From our stack of fluidic lenses, each one of these wavefronts is a description of a single
fluidic lens. Equation 6-1 is the results of purely defocus power where no residual wavefront
measurements are observed. The summed astigmatism lenses orientated at 0 o and 45o relative to
each other produce correction for the two astigmatism orientations while also summing the
defocus term with no residual terms. The combination of the three fluidic lenses therefore
produces the theoretical fluidic phoropter wavefront:
6-4
We find that all three fluidic lenses alter the properties of the defocus lens while each of
the astigmatism lenses produces a Zernike astigmatism term. With an ideal system, we can
balance astigmatism through proper pressure control of the astigmatism lenses. After identifying
the amount of ocular astigmatism error in a given orientation, we control the two astigmatism
lens to correct for the astigmatism errors.
When setting the two astigmatism lenses, we
additionally set the constants that effect the defocus terms for the astigmatism lenses,
. The defocus lens can then be applied to compensate and null the defocus caused by
the astigmatism lenses coupled with the eyes defocus error. This setup allows for the fluidic
phoropter with no residual aberrations to correct for defocus and astigmatism error at any given
orientation for an eye.
Experimentally, the defocus and astigmatism lenses do not only produce these specific
aberrations but additional residual aberrations, as we have observed from the Zernike wavefronts
110
of the Shack-Hartmann wavefront sensor.
additional
astigmatism.
We had found that the defocus lens produces
In addition, the astigmatism lenses produce residual Zernike
astigmatism to the orthogonal astigmatism Zernike term due to the misalignment of the fluidic
lenses relative to the lenslet array. We can therefore expand the terms of 6-1 through 6-3 to
include the residual wavefront terms that affect the wavefront of the fluidic lenses. The residual
terms will be represented with an R subscript.
6-5
6-6
6-7
This observed residual aberration has been found to be in the second order Zernike terms
that we are correcting for. This is advantageous in that we are able to composite for the residual
aberration without adding any additional Zernike terms. A second advantage of these residual
terms is that there magnitude is much lower than the actual correction Zernike terms in each of
the fluidic lenses for their respective wavefront correction. As these residual aberrations are
slight, we are able to compensate for these terms in an optimization approach similar to that of an
optical design software such as ZEMAX or CodeV. We run several iterations of compensation
between fluidic lenses in adjusting the fluid volume per lens to increase the accuracy of our
phoropter system relative to the wavefront measurement until we reached the desired correction
111
result. We analyze the summed Zernike terms for the wavefront of the fluidic phoropter that
takes into account all of the residual terms:
6-8
6.2
Wavefront Analysis of the Fluidic Auto-Phoropter
An objective eye exam is created to identify a patient’s prescription. The adaptive optic
technology must compensate for the users wavefront error to null the wavefront error out for the
auto-phoropter to identify that a patient observes a fully corrected view.
The sum of the
wavefront error of the eye and the phoropter must therefore equal zero to null the wavefront error
out and produce a clear image.
6-9
The closed loop system allows for real time correction of the wavefront.
As we
established earlier, the wavefront correction comes from the optofluidic technology while the
eye’s wavefront measurement is calculated from the Shack-Hartmann wavefront sensor. The
Shack-Hartmann wavefront sensor can measure higher order Zernike’s. We can represent the
wavefront error of the eye as the terms that exit the wavefront sensor.
6-10
112
Equation 6-9 includes defocus, astigmatism, trefoil in x and y, coma in x and y, tetrafoil
in x and y, secondary astigmatism in x and y, and primary spherical aberrations or
through
. In the future, optofluidic technology can be applied to correct for higher order
aberrations, but here we are focused on the second order radial Zernike terms. Our fluidic
phoropter corrects for on
through
as on average the second order terms of defocus and
astigmatism account for approximately 90% of error in the human eye population.
6-11
We can identify the amount of compensation required for the fluidic lenses that are
required to correct for each of the Zernike terms. At the same time, we can extract the wavefront
measurements of astigmatism and defocus for readable prescriptions by combining equations 68, 6-9, and 6-11. The auto-phoropter designs adjust the fluidic lens pressure to adjust the
weighting of 6-12 through 6-14 of each fluidic lens until the most optimized nulled out solution
is achieved.
6-12
6-13
6-14
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7.0 FLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: SYSTEM DESIGN
Our first fluidic auto- phoropter is designed in order to produce automated eye
examinations through the combination of a fluidic phoropter and the objective analysis of a
Shack Hartmann wavefront sensor. A see-through adaptive phoropter provides the ability to
measure a patient’s refractive prescription at any plane. This allows for prescription
measurement at any distance from the eye such as a distance of 20 feet for a Snellen eye chart, a
distance used for reading glasses or even a far enough distance where it is relatively infinity.
The power of a see-through system allows for natural distances to be observed by the patient.
Figure 7-1 Targets at Multiple Planes for Focusing Through Fluidic Auto-Phoropter: View
of targets at various depths where the eye natural focuses on a target and the defocus lens
compensates to clear the image.
An accommodating prescription is achieved experimentally by varying the target locations.
As the system is see-through, the patient can focus at various depth locations. By focusing at
114
different depths, it allows for the eyes to accommodate and converge while we are measuring the
refractive error. The major assumption is that the field of view of the fluidic phoropter is not
occluding the convergence angle of the object location. The mapping of these measurements
develops multiple prescriptions and is corrected almost instantaneously for a patient. The autophoropter design also enables for a smaller compact size than is possible with other adaptive
optic systems. Our first auto-phoropter system uses a fluidic lens module that is combined with
a Shack-Hartmann wavefront sensor to automatically determine a sphero-cylindrical refraction
applicable for any prescription measurement. This design is also capable of measuring higher
order ocular aberrations from a patient’s eyes and in the future will be able to correct for higher
order ocular aberrations. Our first auto-phoropter design is compact and covers a working area
of 1 ft by 1ft. Current models in the market apply reflective rather than refractive elements as
the adaptive optics, which eliminates see-through capabilities. We are designing a compact,
quick, and in expensive approach in measuring an individual’s accommodating visual error.
7.1 Design of Fluidic Auto-Phoropter Prototype One
The design consists of two optical paths that are combined into a single system. There is
an illumination/sensor path and also a line of sight path of the eye. Our designed system is
comprised of three main modules: a fluidic lens, a relay telescope and a Shack-Hartmann
wavefront sensor. We will explain a progression of the light traveling through the optical system
from the source to the detector. After the system design is explained we will summarize the
functionality of the whole system to produce a clearer image of our control mechanisms.
115
CCD
Array
Prism
Mirror 2
IR
Source
Prism
Mirror 3
Lenslet
Array
Lens
Doublet 1
Fluidic
Lens
Eye
Eye Chart
Doublet 2
NIR BS
45:55
Prism
Mirror 1
Prism
Mirror 4
NIR BS
45:55
Figure 7-2 Layout of Optofluidic Auto-Phoropter Prototype One: The Theoretical Setup
where we propagate through fifteen surfaces and reflection points. The green light represents the
line of sight of the prescribed user while the red light represents the light from the IR Light
Source to the Shack Hartmann wavefront sensor.
7.1.1 Fluidic Auto-Phoropter Prototype One: Light Path from Source to Fluidic Phoropter
We first begin with our light source, which has changed through experimentation to a
fiber coupled super luminescent diode (SLD) that operates at 780 nm. We discovered that
coherent light induces high amounts of scatter from the relative close proximity of our optical
parts.
In addition, interference is observed between multiple surfaces, destroying point
information of the Shack-Hartmann measurements. A super luminescent diode (SLD) with low
coherence was the solution to overcome this problem, which works well in the Shack-Hartmann
design; however, the beam shape was harder to control.
We were attempting to produce
collimated light reaching the eye location as to have a plane wave propagate through the system.
Our first SLD source was at the focal location of a lens in order to collimate the SLD light
source. The output that was produced was an elliptical beam shape.
To correct the beam shape we made our SLD into a point source design by fiber coupling
the SLD source. We achieved a collimated circular plane wavefront by using a fiber coupled
SLD operating at 785 nm. The SLD diode that we choose outputs up to 6.3 mW and is the LPS-
116
785-FC SLD from Thorlabs. The output of NIR light exiting the fiber was placed at the focal
point of a collimating optical lens. The light exiting the fiber was a point source placed at the
focal point of the collimating lens, thus producing a 785 nm collimated circular beam.
Figure 7-3 Specifications of Fiber Coupled SLD: We define the circuit specifications required
for our SLD’s to run properly.
The collimated light source was driven by a circuit coupled with a variable power supply.
This circuit was designed in PCB software to run our SLD’s. The circuit board contains two
individual circuits to control each SLD of a binocular system. Each individual closed circuit
system consists of a potentiometer, a resistor, and the SLD. Each separate closed loop circuit
requires a separate variable power supply to run each SLD.
117
Figure 7-4 Circuit used to drive the SLD’s: This is the circuit designed in PCB software
coupled with a variable power supply to run the SLD’s.
Each closed circuit allows for us to drive a single SLD. The variable power supply has
controls to vary the voltage and the current. The potentiometer offers control of the resistance.
We know the basic correlations of current, voltage, resistance and power through Ohm’s and
Joule’s Laws:
(7-1)
(7-2)
Through these equations we determined the proper amount of current and voltage to run
the circuit. We then applied a power meter at the location of where the eye would be placed to
measure the output power of each of the collimated light sources. We added variable power ND
filters and identified the amount of filtering that was required to reduce the light source power.
118
The maximum amount of permitted exposure (MPE) for the near infrared wavelength of 785 nm
with an 8 hr exposure applied onto the eye is approximately 125 W [93]. The near infrared
light at the eye plane from the SLD is controlled to around 10 to 15 W, which is about 10 times
less than what is acceptable by the American National Standards Institute’s maximum
permissible exposure. Each of the SLD sources had a different amount of ND filtering as the
current through each circuit was slightly different. Both paths were controlled down to this low
power range.
The SLD is placed off-axis relative to the line of sight of the patient. In order to achieve
a see-through phoropter it is necessary to shift the light source and detector out of the line of site
of the user. We achieved this through the application of 55:45 pellicle beamsplitters that operate
between 700-900 nm in the near infrared. Collimated NIR light propagates to a coated pellicle
beamsplitter that reflects light towards the eye or the eye model. There is a screwed on pinhole
on the beamsplitter relative to the entrance of the NIR light in order to stop down the source if
necessary. The beamsplitter is fully transparent in the visible. An additional advantage of
applying pellicle beamsplitters is that they slightly vibrate, where the vibration averages out
noise in the system. The NIR light from the beamsplitter reflects 45% of the light to the fluidic
phoropter and to the eye or eye model.
7.1.2 Fluidic Auto-Phoropter Prototype One: Light Path from Optofluidic Phoropter
through the Eye Model
Throughout this work we have developed a foundation in the description of our fluidic
technology. Thus, we have described the theory and mechanical structure in producing lenses
for ophthalmic correction.
We have explained how our astigmatism and defocus lenses
combined to produce ophthalmic correction for defocus, cylinder, and axis. In this section we
119
will discuss additional topics that affect our fluidic phoropter. We will then continue following
the photons within our optical design through the fluidic phoropter back to the telescope system
within our auto-phoropter design. There are a couple of topics that have not yet been explored in
the discussion of our optofluidic phoropter. The two factors are a discussion of fluid selection
and the second is showing the range of the astigmatism and defocus lenses.
7.1.2.1 Fluid Selection for Fluidic Phoropter
Fluid selection began in section 5.2.1 and also in the selection of Methanol in section
5.1.4 where we focused on the optical properties of the fluid for our achromat designs. In those
sections the optical properties that were mentioned were the fluids optical properties of
dispersion control (Abbe number), index of refraction, transparent in the visible spectrum,
toxicity, volatility, and viscosity.
In those sections we focused on the Abbe number, and
visibility. The topics of transparency in the visible and toxicity are necessary for a safe lens
design. These topics were inherently taken into account in the fluid selection, but we have not
expanded on the concepts of volatility and viscosity. In addition, we have not focused on the
concept of fluid density, fluid reactivity, and corrosive effects to other materials in the fluidic
phoropter design.
The resistance that a fluid produces when in the actuation chambers is significant in
determining the rate of change of the lens curvature. Highly viscous fluids increase motion
resistance and hence slow the force of fluid evacuation. The density of the fluid material works
in tandem with the viscosity of the material. One would prefer a fluid with a lower density per
area if that fluid is observed to have a high viscosity. The combination of fluid density and
viscosity are significant in determining the rate of flow of the liquid.
120
From a mechanical standpoint, the fluid volatility and reactivity to system materials are
as important as the optical properties of the fluidic phoropter.
The volatility is a direct
correlation to the vapor pressure which identifies the point the fluid turns from a liquid to a
vapor. If the fluid is unstable, then the fluid will vaporize and produce a double index effect
within the liquid lens. This in turn alters the index of refraction and fluid thickness of our liquid
lens. Optical oils, laser fluids, and emersion fluids offer high stability for many years, making
them great options as desired fluids.
It is necessary to select fluids that have a high stability and do not react to any materials
in the full assembly of the pump control system. There are eleven materials that the fluid
interacts with that can be traced from the lens chamber to the pumps. The fluidic lens frame is
composed of anodized aluminum and a transparent glass window. Epoxy is used to glue the
window onto the metal frame. The connectors between the frame and the tubing are composed
of stainless steel. We apply a valve control as to identify the exact amount of oil for our base
zero point.
The tubing in combination with our valves is composed of Polypropylene,
Polyurethane, Polytetrafluorethylene, and Chlorotrifluorethylene. Finally, the fluid reaches the
glass syringe that is controlled by the actuator. These eleven materials must not react with any of
the fluids as to not cause corrosion of the parts. The combinations of the 11 materials in addition
to the 7 requirements of optical and material fluid properties were assessed in the fluid selection
process.
There were a total of 5 optical fluids found that satisfied a majority of the 18
requirements. The following two charts identify the fluids with numbers 1 to 5. Three of the
fluids are laser fluids and two are index matching fluids. It was found that immersion fluids did
not have stability for long term application of liquid lenses.
121
Fluid
Glass
Polypropylene
Polyurethane
Polytetrafluorethylene
Chlorotrifluorethylene
Aluminum
Acrylic
Stainless Steel
Sylguard 184
Epoxy
Latex
1
x
x
x
2
3
4
x
x
x
x
x
x
x
x
x
Polyethylene Compatible
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
5
x
x
x
No
No
x
x
x
x
x
Table 7-1 Fluid Compatibility with Auto-Phoropter Material: Here we identify the
compatibility of a fluid with an x for the 11 materials the fluids come into contact with. If the
materials were not compatible then we placed a no in the box.
Fluid
1
2
Refractive Index
1.3
1.4
Abbe Number
Viscosity cst
Density g / cc
101
5
1.9
69
17
1.9
3
1.511.512
52.8
1,450
1.32
Stability
High
High
High
Toxicity
Transparent in
Visible
None
None
99100%
Low
97100%
100%
4
1.49-1.50
56.3
10,000
0.888
Slight
Precipitation in
18 Years
Low
99-100%
5
1.571.61
29
177
1.092
High
None
9699%
Table 7-2 Fluid Optical and Chemical Properties: Here we identify 7 optical, material, and
chemical properties that affected the fluid selection process.
Not all of these fluids match the full requirements of our fluidic phoropter. Fluid 5
functions well with fluid 2 in producing an achromatic lens due to the two fluids dispersion
values. Both fluids have relatively low viscosities and thus fluid flow should not be a problem.
A limitation of fluid 5 is that it reacts with the plastic inside the valve and also with aluminum.
122
We have run experiments with fluid 5 and did not experience corrosion. It is highly likely that as
our aluminum is anodized and is protected from direct contact of fluid 5 with the aluminum. The
valves have not been used with fluid 5, but an option would be to select a different valve for this
fluid in order to achieve the achromat design.
It would be best to test the fluidic phoropter system with a lens material that is commonly
known. Fluid 3 and fluid 4 are Bk-7 and Acrylic matching fluids respectively. The index of
refraction of these two fluids is within an index variation of 1x10 -3 for every wavelength in the
visible spectrum relative to the actual glass material. The more common glass material in glass
production is that of Bk-7 or fluid 3. When we reach further into this dissertation we will
describe test results of experiments with fluid 3 and the testing of the liquid lens with this liquid
material. The down fall of fluids 3 and 4 are that they are highly viscous materials. The density
of fluids 3 and 4 is lower than fluids 1, 2, and 5 which increase fluid flow rates. However, the
viscosity of fluids 3 and 4 are orders of magnitude higher than the other 3 liquids. The Acrylic
has a viscosity of 10,000 cst and BK-7 of 1,450 cst. To put this into perspective water has a
viscosity of 1 cst, honey a viscosity of 3,000 cst, and molasses a viscosity of 5,000 to 10,000 cst.
We find that our acrylic fluid material has a resistance that is higher than molasses. Bk-7 is slow
moving and requires a longer time for fluid evacuation to occur. This fluid is advantageous as it
matches glass properties but is not for long term use for the fluidic auto-phoropter
The final two fluids, fluids 1 and 2, are both laser liquids that match the 18 requirements
that we have previously desired. Both of these fluids show no reactivity to the parts used to
assemble fluid control in the system. These fluids show a slighter higher density in composition
relative to the other fluids but have a much lower viscosity, in orders of magnitude. This allows
for a more optimal fluid flow within our chamber system. In addition the materials have a 99%-
123
100% transmission throughout the entire visible range, where these transmission ranges describe
the transmission of the fluids in a 1 cm thick chamber at room temperature.
In comparison of the two fluids, it is found that fluid 1 has a couple of advantages over
fluid 2. The first advantage is in the dispersion of the relative fluid. Chromatic dispersion is a
major concern, as each of the fluid chambers in the stack of fluidic lenses are singlets. With an
Abbe number of 69, liquid lens 2 has a lower amount of dispersion then typical glass, which
ranges between 25 and 65. There are few crown glasses such as FK51 that have a lower
dispersion then this fluid material. This dispersion however may not be low enough to fully
compensate for chromatic effects. There are currently liquid lenses in the market with a single
surface interface. These liquid lenses have an Abbe number of 100 which matches that of fluid
1. Fluid 1’s second advantage is that it is a highly viscous material. Its viscosity is 5 cst, which
is almost equivalent to that of water. Therefore, it would be advantageous to test with liquid 1 in
our optofluidic auto-phoropter as a next step in advancing our research.
7.1.2.2 Test Results with Fluidic Phoropter
We have established control of radius of curvature of the lens, fluid selection, and the
theory behind our liquid lenses. In our auto-phoropter system we have traveled from the light
source to the fluidic phoropter system and the model eye. Here we will show how the fluidic
phoropter functions through fluid control of each lens. The fluidic lens, which is our fluidic
phoropter, are a stack of three adjustable lenses composed of a spherical lens and two astigmatic
lenses oriented 45o to one another that are placed at approximately the spectacle plane of the
user. Any sphere, cylinder and axis combination can be achieved by adjusting the fluid volume
within the fluidic lenses. The defocus lens and the coupled astigmatism lenses have been tested
124
separately. The following results are achieved through the measurement of the defocus lens by
itself in Figure 7-5 and also the measurement of the astigmatism lenses coupled with each other
Figure 7-6. These figures are actual experimental values that were taken with the fluidic lenses.
The lenses performed similarly to what was expected, where the discrete steps within the fluidic
lens control mechanism eliminated the continuity of the circular patterns [17]. There is slightly
an elliptical shape as the cylinder power from each of the astigmatism lenses are not exactly the
same at the zero points.
Figure 7-5 Defocus Lens Power Profile: This shows the variation in defocus power relative to
fluid power within +5 to -5 D [17].
125
Figure 7-6 Double Astigmatic Fluidic Lens Power Profile: The circular plots are cylindrical
power, the radial lines are cylinder angle, and the dashed lines are residual power. This shows
that the lens is capable of 3D of cylinder at any angle [17].
The combination of these fluidic lenses produces the fluidic phoropter and can correct for
error on any axis. The combination of an eye model with the fluidic phoropter produces a clearer
picture of the systems capabilities. The eye model with the fluidic phoropter was focused onto
an image of a cat. The image of the cat was then blurred by placing astigmatism and defocus
lenses in front of the image of the cat. Our fluidic phoropter was applied in the correction of
these lenses through the combination of our fluidic lenses [17].
126
Figure 7-7 Imaging Results of Model Eye Viewed Through the Fluidic Phoropter: The cat is
pictured (a) with no power to the fluidic phoropter, (b) no power to the fluidic phoropter and an
induced refraction error of 1D cylinder and 2D sphere at 120°, and (c) the refractive error is
corrected by the fluidic phoropter [17].
This same correction concept is applied in our fluidic auto-phoropter design.
The
collimated NIR light passes through our phoropter and eye model or eye which is then reimaged
into the Shack-Hartmann wavefront sensor. The system automatically determines the wavefront
that requires correction through a closed loop interaction between the fluidic lenses and the
Shack-Hartmann technology.
The users’ error will be automatically corrected once the
wavefront is properly assessed.
If the eye does not require correction then a plane wave emerges from our pupil plane.
If the eye requires correction, then the wavefront exiting the eye is spherical. Hyperopic or far
sighted individuals produce a diverging wavefront exiting the pupil. Myopic or near sighted
individuals produce a converging wavefront exiting the pupil plane. The power conditions can
be replicated through a lens and a mirror. The mirror can be thought of as our retinal plane.
The relative position of the mirror to the doublet lens adjusts the shape of the outputting
wavefront. If the mirror is placed at the back focal length of the individual then we are
replicating an Emmetropic eye.
By moving the mirror within the back focal length of the
doublet we are replicating the Myopic condition where the light focuses at a location in front of
127
the retinal plane. Similar to the real situation the far point is no longer at infinity but at a
location in front of the eye. If instead we opted to move the mirror further outside the back
focal distance of the doublet, then we are replicating Hyperopic conditions. The far point shifts
to a location behind the eye in addition to the focal location.
Figure 7-8 Modeling Myopia and Hyperopia: The position of the mirror relative to the back
focal length of a doublet replicates these conditions within a model eye.
At this point we have established that the NIR light passes through a beamsplitter into
our fluidic phoropter. On the opposite side of the phoropter is the described model eye that
replicates power conditions of an eye. Additionally, we can add cylinder lenses to adjust the
astigmatism to any orientation. Once the light reflects out of the eye it holds the shape of the
wavefront exiting the eye at the pupil plane. The next step in the propagation of the light
through the system is for the light wave exiting the eye to be reimaged into the Shack-
128
Hartmann sensor. A Keplerian telescope is applied to reimage the wavefront from the pupil
location of the eye model to the lenslet array of the Shack-Hartmann wavefront sensor.
7.1.3 Fluidic Auto-Phoropter Prototype One: Light Path Through Keplerian Telescope
The relay telescope is used to image the eye’s pupil to the lenslet array and to preserve
the shape of the wavefront. The lenslet array samples the incident wavefront and provides the
wavefront shape information as feedback to the fluidic lens stack. The fluidic lenses are adjusted
to null the sphero-cylinder error of the eye and flatten the wavefront incident on the lenslet array.
The relative position of the lenses and telescope system are significant in reproduction of
prescriptions.
210 mm (approximately 8.25 inches)
CCD
Array
IR
Source
Lenslet
Array
65
mm
Collimation
Optics
50
mm
31
mm
Mirror
Circular
Eye Chart
NIR BS
45:55
Doublet 1
Dia = 25 mm
F = 100 mm
Folding
Design Right
Angle Prisms
Doublet 2
Dia = 25 mm
F = 100 mm
NIR BS
45:55
Fluidic
Lens
Eye Model
Doublet
25 mm
15 mm
30 mm
30 mm
12.5 mm
50 mm
12.5 mm
35 mm
5 mm
Figure 7-9 Design of Fluidic Auto-Phoropter Prototype One: Here we identify the physical
positions of all the optical elements to replicate our 4F imaging system. The line of sight of the
user for a monocular setup is transparent.
The second purpose of the relay telescope is to preserve the shape of the wavefront. If
the wavefront exiting the eye is a plane wave, then the wavefront hitting the lenslet array is a
129
plane wave. If the wavefront exiting the eye is a converging spherical wave, then the wavefront
hitting the lenslet array is a converging spherical wave with the same curvature and
magnification. Preservation is achieved by creating 1:1 angular magnification of the eye’s pupil
plane relative to the lenslet array in addition to achieving lateral magnification. We are therefore
preserving the full wavefront by preserving both the angular and lateral size of the wavefront that
is exiting the pupil of the eye. We achieve preservation of lateral magnification by having the
focal length of doublet 1 equal to doublet 2. Also, the separation between the two lenses is two
times the back focal distance of these equivalent powered lenses as is understood for a traditional
Keplerian telescope. The 1:1 angular magnification is achieved by producing a 4F imaging
system. The pupil location is placed 1f from doublet 2 while the lenslet array is placed 1f from
doublet 1. The combination of these positions allow for the reimaging of the pupil plane to the
lenslet array.
A motivation for this design was to compress the optical system into a small region. We
require a physical focal length of each doublet to be at least 75 mm with no tolerance for
mechanical parts as we require the location of the pupil plane to telescope and the lenslet array of
the Shack-Hartmann to the telescope to each have a 1f separation. This minimal distance
develops from the fact that relative to the pupil plane we require a beamsplitter and stack of
fluidic lenses in front of the eye which accounts for 75 mm of space. However, the eye also
requires eye relief of at least 20 mm. This causes the smallest separation between doublet 2 of
the telescope system and the pupil plane to be 95 mm. We therefore chose to apply 100 mm
focal length doublets for our telescopic system. To maintain the integrity of the telescope setup
the doublet separation is 200 mm.
130
In order to keep this system in a compressed region we added folding optics. The folding
optics was a series of four triangle mirror prisms that added a y-dimension component to our
optical system. There are two significant angles that would allow for us to compress the system.
We needed to produce a 200 mm separation between the two doublets while at the same time not
adding stray light into the optical system. The u angle identified the angular separation between
the top of prism 1 to the edge of prism 3. This produced the limit of not reimaging from prism 3
directly into the doublet, hence causing stray light to enter the system. The second significant
angle is that of l which identifies the largest angle that is acceptable to maintain the light into
the prism from prism 1 to prism 2. We wanted to ensure that our system would not maintain
stray light so we calculated for a doublet separation of 150 mm rather than 200 mm. This tight
tolerance allowed for us to find the right prism length Lp which will give results for 75 mm focal
length lenses. If the folding mirror prism functions at 150 mm, then it will function with any
telescope system that uses doublets that have longer than 75 mm focal length
The identification
of the prisms and separation calculations were necessary to eliminate stray light data from
skewing our prescription analysis. In addition, when we are testing Myopics or Hyperopics, the
light will vary in reflection location due to change in the power of the optical system. Therefore,
the higher tolerances were necessary to reduce stray light effects with varying degrees of power
induced in the optical system by the eye.
131
Figure 7-10 Folding Mirror Analysis: This is the setup of the monocular system with the
dimensions of the prism region size as to compress the system.
7.1.4 Fluidic Auto-Phoropter Prototype One: Light Path From Keplerian Telescope to
Shack-Hartmann Wavefront Sensor
Now that we have established the folded mirror telescope system, we must have the light
reach the Shack-Hartmann wavefront sensor.
The lenslet array of the Shack-Hartmann
wavefront sensor is 1F beyond the telescope system, but also it must not be in the line of sight of
the user. An NIR beamsplitter is inserted to direct infrared light towards the final off-axis
Shack-Hartmann module to achieve these results. This second NIR beamsplitter separates the
optical paths of the IR light source and the line of sight of the user. The beamsplitter passes
visible light, allowing for the subject to view external targets such as an eye chart. Concurrently,
it reflects the NIR signal to the Shack-Hartmann wavefront sensor. The system has a self
aligning feature where a slight red dot is observed in the center of the field. If the dot is not in
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the center of the users’ field, then we can adjust the position of one of the monocular arms of the
fluidic auto-phoropter. This NIR light is magnified in Figure 7-11 to show the self aligning
feature within each fluidic auto-phoropter monocular arm.
Figure 7-11 Line of Sight of User: This is the view through a monocular system with the self
aligning NIR source where on the opposite side is a scene of the lab.
The Shack-Hartmann wavefront sensor is placed in a conjugate distance to the location of
the pupil plane. As was explained in the telescope section, we achieve 1:1 angular and lateral
magnification with this design. We experimented with two Shack-Hartmann wavefront sensors.
The first sensor was built in house built. The lenslet array was fabricated on a 25 mm radius lens
with 18 mm focal length lenslets at a pitch of 250 microns.
The second Shack-Hartman
wavefront sensor was bought from Thorlabs. We have fully described the system design by
tracing the photon propagation from the source to the detector.
To simplify the functionality of the design we can break down the system as follows: (1)
Infrared light is shone into the eye and scatters from the retina. (2) The scattered light exits the
eye as an emerging wavefront that is relayed through the fluidic lens to the Shack-Hartmann
sensor. The sensor reconstructs the wavefront and extracts the sphero-cylindrical refractive error.
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This prescription is then applied to adjust the volume of the fluidic lenses in an attempt to null
out the refractive error. Feedback of the wavefront from the eye/fluidic lens combination is then
used to monitor the fluid volume and keep the net refractive error at a minimum. In theory,
prescriptions and automatic correction is achievable within seconds of a patient looking into the
system. The key to achieving these goals is to identify the amount of illumination necessary to
hit the eye that is detectable and ensure this value is below the eyes threshold.
7.2 Fluidic Auto-Phoropter Prototype One: Alignment for Monocular Setup
The alignment of the optical system can be simplified by taking advantage of the optomechanical structure of our optical parts. By purposefully applying cage rods to connect optical
parts we were able to quickly align our optical system.
Figure 7-12 Alignment of Monocular Fluidic Auto-Phoropter Prototype One: This is the
prototype of phoropter one showing the cage assembly setup of an aligned system.
The two NIR beamsplitters are the central pieces of our alignment process. Cage rods
attach the majority of the optics in a t-shape relative to these cube mounted beamsplitters. We
will again follow the photons from start to finish in explaining the alignment of the optics. The
first row of rods connects the light source directly to the first NIR beamsplitter.
Both
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beamsplitters are posted down as they are our support locations. The ND filter in the optical path
between the light source and the NIR beamsplitter is also posted down so that tilt will not be
induced from the source.
The optical path continues upon reflection from the NIR beamsplitter toward the model
eye. Our fluidic phoropter is mounted onto a 30 mm to 60 mm cage plate adapter. The fluidic
phoropter is larger than 30 mm and is blocking the 30 mm cage holes as connectors. We
therefore mount a second 30 mm to 60 mm cage adapter onto the first beamsplitter. We then
apply cage rods from the cage plate adapter attached to the beamsplitter to the cage plate adaptor
connected to the fluidic lens. This allows us to align the center of the fluidic lens to the center of
our light source. Behind the fluidic lens there is an additional 30 mm to 60 mm cage adapter.
Inside this additional adapter is our 18 mm focal length doublet that replicates the focal length of
the eye focusing onto the retina, which as we described is our flat mirror.
As we reflect through the mirror we now propagate the light back through the optical
system to the telescope system. The telescope system is comprised of the two doublets and the
folding prism setup, where the folding prisms configuration is the second optical sub-system.
These two optical sub-systems had to be aligned separately. It is important that the doublets
were in alignment with the fluidic lens and the beamsplitters. The doublets for the telescope
system were aligned into cage rods that connected each beamsplitter to the nearest doublet. A
single rod connects in between the two beamsplitters to ensure that both beamsplitters and
doublets were aligned. This single cage rod allowed for the folding prisms to be placed in the
optical path between the two beamsplitters. At the same time we were able to align both sides of
the telescope system.
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The alignment of the four prisms in the folding setup was a separate sub-system. There
are two platforms holding two prisms on each platform. A rectangular plate that was machined
in the machine shop was placed behind each pair of prisms to make sure that they were aligned
flat relative to each other. The two platforms with the four prisms were then aligned by using
pinholes set at the same height. Each prism platform offered two degrees of freedom in tip and
tilt. The pinholes were placed at a meter separation and the prisms were tipped and tilted until a
collimated light exited out of the system. The prisms were then slide into the optical setup. The
final step in aligning the telescope system was to achieve the proper separation between the two
doublets. The wavefront sensor was applied in producing the proper separation between the
doublets of the telescopic system. To align the sensor we applied the laser beam directly onto
the sensor. We then adjusted the tip and tilt of the reflecting mirror to zero out the residual
aberrations from the mirror. The fluidic lens and eye doublet were removed from the optical
setup and the mirror was placed back into the system. One of the sets of prisms was posted onto
a actuator controlled micrometer translation stage. The wavefront sensor was placed on the
opposite side of the telescope system. We then adjusted the micrometer that shifted the prism
location until the defocus was zeroed out. This approach created a corrected telescope system
with the wavefront sensor placed in its proper distance relative to the pupil plane of the eye
model.
7.3 Fluidic Auto-Phoropter Prototype One: Binocular Alignment and Inter-pupilary
Distance
We can duplicate this monocular auto-phoropter setup, thus producing a binocular testing
system. The alignment of the second auto-phoropter is achievable by again aligning the
beamsplitters, but this time the four beamsplitters that are aligned are between the two
monocular arms. We must first begin the alignment process externally from outside the auto-
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phoropter system. This is achievable by using a beamsplitter, four mirrors, multiple pinholes,
and an external laser. We first align these external parts so that we have created an optical path
in the shape of a rectangle in free-space outside of the auto-phoropter design. The height of the
rectangular cavity is equivalent throughout this area. The rectangular cavity has two light paths
where half the light propagates in a rectangle from one direction and the other half of the light
propagates from the second direction. Both paths follow the same rectangular trajectory which
allows for us to test both auto-phoropters simultaneously. If there is a misalignment or we need
to block any light from one path we can simply place a stop between the two arms. We will at a
later point slide the phoropter setup into the beam path of one of the legs of this rectangular beam
for alignment. This external laser will help us align two beamsplitters, one from each of the
monocular setups.
Before sliding the binocular setup into the path of one of the channels in the rectangular
laser beam path we have to ensure certain conditions. The first condition is that the first
monocular setup is aligned and locked down. The second condition is that the second monocular
setup’s base must be in the same exact position on axis as the first monocular setups base. There
are three additional base’s that were required to achieve alignment of the two monocular bases.
There was a much larger base underneath the monocular bases. The two monocular bases were
wedged between two machined base wedges.
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Figure 7-13 Base Setup of the Binocular Fluidic Auto-Phoropter: We have removed one of
the arms of the binocular setup to observe the base. There are two metal frames in which the
base is screwed onto. The monocular setup is tightly secured between the two frames.
The combination of these three bases with our two monocular setup bases allowed for a
few additional features that were not capable before. The system became mobile, where by
lifting from underneath one can move the entire system to any clinic required for testing. A
second feature is that we were able to adjust one of the arms according to the inter-pupilary
distance of the users. The base of one arm is locked down while the second fluidic autophoropter setup is mobile. The second arm slides until the user observes the self aligning NIR
light source at the center of their line of sight. In order to achieve the proper inter-pupilary
distances a modification was necessary in our 30 mm to 60 mm adapters. These adapters have
an x shape to them. When the second monocular arm slides toward the first monocular arm the x
mounts would hit into each other. We modified the x mounts so that half of the x mount was
138
rounded off on the inner segment where the two monocular setups interact with each other. By
segmenting the x shaped adapter mounts we were able to reduce the separation between the two
monocular systems down to 35 mm. For a small child the inter-pupilary distance is about 40 mm
and so this system is applicable to people of all ages and eye separations. Figure 7-14 shows the
removal of the fluidic lenses so that we can observe the machined 30 mm to 60 mm adapters.
Figure 7-14 Machined Adapters for Inter-pupilary Distance of Binocular Fluidic AutoPhoropter: The fluidic lenses are removed to show the machined optics where the 30 mm to 60
mm x mounts are trimmed, allowing for a 35 mm inter-pupilary separation.
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The machining of the base and the 30 mm to 60 mm adapters allowed us to position the
two monocular fluidic auto-phoropter systems next to each other. In order to align the two
phoropter systems relative to each other we must first remove the light sources from each autophoropter system. We then slide the binocular setup into the path of our external light source.
The first alignment occurs with the first adaptive phoropter. Each system is aligned to two subsystems where one group is that of the folded prisms and the second group is that of the rest of
the system as was described in section 7.2. We have a pinhole facing the input of the external
laser source as was described in 7.1.1. We stop down the pinholes on the beamsplitters and slid
down the binocular system until the light from the external laser passes through the center of the
pinholes which identifies the optical axis of both auto-phoropter arms. In this instance the group
attached to the beamsplitters for both auto-phoropters were raised to the same height and aligned.
The next step in the alignment process was to align the four prisms for each arm of the
binocular auto-phoropter. We removed the fluidic lens and eye model for this alignment and
replaced the optics with a flat mirror. This flat mirror allowed for the light source to propagate
through the entire optical system. The prisms were raised to the height of the rest of the
binocular auto-phoropter system. The prisms had a course alignment as they were aligned before
combining the two systems as described in section 7.2. With the raising of the prism bases there
was slight misalignment. A block in between the two auto-phoropter arms was added to separate
the light in each arm. We then aligned the light traveling through both optical arms at a distance
of 15 feet from our optical setup. After the points were completed aligned we identified that the
height and separation between the beams at 15 feet away were at the same height and separation
of the beamsplitters between the two optical arms.
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Figure 7-15 Spots of Alignment Beam at 15 Feet Away of Binocular Fluidic AutoPhoropter: The spots from the external light source through our fully aligned first binocular
fluidic auto-phoropter prototype.
After alignment was completed, we added both of the NIR SLD light sources back onto the
rails. We then tested to ensure that the separation has not changed as observed 15 feet away.
The binocular fluidic auto-phoropter system had been aligned after the spot positions have been
verified. The fluidic lenses are then added onto the system and testing of the system can begin.
Figure 7-16 User Position in a Fully Aligned Binocular Fluidic Auto-Phoropter: The position
of the user is observed relative to the designed system. The red lines indicate the optical path of
the external source. This external source was turned off and blocked by the SLD as this image
represents the fully aligned system.
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8.0 FLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: MODELING
A significant step prior to testing a system is to model the functionality of the design. We
modeled the system first with ZEMAX lens design software. This modeling scheme did not
include power in the fluidic lenses. We were identifying the dynamic range of the sensor with
the relative position of the cornea, telescope, and wavefront sensor. The relative positions of the
optics define the expected measureable results. The next step was to model the system with
illumination software. The fluidic phoropter was varied for defocus and astigmatism in this
modeling when coupled to the test system. The illumination software was applied to identify if
stray light will reduce the optical quality of our results. In addition, we modeled the expected
results of both the astigmatism and defocus lenses. The results of the ZEMAX model are not
altered by the fluidic lens, as we did not apply power into the fluidic lenses to adjust the power of
our system. The ZEMAX modeling was created to determine the physical range of the autophoropter system. The following step was to determine the amount of power variation that is
measurable with the fluidic phoropter while keeping the model eye constant. This was achieved
in our modeling of the system in FRED. The FRED illumination software additionally will
accurately identify stray light and point resolution. The difference between the results of the
physical measurements in the next section and the modeling of the system in this chapter is in
that our modeling matches ideal control of the fluidic phoropter with no residual error rather than
experimental results of the fluidic phoropter.
8.1 Lens Design Model of Dynamic Range of Auto-Phoropter
We first begin with a model of the auto-phoropter system. We are testing a single
monocular setup to determine the dynamic range of our optical setup with the designed positions.
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It is assumed that both monocular setups in the binocular setup will have approximately the same
results as the two arms are mirror images of each other. The optical design for the auto-phoropter
can be replicated non-sequentially within ZEMAX and recombined to develop a fully functional
monocular design. A code was developed to achieve the design of the optical system. The
design of the phoropter was developed to the dimensions of the optical elements chosen. This
allowed for us to achieve the proper vignetting of the optical system.
Figure 8-1 ZEMAX Layout of Monocular Setup of Auto-Phoropter: The blue light is a
collimated light coming out of the SLD where half of the light is stray and passes through. The
red is the reflected light that hits the eye and then reflects through the optical system to the
sensor. The Green light is the line of sight of the user. The designed system on the left shows a
fully collimated system while the system on the right shows the system with a corneal radius of 7.3 mm.
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The above design describes a collimated SLD light source propagating through our
optical system. The first beamsplitter drops about 45% of the light as stray light passing through
the optical system. A stop is placed between the two arms of the optical system to ensure this
light is not trapped between one arm to the other. The rest of the light reflects to our fluidic
phoropter that offers zero power variation and then the eye model. Our eye model is designed to
the radii of curvature as prescribed by the Arizona Eye Model. The light reflects through the
model back through the phoropter and beamsplitter to the telescopic system. The telescopic
system is compressed to two doublets with equal focal length and 4 mirror prisms. The 4 mirror
prisms are represented as flat mirrors in ZEMAX. The telescope reimages in the same fashion as
was described in earlier sections. The green light that passes through the beamsplitter is stray
light loss of NIR light for the ZEMAX model, but also identifies the line of sight of the user.
It is important to remember the intensity of light that the system operates with. The
intensity of the NIR light must be between 10-25 W as we do not want to induce damage to the
eye. Light reflects off of two beamsplitters, where 45% of the energy is reflected per reflection,
and also light is transmitted through a beamsplitter, where transmission is 55%. The output of
the light source is setup that 10-25 W reaches the eye model after these two reflections occur.
Therefore, the intensity at the light source is higher than the 10-25 W and is designed for this
intensity at the eye model. Approximately 10% of the light reflects out of a human eye and so
the amount of energy from our source drops down to 1-2.5 W reflecting out of the eye. We
observe one transmission and one reflection off of the beamsplitters before reaching the detector,
dropping the intensity at the detector plane from the source to 0.25 to 0.62 W.
Energy
conservation is therefore a significant factor in the positioning of the optical telescope relative to
the eye model and lenslet array and this requires continued review when testing with humans.
144
ZEMAX model does not identify the intensity of light propagating through the system to the
sensor as we did not prescribe energy loss coefficients for the surfaces. The collimated design
provided the following irradiance pattern, identifying that the lenslet array and the collimation
systems were modeled properly.
Figure 8-2 Model of Image Plane of Shack-Hartmann Wavefront Sensor in ZEMAX: The
designed results of collimated light reaching the detector of our Shack Hartmann wavefront
sensor after propagating through our design.
Figure 8-2 shows the point by point identification of collimated light reaching the
detector plane with our aligned optical system. In this design, we have produced a collimated
system with a corrected eye that has a corneal radius of -7.8 mm, where the points in the
horizontal and vertical direction have a x, y separation of about 250 microns. The 250
microns show that the model separation matches the separation of the lenslet in the lenticular
array. The spot diagram has continual even separation on axis for each of the lenslets, producing
a properly aligned optical system.
To identify the dynamic range of the optical system, one must vary the curvature of the
test plane, such as the radius of curvature of the cornea, to measure the slope variation at our
detector plane. We can therefore apply the slope variation that was described in section 3.2.4 to
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allow for us to reconstruct the wavefront. By adjusting the power in the optical system the
observed wavefront error is measured through slope measurement equations:
8-1
A well functioning system would allow for the measurement and correction of defocus
aberration in the eye that varies between -20 to 20 Diopters. To see if this optical design is
physically capable of replicating the required Diopter range the power variation was modeled by
controlling the surfaces at the model eye location. We modeled the amount of power correction
at the cornea by creating compensating power at the fluidic lens location. This was achieved by
shifting the x and y dimension as the radius of the cornea was adjusted. For each corneal radius
the positions were mapped relative to the amount of shift. A second approach was to introduce a
paraxial focal length in front of the cornea and identify the point variation at various focal
lengths. With both approaches, the shift was identified and then equations from 8-1 were applied
to determine the change of power observed for each corneal radius.
146
Corneal
df
Radius
(x,0) in mm
(0,y) in mm
Dx in mm
Dy in mm r (mm) f (mm)
(Diopters)
(R) mm
-7.3
214.34
213.92
-38.16
-38.58
54.26
18.53
38.09
-7.4
224.18
224.22
-28.32
-28.28
40.022
19.174
36.8784
-7.5
232.58
231.96
-19.92
-20.54
28.612
19.733
35.9535
-7.6
240.16
240.01
-12.34
-12.49
17.557
20.226
34.9174
-7.7
246.72
246.56
-5.78
-5.94
8.288
20.655
34.6983
-7.8
252.5
252.5
--
--
--
--
--
-7.9
257.5
257.43
5
4.93
7.0217
21.41
-33.26
-8.0
262.5
262.53
10
10.03
14.163
21.731
-32.49
-8.1
266.66
266.61
14.16
14.11
19.99
22.023
-32.08
-8.2
270.83
270.86
18.33
18.36
25.943
22.290
-31.75
-8.3
274.16
274.14
21.66
21.64
30.617
22.536
-31.36
-8.4
277.9
277.8
25.4
25.3
35.850
22.762
-30.943
Diffraction
-8.5
Limit
Table 8-1 Power Shift of Auto-Phoropter System Due to Variation in Corneal Radii:
Identifying the amount of compensating power produced by varying cornea radii.
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The lenslet array produced resolvable points that were outputted in a spot diagram from
ZEMAX. To achieve quantifiable results from the spot diagram, the image plane was scaled to
the size of the CCD array. From this information we can visually verify the limit of our autophoropter range. The higher limit, as is shown in Figure 8-3, was measured to + 500 D. The
system could have been measured even further; however, the majority of eyes do not exhibit
higher than + 20 D of defocus error. For this reason we find that there are no system limitations
on the higher positive powers. The higher Diopter powers will be limited by the power range of
the fluidic lens.
The lower limit of our auto-phoropter was identified to be approximately -30 D by both
modeling metrics. Figure 8-3 shows the lower range of detection from both systems. The two
approaches show that at these higher negative powers our points form coma shapes and reach
resolvable limits. This suggests that our auto-phoropter system can measure optical error from
the eye between -30 to 30 Diopters, with prototype one at 4f imaging with two 1oo mm focal
length lenses. The dynamic range of our auto-phoropter measures the entire Tscherning ellipse,
which identifies the amount of power correction needed for spectacle lenses. Our system can
therefore measure the prescriptions for the majority of users. The additional component of our
auto-phoropter includes for the correction achieved by the fluidic lenses. If for example our
fluidic lenses compensate for -30 to 30 Diopters of defocus power, our system would
automatically correct for the full range of prescriptions. If our fluidic phoropter technology
reaches a dynamic range of -35 Diopters to 35 Diopters of correction, we will be limited by the
system design. The system would have the capability of correcting the upper limit of 35
Diopters defined by the fluid lenses and a lower limit of -30 Diopters defined by the autophoropter design. The model shows that our optimum range would be for the fluidic lens to
148
operate between -30 Diopters to 30 Diopters. This will allow the sensor to be the limiting factor
and thus we have optimized the physical system as is observed with the physical positions
prescribed in prototype one.
Figure 8-3 Dynamic Range Limits of Auto-Phoropter: Here we identify the limits of the autophoropter system where the fluidic lenses were zeroed to model the limits of the physical
position of the optics by varying the power of the eye.
8.2 Illumination Model of Dynamic Range of Fluidic Auto-Phoropter
We have defined the physical measuring range of the auto-phoropter without the fluidic
phoropter compensation. We require additional modeling on the effects of the fluidic autophoropter and also the stray light entering the system. FRED illumination software was selected
to fully model the functional fluidic auto-phoropter design. Here we model the setup exactly as
we had modeled the system in ZEMAX. The illumination software identifies the blurring of
points, if overlapping occurs, and the amount of correction in both cylinder and defocus lenses.
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Figure 8-4 FRED Model of Binocular Fluidic Auto-Phoropter: The SLD light source was
imported directly from Thorlabs while the rest of the optics was modeled to the specifications of
our optical system. We show how two monocular systems combine to produce a binocular
system.
The FRED model replicates the physical system. The light source was imported through
a CAD file in Thorlabs. The optical beamsplitters are of the same size and reflective properties
in the NIR range of 700-900 nm. The doublets were imported from the Edmund catalog. Our
fluidic lenses were designed relative to DI water in the chamber system. When we measured the
results at the detector plane we measured each monocular surface at a time. The system was
fully aligned as we observed equally spaced points in the image plane. Figure 8-5 illustrates the
light intensity distribution of the focused singular points with equal physical separation. Here we
imaged a small area to magnify the effects of power variation from the fluidic lenses.
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Figure 8-5 Model of Image Plane of Shack-Hartmann Wavefront Sensor in FRED: The
designed results of collimated light reaching the detector of our Shack Hartmann wavefront
sensor after propagating through the full optical system. The fluidic phoropter lenses exhibit
zero power variation. Here the intensity distribution is shown to vary from the center of each
point.
We first identify the limiting factors of the system to accurately assess the compensation
range that our fluidic auto-phoropter can achieve. As we had identified through ZEMAX
modeling, the system has a capability of measuring - 30 to + 30 D of error. Our fluidic phoropter
does not have this physical range and thus our limiting factor is the fluidic lens. In order to
model the fluidic auto-phoropter properly, we first identify the fluidic lenses physical range. The
fluidic lenses power range was calculated empirically by determining the physical range of the
phoropter’s radius of curvature as was described in section 5.1.4. De-ionized (DI) water was
first used to characterize the fluidic lens’ radius of curvature. DI water has an Abbe number of
55.74 and the indices of refraction are known for a wide scope of wavelength ranges [68]. The
focal lengths of the DI water based fluidic lens was first measured using red (HeNe 633 nm),
green (HeNe 543 nm), and blue (Argon 488 nm) lasers.
151
.
Figure 8-6 Power Range of Defocus Lens of Fluidic Phoropter: The physical range of the
fluidic lens for 0.5 mm evacuation of fluid is about 10 Diopters, which is much smaller than the
dynamic measuring range of the auto-phoropter. Thus the limiting factor of the system is the
fluidic lenses.
As was previously stated, we applied DI water with known indices of refraction per
wavelength in identifying the fluidic lenses radius of curvature range. For a given amount of
fluid in the lens, we measured the focal length at each of the three designed wavelengths. The
radius of curvature, r, of the lens surface was calculated using Ф= 1/f = (n air-nDI)/r, where  is
the surface power and nair and nDI are the indices of refraction for air and DI water per index,
respectively. The focal length, f, of each measurement was equal to the back focal distance of the
fluidic lens using the thin lens approximation. Each radius of curvature was calculated at red,
green, and blue wavelengths and averaged to determine a single radius of curvature per fluid
volume. The experiment was repeated as we increased the fluid volume in the lens by increments
of 50 µL. We averaged several tests to determine the range of the radius of curvature for our
152
fluidic defocus lens. The following chart illustrates how we placed empirical data into an excel
spread sheet to determine the radius of curvature range. The pump control broke our increments
to 41 values that ranged from a notch of 20 to a notch of -20, where each notch identified a fluid
evacuation of 50 l. We were measuring radii of curvature limits and so the large notches away
from the center location were the most relevant results.
Focal
Pump Length
Control Red
(mm)
Notch
Focal
Length
Green
(mm)
Focal
Separation Separation
Green
Length
between
between
Light
Blue
Red and
Red and
(D)
(mm)
Blue (mm) Green (mm)
Separation Vf of
Radius of
between fluidic
Sag
Curvature
Green and lens
(mm)
(rc) mm
Blue (mm) using f
20
138.80 139.65 141.60 7.1607
0
0
0
5904
-2.800
-0.850
-1.950
-49.87
46.28001 1.0932
19
140.83 142.00 144.13 7.0422
3
0
3
53521
-3.300
-1.167
-2.133
-43.03
47.0588 1.0747
18
143.13 144.65 146.83 6.9132
3
0
3
38852
-3.700
-1.517
-2.183
-39.09
47.93701 1.0546
17
145.96 147.30 149.53 6.7888
7
0
3
66259
-3.567
-1.333
-2.233
-41.29
48.81522 1.0352
16
148.70 150.00 152.70 6.6666
0
0
0
66667
-4.000
-1.300
-2.700
-37.5
15
151.86 153.20 156.16 6.5274
7
0
7
15144
-4.300
-1.333
-2.967
-35.62
14
154.96 156.72 159.83 6.3806
7
5
3
02967
-4.867
-1.758
-3.108
-32.20 51.938665 0.9717
49.71
1.0162
50.77048 0.9945
Table 8-2 Empirical Measurements of Defocus Lens and Radii of Curvature: Identifying the
amount of compensating power and change in radii of curvature of the fluidic lens by altering the
amount of fluid in the lens cavity. We show only 7 of the 41 notches as an example of our
measuring approach. Defocus lens one has a 40 mm radius of curvature while defocus lens one
has a 25 mm radius of curvature.
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These empirical results define the fluids range in which we simulate the fluidic lens
within the FRED software. The approach in simulating the change in power of the fluidic lens
was to adjust the radius of curvature in FRED, where the radius of curvature and focal length
ranges are now predefined by the actual lens range. When we adjust the radius of curvature of
the lens, we are physically adjusting the power of the full optical system. The following two
figures are a clear illustration of how the propagating rays alter in direction once the power of the
fluidic lens is changed. Figure 8-6 on the left shows collimated light entering the detector. With
no power from the fluidic lens, the light is also exiting the eye model and the relay telescope
collimated. Once we induce power to the fluidic lens we induce power entering the users’ eye.
In this model, the retina is perfectly collimated but the fluidic defocus lens induces power. The
defocus power variation continued through the entire optical system. Where when power is
induced by the fluidic lens we observe a focusing location along the optical axis as is observed in
figure 8-7. This condition identifies a limit of our fluidic auto-phoropter system. If the focal
location is at the lenslet array we find that the wavefront slopes are not measurable with our
wavefront technology. The physical limitation in the system can also be observed by the eye
model inducing power and no power from the fluidic lens. There will still be a variation in the
slope variation of the propagating rays. By producing a power from the fluidic phoropter that is
equal and opposite of a user’s eye, we are able to correct prescriptions in real time.
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Figure 8-7 Power Variation of Defocus Fluidic Lens in FRED of Fluidic Phoropter: The
traces of rays have shifted from a neatly collimated beam entering the sensor in the left to an
optical system with high amounts of power when defocus is induced by the fluidic lens.
The defocus is detectable when we vary the radius of curvature as was previous stated.
Between infinity and the near focal point we can control the radii of curvature. The following
images show the induction of negative power into the phoropter’s defocus lens. We observe that
the points are collapsing inwards, indicating that the negative power is causing the slopes of the
wavefront to shift inward. By assessing the slope we are able to determine the actual power that
is observed relative to this image location for the whole system.
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Changing Curvature of Defocus Lens
r = -1200 mm, = -.4265 D
r = -60 mm, = -8.53 D
r = -900 mm,  = -.5687 D
r= -50 mm, = -10.2236 D
r = -200 mm,  = -2.559 D
r = -35 mm,  = -14.605 D
r= -100 mm,  = -5.118 D
r = -26.2 mm,  = -19.5854406 D
Figure 8-8 Defocus Lens Power Variation and Effects on Fluidic Auto-Phoropter: The
radius of curvature is altered matching the physical range of the defocus lenses. The point
separation observed on the Shack-Hartmann wavefront sensor identifies changed power observed
in the system caused by the defocus lens.
Modeling of astigmatism with FRED had been advantageous. FRED allows for the user
to enter a surface plane and quickly alter the lens shape in one dimension. This enables us to
replicate cylinder lenses with varying powers. As we have two fluidic astigmatism lenses that
are orientated 45o relative to each other, we must control each surface individually with
deflection direction 45o relative to each other. We modeled several conditions where the fluidic
lens had various amounts of cylinder power. To magnify the great variation that our optical
system can measure we choose extreme amounts of astigmatism correction.
A traditional
phoropter system would require less than -5 to +5 Diopters of astigmatism correction to cover a
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majority of astigmatism cases.
The following three images show various amounts of
astigmatism. Figure 8-9 shows 20 Diopters of astigmatism in the x plane. This amount of
astigmatism reaches about the limitation of our detector system, as the lenslet focal points
approach each other. Figure 8-10 shows 10 Diopters of astigmatism in the y plane. It is seen that
the amount of astigmatism in each plane is controllable. As we increase the power on the fluidic
phoropter, the points come closer in one dimension. By showing that we are able to measure
conditions well beyond the astigmatism observed in the human eye, we can prove our fluidic
auto-phoropter is able to measure power variation due to the eye and the astigmatism fluidic
lenses can compensate the eye’s power. We can therefore identify the wavefront variation
caused by the eye in our optical system. We can then compensate the wavefront error with our
control in cylinder and power on any axis with our fluidic phoropter. After the error is nulled
out, we are able to produce an automated prescription.
Figure 8-9 Astigmatism Lens One Power Variation and Effects on Fluidic Auto-Phoropter:
The radius of curvature is altered on one of the astigmatism lens. The point separation observed
on the Shack-Hartmann wavefront sensor outputs astigmatic variation of 20 Diopters in the x
dimension.
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Figure 8-10 Astigmatism Lens Two Power Variation and Effects on Fluidic AutoPhoropter: The radius of curvature is altered on the second of the astigmatism lenses. The point
separation observed on the Shack-Hartmann wavefront sensor outputs astigmatic variation of 10
Diopters in the y dimension.
Figures 8-9 and 8-10 are extreme values of astigmatism that are not reasonable for human
vision correction. We can replicate conditions that are more reasonable to what would be
expected from human vision. As there are three fluidic lenses, we can correct for astigmatism
and defocus simultaneously. As an example, we show in Figure 8-11 a combination of 4 D of
defocus and 2 D of astigmatism. This figure illustrates that any combination of astigmatism and
defocus is correctable by our fluidic phoropter within a reasonable range of human vision
wavefront error.
Figure 8-11 Defocus and Astigmatism Lens Two Power Variation and Effects on Fluidic
Auto-Phoropter: The radius of curvature is altered on the second of the astigmatism lenses and
also the defocus lens. The point separation observed on the Shack-Hartmann wavefront sensor
outputs astigmatic variation of 2 Diopters in the y dimension and 4 Diopters of Defocus.
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9.0 OPTOFLUIDIC AUTO-PHOROPTER PROTOTYPE ONE: TESTING
Chapters 7 and 8 have described the modeling and design of the first prototyped autophoropter. After a system is modeled and designed the next logical step is testing of the optical
system. The system has not yet been tested with humans and so as a proof of concept we must
establish an alternate approach in testing the system.
In this chapter we will describe an
approach for testing on either a human eye or a model eye. From there we expand on our
measuring approaches for the model eye when coupled with our auto-phoropter system that
excludes the fluidic phoropter. The exclusion of the fluidic phoropter enables us to measure
various amounts of power induced by the model eye and the measurements extracted by the
system. The model eye is then removed and replaced with the fluidic phoropter system.
In this section we test the defocus phoropter with DI water and also with one of our
selected oils. Test results describe the variable wavefronts for astigmatism and defocus and also
the sphere, cylinder and axis for all of our fluidic setups. These readings are a description of the
entire auto-phoropter system.
We can compensate the model eye and the auto-phoropter
combined to null out the error as was previously described.
The two defocus lenses are
compared in optical quality relative to each other. In addition, both lenses are tested with 3 mm
and 6 mm stops setup for the auto-phoropter designs. These stop sizes were determined to
replicate the variation in Iris size within the eye dependent on lighting conditions. We identify
the significance of stop size and how it alters our prescription results from the designed system.
The astigmatism lens has been tested with auto-phoropter prototype one. When testing
the astigmatism lens we measured each individual lens separately. We then combined the two
astigmatism lenses to measure the variation of astigmatism power. Variable amounts of fluid
159
were withdrawn from either the horizontal or the 45 o set fluidic lenses and then the wavefront
was measured. These measured values are lastly compared to the fluidic phoropter system.
Testing of the auto-phoropter is achieved through four basic steps. The first step is to
zero out residual aberrations within the system. This was achieved in chapter 7 when we aligned
the optical system. Secondly, we add a model eye to calibrate the optical system. The model
eye is tested with known amounts of power to identify the auto-phoropter system wavefront
measurements with each power measurement. The third step is to remove the model eye and
insert our fluidic phoropter system. The fluidic phoropter is calibrated within the auto-phoropter
system. Wavefront measurements are performed by varying the fluid volume in the actuated
syringes and identifying the wavefront correction that occurs with the optical system. These
wavefronts can be transferred to prescriptions based on sphere, cylinder, and axis for the entire
auto-phoropter system. Lastly, the measurements from the model eye with the entire autophoropter system are nulled by the entire auto-phoropter system and the fluidic lens adjusted to
the proper amount of fluid. Once the entire system is nulled out, we are able to identify the
correlation of a given amount of defocus power within the eye model or the eye to the reading of
our nulled system.
9.1 Testing Approach: Measurements of a Model Eye
Here we begin with the first step in the testing process as the eye or eye model is placed
in the conjugate plane of the detector. We place a flat mirror as our retinal plane and remove the
fluidic lens to eliminate any undesired distortion of the wavefront. The model eye is first aligned
so that collimated light is outputted from the optical system. This is achieved by placing the
mirror at the back focal length of the eye model lens. The back focal distance of the eye model
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lens was 14.91 mm. We then identify any residual aberrations which occur within the optical
system. The mirror is adjusted so that the tip/tilt values are zeroed out and the optical axis of the
model eye is aligned with the optical system. There should be no optical power induced at this
point as we are applying our collimated eye model in addition to a telescopic system.
CCD
Array
Prism
Mirror 2
Prism
Mirror 3
IR
Source
Lenslet
Array
Lens
Stop
Eye Chart
NIR BS
45:55
Doublet 1
Prism
Mirror 1
Prism
Mirror 4
Doublet 2
NIR BS
45:55
Eye
Model
Mirror
Figure 9-1 Step 2: Testing Auto-Phoropter with Eye Model: The fluidic phoropter is removed
as to not induce undesired wave distortion. By adjusting the mirror of the model eye we are
replicating power aberration of an eye. We then measure the wavefront power variation of the
full optical system and determine the wavefront variation at a given amount of power error from
the model eye.
After this alignment is achieved, we recalibrate the model eye to identify the amount of
aberration induced to the full auto-phoropter system. It is non-trivial to note that this defocus
wavefront is a measurement of the power of the eye or model eye, in this instance a model eye,
coupled with the full auto-phoropter. The power exiting the model eye can be explained through
an unfolding of the optical system. The eye model, as in the actual eye, has a double pass of the
light entering the eye and then exiting the eye. We are able to unfold the optical path of this
propagating light to treat the model eye as a telescopic system. We are able to model this
telescopic condition in ZEMAX.
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Figure 9-2 Unfolded Eye Model: The top left eye model shows the double pass of the
propagating light. This eye model is Emotropic and so when the optical path is unfolded the
system is replicated as a telescope. As we adjust the separation of the mirror to the doublet, we
are adjusting the power of the model eye. The bottom image shows when we alter the separation
that power is produced by our lens system.
The separation of this telescopic system is twice the 14.91 mm focal distance, which
represents a collimated and corrected Emotropic eye, as this system is a double pass design. The
power of the physical system is measured through
, where EM is the optical power of the doublet eye model lens and  is the separation
between the two lenses in the unfolded system or twice the mirror shift distance. The doublet
that is used for the eye model is Edmund Optics 49-314 which has a focal length of 18 mm and a
back focal length of 14.91 mm. This back focal length is applied for the optical power of the eye
model lens and thus is the variable separation between the lens to the mirror. The power that is
outputted from the model eye can be measured by controlling the lens separation. By slightly
adjusting the physical separation of the lens with the mirror at a rate of 50 microns we are able to
replicate power variations of our eye model in approximately .25 Diopter increments. Current
eye exams have .25 Diopter shifts in their lenses. By decreasing the shift of the mirror to less
than 50 microns, we can measure defocus power of the model eye in less than .25 D increments.
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For a proof of concept we have applied 50 micron shifts of the mirror in our eye model.
We then measured the aberrated wavefront exiting the optical system. The eye model was
properly aligned to the auto-phoropter system and thus additional odd aberrations were
negligible. The only term that was observed to drastically vary was that of the defocus term, as
this was the expected result. This defocus term of the full optical system was then correlated to
the power variation in the model eye. This is significant, as our fluidic phoropter is coupled to
the full optical system. We are able to null out a given amount of defocus error of the eye with
the fluidic phoropter, but we must also know the amount of error that this equates to in a users
eye. The described approach was modeled for both 3 mm and 6 mm stop sizes. The doublet
was chosen with a 9 mm active area as to ensure stop control of the system. We additionally
stopped down the optical system to a 3 mm to 6 mm range. We chose this range as this is
approximately the dynamic range of the iris size within the user’s eye. We are replicating the
stop size to identify how the defocus values within our full auto-phoropter design shifts.
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Auto-Phoropter 3 mm Stop
Model
Eye
Power
Actual
Separation Defocus
(mm)
Wavefront
Auto-Phoropter 6 mm Stop
Model
Eye
Power
Actual
Separation Defocus
(mm)
Wavefront
15.75
2.47
15.75
8.63
+5 D
15.7
2.36
15.7
8.29
15.65
2.24
15.65
7.8
15.6
2.12
15.6
7.36
+4 D
15.55
2
+4 D
15.55
6.96
15.5
1.86
15.5
6.53
15.45
1.7
15.45
5.98
15.4
1.55
15.4
5.42
+3 D
15.35
1.47
+3 D
15.35
5.13
15.3
1.38
15.3
4.8
15.25
1.24
15.25
4.36
+2 D
+2 D
15.2
1.03
15.2
3.63
15.15
0.88
15.15
3.02
15.1
0.7
15.1
2.44
+1 D
+1 D
15.05
0.6
15.05
2.01
15
0.49
15
1.61
14.95
0.17
14.95
0.48
0D
14.9
0
0D
14.9
0
14.85
-0.1
14.85
-0.29
14.8
-0.32
14.8
-1
-1 D
14.75
-0.43
-1 D
14.75
-1.47
14.7
-0.69
14.7
-2.4
14.65
-0.88
14.65
-3.07
-2D
14.6
-1.09
-2D
14.6
-3.81
14.55
-1.31
14.55
-4.61
14.5
-1.58
14.5
-5.58
14.45
-1.81
14.45
-6.41
-3 D
-3 D
14.4
-2.03
14.4
-7.16
14.35
-2.25
14.35
-7.94
14.3
-2.47
14.3
-8.67
-4 D
14.25
-2.64
-4 D
14.25
-9.28
14.2
-2.84
14.2
-9.95
14.15
-3.04
14.15
-10.82
-5 D
14.1
-3.22
-5 D
14.1
-11.38
Table 9-1 Results of Auto-Phoropter with Eye Model: The amount of power measured within
the eye is correlated through the separation of the mirror and lens to the defocus power of the full
optical system. This defocus power will be negated by the fluid phoropter.
+5 D
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The chart shows the system capabilities of measuring power separation for the model eye.
We measured the defocus wavefront of the optical system relative to the power of the model eye.
There are two trend lines that are observed when the model eye power is graphed relative to the
defocus wavefront. It is seen that the slope of the wavefront is linear as we adjust the power of
the model eye. This is necessary to be able to provide a controlled correlation between fluid
volume, wavefront readings of the system, and equivalent ocular error measurements. The slope
of the 6 mm pupil is approximately 4 times the slope of the 3 mm pupil. The slope radius of the
larger pupil is twice that of the smaller pupil and this radius term squared equals 4. Radius
squared can be correlated to f-number squared which matches the anticipated change in defocus
relative to a shift in the image plane, showing these results match theory. An important factor
identified from these results is that the shift in defocus slope shows the significance of stop size
at the iris when determining the wavefront correction needed for the error term. The pupil size is
an important factor in determining the correction required for our optical system.
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Model Eye Power vs. Defocus Wavefront
Defocus Wavefront Measurement (Waves)
15
y = 1.9989x - 0.4391
10
5
y = 0.5695x - 0.1191
0
6 mm Stop
3 mm Stop
-5
-10
-15
-5
-4
-3
-2
-1
0
1
2
3
4
5
Model Eye Power (Diopters)
Figure 9-3 Model Eye Power vs. Defocus Wavefront Relative to Pupil Size: It is observed
that our auto-phoropter produces linear measurements with varying slopes as we adjust the pupil
size.
Table 9-1 and Figure 9-3 have mapped the effects of a model eye that varies in defocus
between -5 D to 5 D. This power range is efficient for proof of concept measurements but does
not encapsulate the entire population that requires vision correction. This is not the physical
limitation of our optical system or the measurement capabilities of our model eye. We applied
this range to show that the auto-phoropter can detect these defocus powers. Furthermore, we
experimented with replacing the model eye lens with various powered lenses. As was described
in chapter 8, the system can detect from -30 D to +30 D. Figure 9-4 shows an example of two
eye lens systems that we have replicated. This figure shows that we are able to experimentally
identify users with over -20 D of error. The points for -20 D have a large separation between
them in that we observe a further power range that is achievable. The experimentally observed
limit of our phoropter with the model eye is at -28 D, slightly less than the theoretical -32 D
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range that was modeled through ZEMAX. This auto-phoropter design is capable of measuring
severe Myopia and Hyperopia beyond the common populous.
Figure 9-4 Defocus Measurements through our Auto-Phoropter System: To the left is 1.5
Diopters of Defocus and to the right is 20 Diopters of Defocus induced by our eye models, the
system limit.
9.2 Testing Approach: Measuring Fluidic Phoropter
To compensate for the ocular errors, one must identify the correlation between fluid
volume and power induced in the full optical system. After alignment and identification the
correlation between ocular error and wavefront measurements, the third step in calibrating the
optical system is producing measurements of the auto-phoropter coupled with the fluidic
phoropter stack. Here we remove the focusing lens of the model eye. The mirror in the model
eye represents the retinal plane. Therefore, the mirror is left in the location of where the model
eye was calibrated. We place our fluidic phoropter into its designated location after removing
the model eye lens. To test the fluidic lens surfaces we measure the results one surface at a time.
When testing the defocus lens we test the system with the single fluidic defocus lens and the
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astigmatism lenses removed. After measuring the defocus lens we lock the stack of astigmatism
lenses to the defocus lens. We zero out the defocus lens so that no astigmatism is induced by the
defocus lens. A fixed amount of defocus is added to the auto-phoropter system from the defocus
lens. We then measure the outputted wavefront for the fluidic auto-phoropter system.
CCD
Array
Prism
Mirror 2
Prism
Mirror 3
IR
Source
Lenslet
Array
Lens
Eye Chart
NIR BS
45:55
Doublet 1
Prism
Mirror 1
Prism
Mirror 4
Doublet 2
NIR BS
45:55
Fluidic
Phoropter
Mirror
Figure 9-5 Step 3: Testing Auto-Phoropter with Fluidic Phoropter: The fluidic phoropter is
placed into the system and the lens for the eye model is removed. We alter the curvature of the
fluidic lenses by adjusting the fluid pressure. We then measure the wavefront variation by the
full auto-phoropter system and map the fluid volume relative to the wavefront error.
We can quickly convert from the Zernike values that are in microns and the radius in
terms of mm to the refraction terms that are set for prescriptions through the following
definitions:
(9-1)
(9-2)
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(9-3)
The Zernike coefficients can be converted into the sphere, cylinder, and axis prescriptions
through the above definitions to the plus cylinder form or the minus cylinder form [19]. The
refraction formulas can be written in two distinct formulations:
(9-4)
(9-5)
The determination of which set is minus cylinder and which set is positive cylinder is
formulated on the magnitude of our defined terms 1 and 2. Under the condition that
, then the form of 9-4 is plus cylinder and the form of 9-5 is minus cylinder. If the
condition is inverted that
, then the form of 9-5 is plus cylinder and the form 9-4 is
minus cylinder. In the world of prescriptions, ophthalmologists traditionally prescribe plus
cylinder and optometrists traditionally prescribe minus cylinder.
The axis term has one
169
additional stipulation in that the axis may not be lower than 0o or higher than 180o. If the Axis
term is below 0o then 180o is summed to that value to correct for the term. If the axis term is
above 180o then the axis term is subtracted by 180o for correction of the value. Through this
approach we are able to convert from our optical Zernike polynomial terms to prescription terms
applied in ophthalmic optics. These conversions will be applied in the following sections with
the forms displayed.
9.2.1 Defocus Lens Filled with DI Water Based Fluid Volume Tested with Auto-Phoropter
for 3 mm and 6 mm Stop Sizes
Two defocus lenses were tested with the first being filled with DI water and the second
with oil #3. Tests for both oil # 3 and DI water were applied to the limits of our stop size of 3
mm and 6 mm. The measured defocus error of the model eye coupled with the auto-phoropter
system was measured for both these stops. To null the defocus error we would require the
coupled fluidic lens with the auto-phoropter system to have an equal and opposite defocus
measurement to the model eye. This is required to null out the measurements at either the 3 mm
or 6 mm stops. Again, this is testing the system with one fluidic defocus lens. With this
stipulation, we can equate the fluid volume necessary to correct for a given amount of defocus
error to the equivalent error in a users eye. We are able to prove experimentally that our optical
system can identify and compensate for the eye model error by showing that we can compensate
for the iris stop size of 3 mm to 6 mm.
By identifying the change in astigmatism and defocus we are able to model the
prescriptions produced by the fluidic lenses. The sphere, cylinder and axis prescription is
correlated to these wavefront results. The results that we have graphed identify the prescription
of the full auto-phoropter system that includes the telescope system, the fluidic lens, and the
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relative position of the mirror coupled with the eye doublet. The relative positions of the optics
define the defocus variation that is observed in the optical system.
We can map the prescription that would be observed through the use of the second order
radial Zernike terms of defocus and astigmatism when comparing the limits of our stop size
range of 3 mm to 6 mm. Again, we observe that the defocus terms have been scaled by
approximately 4 times for the defocus terms when comparing Figures 9-6 and 9-7. There is a
difference in scaling however, as the physical position of the fluidic lens and the model eye lens
varies, causing different power effects on the system. For this reason it is significant as a next
generation system to identify the pupil size when measuring ocular error.
Figures 9-6 and 9-7 map the wavefront error compared to that of the fluid volume. The
fluid volume is measured in L and the sampling between fluid volume was performed at every
5 L. The 3 mm stop required fluid volume extraction that ranged from 25 to -55 L while the
6 mm stop required 30 to -70 L of fluid extraction to compensate for the eye model results
observed to distort the wavefront from -5 to +5 D of optical error for the model eye for prototype
one, as seen in section 9.1. Again, the stop size effects the amount of fluid volume required to
compensate for the measured wavefront error. Both stop sizes require 100 L or less of fluid
volume to compensate for a 10 D range of ocular error. Fluid volume within the defocus lens
can vary up to 2 ml or 20 times the range required for compensation of the fluid lens required for
the 10 D change in power.
The chart shows that the values of the measurements for both defocus and astigmatism
were linear, which again is the desired results of our fluidic lens. The defocus lens shows a
much larger variation in defocus then was observed in astigmatism for both the 3 mm and 6 mm
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stopped systems. The slight amount of astigmatism was predicted by our analysis of the fluidic
phoropter wavefront in section 5.2.1. We observe that both for the 3 mm and 6 mm stop sizes
the astigmatism lens has a negative slope.
We can further determine the effects of the
astigmatism terms in the cylinder and axis refraction terms.
Wavefront Measurement (Waves)
Fluidic Auto-Phoropter With DI Water and
3 mm Stop
4
3
2
1
0
Z2,0
-1
Z2,-2
-2
Z2,2
-3
-4
-55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5
0
5
10 15 20 25
Fluid Volume Extraction (L)
Figure 9-6 Wavefront Measurements with DI Water and 3 mm Stop for Defocus Lens:
Empirical data of the linear effects on astigmatism and defocus when altering the fluid volume
inserted into the defocus lens.
172
Fluidic Auto-Phoropter With DI Water and
6 mm Stop
Wavefront Measurement (Waves)
15
10
5
Z2,0
0
Z2,-2
-5
Z2,2
-10
-15
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
Fluid Volume Extraction (L)
Figure 9-7 Wavefront Measurements with DI Water and 6 mm Stop for Defocus Lens:
Empirical data of the linear effects on astigmatism and defocus when altering the fluid volume
inserted into the defocus lens for a 6 mm stop in the auto-phoropter system.
Figures 9-8 and 9-9 show the variation of the sphere, cylinder, and axis variation between
the 3 mm and 6 mm. The slope of the sphere term produces the same values between the 3 mm
and 6 mm terms. The variation between the 3 mm and 6 mm stop sizes were found in the
cylinder and defocus terms. It appears that the fluid lens has relatively stable axis values of 18 o
for the 3 mm stop. The 6 mm was also observed to hover around 18o but the values do not
follow a constant line. The error varies within a couple of degrees relative to the average. It
appears that the DI water, with a viscosity of 1 cSt, enters the chamber quickly and alters the
pressure in the fluid chamber. With the tensioner locked symmetrically about the center, it is
possible that the surface is not equally locked down in the periphery. The peripheral flanges
cause slight variations to the circularly symmetric pressure, which appear to be observed in the
cylinder and astigmatism terms of the wavefront. There also is evaporation of the fluid volume
173
which causes pressure variation in the fluid chamber at different times, where results vary over 4
hour increments which can also skew the results.
Refraction Terms of Auto-Phoropter With DI
Water Filled Defocus Lens and 3 mm Stop
20
y = 0.002x + 18.14
15
Sph/Cyl x Axis
10
Sphere (Diopters)
5
Cylinder (Diopters)
0
Axis (Degrees)
-5
-10
-45 -40 -35 -30 -25 -20 -15 -10 -5 0
5 10 15 20 25 30
Fluid Volume Extraction (L)
Figure 9-8 Refraction Terms with DI Water and 3 mm Stop for Defocus Lens: From the data
sets we are able to determine the refraction terms that are produced for a prescription. These
terms are inclusive the fluidic lens within the auto- phoropter system where the stop is set at 3
mm.
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Refraction Terms of Auto-Phoropter With DI
Water Filled Defocus Lens and 6 mm Stop
25
20
y = -0.0275x + 18.84
Sph / Cyl x Axis
15
Sphere (Diopters)
10
Cylinder (Diopters)
Axis (Degrees)
5
0
-5
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
Fluid Volme Extraction (L)
Figure 9-9 Refraction Terms with DI Water and 6 mm Stop for Defocus Lens: From the data
sets we are able to determine the refraction terms are produced for a prescription. These terms
are inclusive the fluidic lens within the auto- phoropter system where the stop is set at 6 mm.
9.2.2 Defocus Lens Filled with BK-7 Oil # 3 Tested in Fluidic Auto-Phoropter for 3 mm and
6 mm Stop Sizes
It is necessary to compare the defocus lens filled with DI water to a second defocus lens
to determine the consistence of our auto-phoropter system and defocus lens designs. In addition,
we can compare the variation of fluid volume and its effect on the stability of our results. The
second fluidic phoropter applies oil # 3, which is a BK-7 index matching fluid. The optical
properties almost replicate that of BK-7 glass in the visible spectrum. Again, we measure the
wavefront properties of the propagating light to identify the BK-7 based oil measurements
relative to fluid volume.
175
We begin by comparing the wavefront measurements between the BK-7 defocus lens set
with a 3 mm and 6 mm stop. Similarly to previous experimentation, the defocus lenses fluid
range was used to compensate our eye model wavefront error, proving that we are able to correct
for power error from -5 to + 5 D.. In this instance we set a standard amount of fluid volume
range of -35 to 25 L as to compare the wavefront directly to each other. The defocus terms
appear to have a similar ratio of 4 times the defocus term for fluid volumes from 20 to -15 L,
where -15 L is the intersection of 0 Defocus error for both stop sizes. The slope changes for the
experiments with the BK-7 oil and 6 mm stop when extracting fluid from -15 to -35 L. The
ratio of defocus wavefront error for 6 mm to 3 mm stop size reduces by half of the previous
slope. The measurements in this range appear to have altered trajectory with the 6 mm stop size.
This trend did not occur with the DI water based defocus lens. We believe this is due to the
viscosity of the fluid. The viscosity of Bk-7 oil # 3 was 1,450 cSt, which is thick and shows high
resistance. As the fluid was withdrawn by the actuator system, suction was observed that varied
the relative evacuation rate of the fluid volume. This higher resistance caused a variation in
wavefront slope measurement for our thicker fluids.
There appears to be more consistent readings for the astigmatism terms of the defocus
lenses between the data for prototype one stopped at 3 mm and 6 mm. stop. The ratio between
the two Zernike terms of the stop sizes is proportional to the expected values. It is observed that
this defocus lens has larger amounts of astigmatism compared to the DI water based fluidic lens.
In addition, the astigmatism Zernike terms for the fluidic auto-phoropter with a 3 mm stop
appear to be symmetrical about 0 waves of error.
There is also symmetry between the
astigmatism Zernike terms of prototype one stopped at 6 mm, however the mirror symmetry
appears to match relative to 2.5 D of wavefront error. These values follow similar slopes relative
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to each other but different slopes compared to the first defocus lens with DI water. The DI
defocus lenses slopes were both negative slopes as we increased fluid volume. The slopes for
the DI water based defocus system had both Zernike terms with approximately the same point
values. The difference between these two terms is further expanded when observing the axis
values of the refraction terms for the fluidic auto-phoropter.
Defocus Lens With BK-7 Oil and 3 mm Stop in
Fluidic Auto-Phoropter
4
Wavefront Measurement (Waves)
3
2
1
Z2,0
0
Z2,-2
Z2,2
-1
-2
-3
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
Fluid Volume Extraction (L)
Figure 9-10 Wavefront Measurements with Bk-7 Oil and 3 mm Stop for Defocus Lens:
Empirical data of the linear effects on astigmatism and defocus when altering the fluid volume
inserted into the defocus lens. The slope of the defocus Zernike is much larger than the
astigmatism Zernike terms. The astigmatism Zernike terms have equal and opposite slopes that
are mirror images about the 0 axis.
177
Defocus Lens With BK-7 Oil and 6 mm Stop in
Fluidic Auto-Phoropter
Wavefront Measurement (Waves)
20
15
10
Z2,0
5
Z2,-2
Z2,2
0
-5
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
Fluid Volume Extraction (L)
Figure 9-11 Wavefront Measurements with Bk-7 Oil and 6 mm Stop for Defocus Lens:
Empirical data of the linear effects on astigmatism and defocus when altering the fluid volume
inserted into the defocus lens. The slope of the defocus Zernike is much larger than the
astigmatism Zernike terms. The astigmatism Zernike terms has equal and opposite slopes that
are mirror images about the 2.5 waves error line.
The refractive terms of the fluidic auto-phoropter with the BK-7 oil in the defocus lenses
appear to have the same pattern. The sphere and cylinder terms of Figures 9-12 and 9-13 have
the same slopes and values as we adjust the fluid volume of the liquid lens. The observed
difference between the refraction terms of the auto-phoropter with the 3 mm and 6 mm stops is
that of the axis value. The auto-phoropter system with a 3 mm stop has an average axis value of
67o while the system with a 6 mm stop has an average axis value of 76o. The sampled point at
each shift of 5 L appears to have almost no variation in either of the graphs. We believe that
the thicker fluid material with the higher viscosity produces a more stable and repeatable results
as is seen in Figures 9-12 and 9- 13.
178
Refraction Terms of Auto-Phoropter With BK-7
Oil in Defocus Lens and a 3 mm Stop
70
y = -0.1018x + 66.768
60
Sph / Cyl x Axis
50
40
30
Sphere (Diopters)
20
Cylinder (Diopters)
10
Axis (Degrees)
0
-10
-25
-20
-15
-10
-5
0
Fluid Volume Extraction (L)
5
10
Figure 9-12 Refraction Terms with BK- 7 Oil and 3 mm Stop for Defocus Lens: From the
data sets we are able to determine the refraction terms are produced for a prescription. These
terms are inclusive the fluidic lens within the auto- phoropter system where the stop is set at 3
mm.
Refraction Terms of Auto-Phoropter With BK-7
Oil in Defocus Lens and a 6 mm Stop
80
y = 0.077x + 76.075
70
Sph / Cyl x Axis
60
50
40
Sphere (Diopters)
30
Cylinder (Diopters)
20
Axis (Degrees)
10
0
-10
-25
-20
-15
-10
-5
0
5
10
15
Fluid Volume Extraction (L)
Figure 9-13 Refraction Terms with Bk-7 Oil and 6 mm Stop for Defocus Lens: From the data
sets we are able to determine the refraction terms are produced for a prescription. These terms
are inclusive the fluidic lens within the auto- phoropter system where the stop is set at 6 mm.
179
There are tradeoffs when using thicker fluids with higher friction forces. We believe the
fluid with the higher viscosity is stabilizing the repeatability of the fluidic lens. It is observed
when comparing the defocus lens with DI water to the lens with BK-7 oil that the BK-7 oil has
higher viscosity which produces higher repeatability. The tradeoff with a higher viscosity is that
there is a loss in actuator speed as the fluid takes longer to evacuate out of the fluid chamber.
This decreases the system response time which becomes detrimental for patient care. It is
desirable to test an oil based fluid such as fluid #1 or fluid #2 from Table 7-2 that has a much
lower viscosity and is an oil based fluid. If fluid # 1 or 2 produces stable and repeatable results
similar to the BK-7 fluid (fluid # 3 of Table 7-2) then a different factor relative to viscosity was
causing the instability of our first defocus lens with DI water. Another possibility of lens
instability for the axis values would be the volatility of DI water as it evaporates. This was
mentioned in the previous section as a cause of variation in accuracy of the fluidic lens relative
to the axis. DI water produces stable and repeatable results in the order of 4 hour increments.
As the fluid evaporates, there are variations in power control by approximately half a Diopter.
9.2.3 Astigmatism Lens Filled with DI Water and Fluidic Auto-Phoropter Set at a 3 mm
Stop Size
Adjustments were made for testing of the astigmatism lens. The mounts of the fluidic
phoropter to the external adapter is attached to the frame of the defocus lens. As was mentioned
in section 9.1, the astigmatism lens locks onto the defocus lens and thus forms the stack of
fluidic lenses. In order to measure the astigmatism power of only the astigmatism lenses we zero
out the astigmatism value of the defocus lens prior to adding the astigmatism lenses onto the
frame. This induces a slight amount of defocus by the astigmatism lens which we null out with
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the Shack-Hartmann wavefront sensor. We then lock the astigmatism lenses onto the defocus
lens and mount it into the auto-phoropter system. We are now able to measure results from the
astigmatism lenses with the optical system. In order to achieve zero power from both lenses we
added a dual fluidic valve controller for each of the fluidic astigmatism chambers.
Figure 9-14 Fluidic Valve Control System: The valve controls the exact amount of fluid with
one valve direction. When we switch to the opposite direction, which is set half way in between,
we can control the exact amount of fluid we are testing with.
This valve has direct path with only one of the two paths to the fluid chamber. Each of
the astigmatism lenses has a 3-2 valve connected to their channel. The fluid chambers are
manually adjusted until we observe zero astigmatism power on the Shack-Hartman wavefront
sensor. We then switch both valves to the second path that is connected to another syringe.
These syringes hold 100 l with a notch identification of 1 l. We can create as small as 1 l
iterations manually with this setup. Each of these syringes was set at 50 l which allowed for a
range of ± 50 l relative to our identified zero points. The measurements that were performed
were again 5 l increments from -30 to +30 l for each of the fluidic lenses.
Each of the fluidic astigmatic lenses of the fluidic auto-phoropter was measured
individually while the opposite fluidic lens was set at zero astigmatism. The auto-phoropter was
181
set at a 3 mm stop to more accurately represent the iris size in lighted conditions. Plots 9-16 and
9-17 identify the wavefront measurements observed from the two fluidic lenses. The slope for
astigmatism lens one offers less of a power variation then astigmatism lens two. The two
astigmatism lenses are coupled onto each other with a glass plate separating the two fluidic
chambers. The physical position of the membrane surface is therefore displaced by about 30
mm. This displacement within the fluidic auto-phoropter design induces a shift along the optical
axis, causing a defocus shift along the image plane. The physical position of astigmatism lens 1
is external to the stack of fluidic lenses. The physical position of astigmatism lens 2 is within .5
to 5 mm relative to fluidic defocus lens, but approximately a 20 mm separation with astigmatism
lens 1. The separation between the lenses would require further testing when syncing the three
lenses together; however, our goal here is to illustrate that the fluidic astigmatism lenses can
function together to produce any cylinder power with any axis orientation.
Figure 9-15 Fluidic Phoropter Combination: This is also Figure 6-3 and is a refresher of the
physical position of the three lens combination. Astigmatism lens 2 is placed on the interior
facing the defocus lens. The separation between these two optical elements varies between .5-5
mm depending on the chosen deflection angle, power and separation. Astigmatism lens 1 is on
the external surface.
182
The orientations of the astigmatism chambers cause the astigmatism lenses to have a 45 o
rotation relative to each other. This 45 o relative position is observed in the slopes of our Zernike
terms
and
when comparing the terms between the two astigmatism lenses as seen in
Figures 9-16 and 9-17.
The slopes of astigmatism lens one are in the matching negative
direction while the slopes of astigmatism lens 2 are in opposite directions. This is a clear
indication that these lenses are producing different axis values.
The combination of these axis
values will allow for us to replicate axis control.
Astigmatism Lens One with DI Water and 3 mm
Stop in Fluidic Auto-Phoropter
Wavefront Measurement (Waves)
1.50
1.00
0.50
Z2,0
0.00
Z2,-2
-0.50
Z2,2
-1.00
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
Fluid Volume Extraction (L)
Figure 9-16 Wavefront Measurements with DI Water and 3 mm Stop for Astigmatism Lens
One: The slope of the defocus term
shows a higher amount of power variation then the
astigmatism terms. The astigmatism terms have slopes that are in the same direction with each
other.
183
Astigmatism Lens Two with DI Water and 3 mm
Stop in Fluidic Auto-Phoropter
Wavefront Measurement (Waves)
3.00
2.00
1.00
Z2,0
0.00
Z2,-2
-1.00
Z2,2
-2.00
-3.00
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
Fluid Volume Extraction (L)
Figure 9-17 Wavefront Measurements with DI Water and 3 mm Stop for Astigmatism Lens
Two: The slope of the defocus term Z2,0 shows a higher amount of power variation then the
astigmatism terms and also the slope of astigmatism lens one. The physical position of the
astigmatism lenses in the auto-phoropter system causes this steeper slope in variation of defocus
to be observed.
The axis values produced by each of these astigmatism lenses individually, in addition to
their combinations, shows the capabilities of replicating astigmatism values with any orientation
and cylinder power. When we analyze the axis values of our refractive measurements from
Figures 9-18 and 9-19, we observe that each lens produces two axis values. The orientation of
the stack of astigmatism lenses is so that astigmatism lens one when fluid is inserted faces the
auto-phoropter’s Shack-Hartman wavefront sensor. Another way to phrase this is that as we
insert fluid into astigmatism lens one, the deflection flexes in a positive power direction away
from the users eye. Inversely, the withdrawal of fluid causes the cylinder to have a concave
shape relative to the users’ eye. This allows for fluidic lens one to have two defined axis
orientations. Astigmatism lens one produces axis values of 107 o when we withdraw fluid and
17o when we insert fluid relative to our zero axis point. The axis values are exactly 90 o apart as
184
is expected with the inversion of the surface. The zero axis point is observed to be between a
fluid volume of 0 and -5 l, but close to -5 l. We measured in 5 l increments so our sampling
is not high enough to identify the exact zeroing of our fluid system.
Similarly, fluidic astigmatism lens two produces two orientations, but the orientations are
inverted relative to fluid insertion and withdrawal. The physical position of fluidic lens two is in
that the fluid chamber faces the user. As we insert fluid into the lens, we produce a concave
deflective surface relative to the perspective of the users. If we withdraw fluid, the fluid curves
closer toward our astigmatism chamber. The astigmatism chamber is further from the user then
the membrane surface of astigmatism lens two. This creates a positive cylinder lens relative to
the user. Astigmatism lens two produces two axis orientations as was observed with astigmatism
lens one. Astigmatism lens two has fluid orientations of 62 o and 152o with again a zero point
near -5 l.
It is observed that with the design of the astigmatism lens the axis are highly stable. Axis
stability is necessary to control astigmatic power. There are a total of four orientations that are
produced from the combination of the two astigmatic lenses: 17 o, 62o, 107o, and 152o. Each of
these orientations are 45o relative to each other and if we subtract 17o from all 4 axis values we
see the follow four orientations: 0 o, 45o, 90o, and 135o. The constant 17o shift of the four terms
is caused by the relative orientation of the coupled astigmatic lenses relative to our ShackHartmann wavefront sensor. We therefore have identified a constant rotation within the optical
system. More importantly we have identified that our two astigmatism lenses can produce four
primary axis orientations within our fluidic auto-phoropter system. We can combine any two of
these four orientations to replicate astigmatism power in any direction. This allows for us to
produce correction of cylinder errors in real time of any cylindrical power and axis.
185
Axis Refractive Term of Auto-Phoropter with DI
Filled Astigmatism Lens 1 and 3 mm Stop
110.00
90.00
Axis (Degrees)
70.00
50.00
Axis
30.00
10.00
-10.00
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
Fluid Volume Extraction (L)
Figure 9-18 Axis Term for Astigmatism Lens One with DI Water and 3 mm Stop for Fluidic
Auto-Phoropter: We observe the two orientations of fluidic lens 1 of 107 o and 17o, which are
90o apart. We also observe the stability of the two axis and the zero point as measured.
186
Axis Refractive Term of Auto-Phoropter with DI
Filled Astigmatism Lens 2 and 3 mm Stop
180.00
Axis (Degrees)
160.00
140.00
120.00
100.00
Axis
80.00
60.00
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
Fluid Volume Extraction (L)
Figure 9-19 Axis Term for Astigmatism Lens Two with DI Water and 3 mm Stop for
Fluidic Auto-Phoropter: We observe the two orientations of fluidic lens two of 62 o and 152o,
which are 90o apart. We also observe the stability of the two axis and the zero point as
measured.
The combination of two axis values allows for us to produce any orientation of
astigmatism but the magnitude of the astigmatism is determined by the magnitude of our cylinder
values relative to the fluid volume from both astigmatic lenses. Figures 9-20 and 9-21 show
each fluidic lens and the magnitude of their cylinder power. The cylinder values measured
between -30 to + 30 l was found to have a range of -3 to +3 D for both lenses. Again the
cylinder slopes are inverted as is expected by the orientation of the astigmatic lenses relative to
each other. The magnitude of the spherical terms of the fluidic astigmatism lenses possesses
variation in physical position in the fluidic auto-phoropter.
187
Sphere and Cylinder Refractive Terms of Auto-Phoropter with
DI Filled Astigmatism Lens 1 and 3 mm Stop
4.00
3.00
Sph / Cyl (Diopters)
2.00
1.00
0.00
Sphere
Cylinder
-1.00
-2.00
-3.00
-4.00
-5.00
-30
-25
-20
-15
-10
-5
0
5
10
Fluid Volume Extraction (L)
15
20
25
30
Figure 9-20 Cylinder and Sphere Term for Astigmatism Lens One with DI Water and 3 mm
Stop for Fluidic Auto-Phoropter: The cylinder value exhibits -3 to 3 D of power between our
60 l selected range. The orientation of the slope is defined by the physical position of the
membrane being further then the separation relative to the users’ eye.
188
Sphere and Cylinder Refractive Terms of Auto-Phoropter with
DI Filled Astigmatism Lens 2 and 3 mm Stop
Sph / Cyl (Diopters)
6.00
4.00
2.00
0.00
Sphere
Cylinder
-2.00
-4.00
-6.00
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
Fluid Volume Extraction (L)
Figure 9-21 Cylinder and Sphere Term for Astigmatism Lens Two with DI Water and 3
mm Stop for Fluidic Auto-Phoropter: The cylinder value exhibits -3 to 3 D of power between
our 60 l selected range. The orientation of the slope is inverted relative to astigmatism lens
One as the position of the astigmatism glass separator is further than the position of the
membrane relative to the eye.
From the experimental results of each astigmatism lens we can produce a mapping of the
combined cylinder powers and axis values. The previous charts show that we have the sphere,
cylinder, and axis values of each of our sphero-cylinder astigmatic lenses individually. This
identifies that for every given amount of inserted or withdrawn fluid volume, in 5 l increments,
we have sphere, cylinder, and axis values of each lens. Through power vector analysis or
astigmatic decomposition, we are able to produced a summed sphere, cylinder, and axis value at
the summing of measured fluid volumes of the previous section
Astigmatic decomposition
combines the sphere, cylinder, and axis orientation through the following equations [19].
9-6
189
9-7
9-8
9-9
9-10
9-11
From the sum of these equations we are able to identify the amount of fluid from each
astigmatic lens and the amount of cylinder power that is outputted from that lens. Figure 9-22
shows the combination of our two fluidic lenses and their cylinder power for our fluidic autophoropter. A similar graph was formed in the description of the fluidic phoropter by itself as was
reimaged in Figure 7-6 [17]. Our graph shows a mapping of the cylinder power from 0 to + 3
Diopters. We are able to reproduce the power with any axis direction, where the cylinder power
near circles. The wavefront measurements for astigmatism lens one and astigmatism lens two
190
were measured manually at 5 l increments. We believe that we under sampled and should have
used 1 l increments to achieve higher quality data points. In addition, we have a pump control
system that more accurately shifts the fluid volume. The fluidic auto-phoropter results show in
Figure 9-22 did not apply pump controls as we did for the fluidic phoropter results show in
Figure 7-6, but rather used manual control of the syringes to achieve measurements. Our manual
approach has a fluid variation of 200 nl, which skews the quality of our circular cylinder powers.
As a proof of concept however, we show that we are capable of producing cylinder power in the
auto-phoropter design at all axis directions.
191
Figure 9-22 Astigmatic Mapping of Auto-Phoropter System: The cylinder power and axis are
mapped relative to the fluid volume of each of the fluidic lenses.
9.3 Nulling Error with the Fluidic Auto-Phoropter: Fluidic Phoropter Cancels Model Eye
Error
Sections 9.1 and 9.2 described the empirical data required to perform a correction of a
user’s measurement. We equated the wavefront error in the optical system to defocus error
within a model eye. We also identified the compensation for the model eye at various pupil sizes
and different fluids in correcting for that error. Similarly, we showed that our fluidic autophoropter can correct for sphere and cylinder error at all orientations. The last step was to show
that the defocus lens can compensate for the error in the model eye which is shown in Figure 9-
192
23. The error is compensated so that once the wavefront measurement observes zero defocus
error we have a fully corrected system. The model eye was set to have an error of 1 D and the
fluidic lens compensated -1 D to null the error out.
Figure 9-23 Nulled Defocus Error with Eye Model at 1 D defocus and -1 D defocus of
Fluidic Phoropter: Within the system, this is the corrected output viewed on the ShackHartmann Sensor when viewing the correction of the eye model.
9.4 Limits of the Optical Design
There are limitations to our optical design that affect the dynamic range, field of view,
optical quality, and induced aberrations that would require for modifications to the design. We
first begin with a discussion of the propagating wavefront. When the user has an Emotropic eye,
approximately 10% of the collimated light entering the eye reflects back collimated as is
observed from the exit pupil of the eye. Under these conditions, the system is fully unvignetted.
As we increase the power as in Myopia or decrease the power as in Hyperopia, we find that the
power variation propagates in a converging or diverging fashion. The higher the power variation
193
induced by the eye, the less light passes through the optical system. As was mentioned earlier,
only a fraction of the light passing through the system reaches the detector plane. If the light
intensity becomes so small that the detector plane cannot detect a signal we must take advantage
of our fluidic lens technology. We can adjust the defocus lens until enough positive or negative
power is induced to reduce the amount of vignetted light.
As we discuss the signal at the sensor plane it is important to achieve only a single image
plane that reflects back through the optical system to the detector, rather than the multiple
reflections, and that is the light exiting from the retina. A problem in testing of the astigmatism
lens was that more than one plane of information reached back to the Shack-Hartmann wavefront
sensor. It was discovered that the fluidic phoropter caused more than one image plane to reflect
as the two flats in the fluidic phoropter design were uncoated surfaces. These surfaces were too
close to either the beamsplitter or the model eye, causing more than one surface to be observed
as power changed on our fluidic lenses. We determined that the flats were causing the multiple
signals and turned the fluidic phoropter so that astigmatism lens one faced the auto-phoropter
system. We reduced the effect of the multiple signals by adjusting the orientations of the fluidic
phoropter so that the membrane surface faced the auto-phoropter plane and the glass flat faced
the model eye plane, with a 30 mm separation between the fluidic phoropter and beamsplitter.
This worked well for testing with the single defocus lens. We found that with the three lens
system the double pass of light caused two signals to return from the optical system when testing
the astigmatism lens. We were able to thus individually test each astigmatism lens, but could not
couple the two fluidic lenses together. For this reason, we assessed the combination of the two
astigmatic lenses through our experimental results of each lens and combined the lenses
mathematically in section 9.2.3 rather than direct measurements of varying each fluidic lens. We
194
believe the multiple reflections are caused by the double pass through the fluidic phoropter with
multiple reflections between the two glass surfaces. The reflections are correctable if we replace
the two flat optics with flat optics that are coated in the NIR. Theoretically, this will reduce the
reflections that are producing multiple signals and only the aberrated light exiting the retina will
be signaled back.
We must analyze the telescopic system when discussing induced aberrations and
aberrated light reflecting in the optical system. If the telescopic system is slightly misaligned,
the aberrated wavefront can be corrected. Prior to testing we null out the aberrated wavefront
induced by the telescopic system by placing a flat mirror in the location of the eye. The concern
however with this design is that the telescopic system is in the line of sight of the user. If there is
a slight variation in power from the telescope the user will also observe this power variation and
it will alter the eyes power required to resolve our targeted images. This in turn would produce
an inaccurate prescription. Therefore, it is desired to take the telescopic system out of the line of
sight of the user. By bringing the telescope off axis with the Shack-Hartmann wavefront sensor
we can still correct for any slight misalignments of our telescopic system relative to each other.
In addition, the only optical power in the line of sight of the user is now the fluidic phoropter.
This allows for a higher control of aberration compensation. A second desired advantage of
shifting the optical system off axis is to increase the field of view.
195
XP
EP
QHFOV
NIR BS
45:55
Doublet 1
f
Doublet 2
2f
Fluidic
Lens
=0
NIR BS
45:55
f
Figure 9-24 Line of Sight Limit of Fluidic Auto-Phoropter: The limit for our 4f imaging
systems field of view is that of the pellicle beamsplitter.
The field of view is quickly measureable for our 4F imaging system. The entrance pupil
of the eye is matched at the exit pupil (XP) of the telescopic system. The fluidic lens is placed at
zero power as to not adjust the entrance pupil position. We created a 4F imaging system to
eliminate cropping of the wavefront and vignetting at the reimaged plane.
Therefore, as is
shown in Figure 9-24, the half field of view (HFOV) is equivalent to the subtended angle of the
chief ray entering the telescopic system. The limiting factor of this design is the size of the
beamsplitter. The beamsplitter has a 25.2 mm sized clear aperture but is set at 45 o to the optical
axis. This causes the lateral clearance on our line of sight perpendicular to our optical axis to
have a width of 17.8 mm. As the edge of our beamsplitter is near the doublet, we estimate with
a slight tolerance that the length of the edge is 100 mm along the optical axis from the stop.
With a lateral width of 17.8 mm and a distance of 100 mm our full field of view is 10 o.
Similarly we can identify the field of view of a new design where a cubed pellicle beamsplitter
reflects the optical system off axis.
196
CCD
Array
Lenslet
Array
IR
Source
Collimating
Lens
IR BS
45:55
30 mm = z
IR BS
45:55
Doublet 1
Doublet 2
IR BS
45:55
Fluidic
Lens
 =0
30 mm
=z
5 mm = z
20 mm = z
QHFOV
Figure 9-25 Line of Sight Limit of Off – Axis Fluidic Auto-Phoropter: The beamsplitter now
brings the optics off-axis to slightly increase the field of view while still maintaining the same
optical components in the system.
As is seen in Figure 9-25, we have decreased the optical elements in the line of sight of
the user. There is a total of two optical elements in the line of sight of the user: a pellicle
beamsplitter and our fluidic lens. There still is an eye relief of 25 mm between the pupil and the
fluidic lens. By keeping the fluidic lens at zero power, this optical system has no power in the
line of sight along the optical axis, which implies that our field of view is at the pupil of the eye.
The subtended angle is again limited by the occluded object with the least width which again is
the beamsplitter. Through this approach we have eliminated the separation between the fluidic
lens and the beamsplitter, making the separation between the 17.8 mm lateral width and the pupil
85 mm along the optical axis, which equates to a full field of view of 11.8o.
The most optimal design for field of view is when the fluidic phoropter becomes the
limiting factor in the field rather than the fluidic auto-phoropter. The fluidic phoropter is fixed
near the spectacle plane of the user, which is around 25 mm for eye relief. There are two flats in
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the fluidic phoropter, that of the astigmatism lens and that of the defocus lens. The astigmatism
lens is further from the eye by approximately 15 mm in addition to the eye relief or a total of 40
mm along the optical axis. This suggests that the maximum field of view with the current fluidic
phoropter is the 10 mm lateral width at a distance of 40 mm from the pupil location or a 14o field
of view. In order to achieve a field of view where the fluidic phoropter is the limiting factor of
our system, we must make the beamsplitter wider laterally. It is calculated that the lateral width
of the beamsplitter must be at least 25 mm to have the fluidic phoropter as the limiting factor in
the field of view with this second design. The beamsplitter must be at an angle to split the light
and so the size of our beamsplitter becomes a function of 25/sin(x), where x is the relative angle
chosen for the beamsplitter to deflect the light towards the rest of our optical system. If the
beamsplitter is set at 45o, for example, then the beamsplitter size must be larger than 36 mm
along the hypotenuse of the triangle. This relation will become useful when we use optics such
as holographic optical elements as our beamsplitters.
We have described limiting factors of field of view, vigneting, induced aberrations, and
reflections. Lastly, we will discuss the limiting factor on the dynamic range of our power
measurements. Through experimentation we have found that defocus by the eye alters the
location of the focal plane. There are two reference points that are applicable when performing
measurements with the Shack-Hartmann wavefront sensor: the plane where light focuses to
infinity and the plane where light focuses on the detector. We find that the relative positions of
the optics completely define the dynamic range of each designed optical system.
When
measuring with this optical system it is helpful to identify when the Shack-Hartmann sensor
focuses at infinity and when the light is focused at the detector.
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10.0 FLUIDIC AUTO-PHOROPTERS: OFF-AXIS OPTICAL DESIGNS
Chapters 6 through Chapters 9 described in detail the functionality of our fluidic autophoropter design. These chapters described the design fabrication, design, and testing of the first
prototype of the automated see-through fluidic auto-phoropter. The additional systems described
in this section are comprised of the same three module design: a fluidic lens, a relay telescope
and a Shack-Hartmann wavefront sensor. The stacks of fluidic lenses are the same three
adjustable lenses composed of a spherical lens and two astigmatic lenses oriented 45 o to one
another. Any sphere, cylinder and axis combination can be achieved by adjusting the fluid
volume within the fluidic lenses as was shown in Chapter 9. We will not focus on this aspect of
the fluidic lens coupled with our optical system as we have proven this functionality. As a proof
of concept for additional systems we will show a nulled image of the fluidic auto-phoropter and
its functioning results with a model eye.
In this chapter our primary focus is on the telescopic system and redesigning the autophoropter. The telescope will be designed so that the primary optics with power will not affect
the line of sight of the user. This is highly advantageous as the user will observe a natural scene
as they view through the system. In other words, the only optics with power in front of the user
will be the fluidic phoropter. We will show the testing of an off-axis design and describe the
testing of a second design, which we will call our second and third prototypes. Both systems
take advantage of a traditional telescopic system with two lenses off axis forming a telescope
system. At the end of the off axis telescope is the same Shack-Hartmann wavefront sensor
technology that was previously described. To prove that prototype two functionally work, we
have tested the system with our eye model approach described in 9.1. For the fluidic autophoropter system, we nulled out a given amount of optical error observed for an eye model with
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our defocus lens. This shows that the fluidic lens technology is capable of nulling out the error
from the eye within our optical system.
Further, we will expand on the shortfalls of the second prototype in field of view and the
geometric optical properties. We then will propose a third prototype that is a combination of
prototype one and prototype two. We will produce an off-axis telescope so that the only power
in front of the users’ eye is that of the fluidic phoropter. In addition, prototype three is designed
so that we can maintain 4f imaging capabilities.
10.1 Fluidic Auto-Phoropter with Traditional Off-Axis Optics
There are several advantages to producing a fluidic phoropter with an off axis telescopic
system. As was described in section 9.4, we are able to increase the field of view, compress the
size of the optical system, and also produce a more natural view for the user. The field of view
and natural view of the user is significant. This allows for us to measure the true accommodation
and convergence of the user as they observe images at various plane. Convergence has a direct
correlation to the field of view and hence maximization of the field of view improves the
convergence range of the optical system.
The optical functionality of our second prototype was altered to reduce the system size.
The first prototype was setup to produce a 4f imaging system. There were many advantages to
our 4f design such as wavefront preservation, increased throughput, and hence a higher quality
measurement of the aberrated wavefront at the detector plane. The binocular system of the first
prototype was approximately a 1 ft by 1 ft area. We reduced the size of the optical system to an
approximately area of 3.5” by 1.5’ area by eliminating the 4f properties of the optical system.
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This was achieved by changing the focal length of our optical system from 100 mm focal lengths
to 35 mm focal lengths and shifting the optical elements off axis as was mentioned earlier.
Functionally, the second prototype operates in the same fashion as the first prototype. (1)
Infrared light is shone into the eye and scatters from the retina. (2) The scattered light exits the
eye as an emerging wavefront that is relayed through the fluidic lens to the Shack-Hartmann
sensor. The sensor reconstructs the wavefront and extracts the sphero-cylindrical refractive error.
This prescription is then applied to adjust the volume of the fluidic lenses to null out the
refractive error. Feedback of the wavefront from the eye/fluidic lens combination is then used to
monitor the fluid volume and keep the net refractive error at a minimum
220 mm = 8.66 inches
Circular
Eye Chart
30
mm
z = 30
mm
Lenslet
Array
Dia = 25 mm
F = 35 mm
Dia = 25 mm
F = 35 mm
CCD
Array
IR BS
45:55
30 mm
z = 30
mm
ShackHartmann
Sensor
Telescopic
System
IR BS
45:55
70 mm
30 mm
60 mm
30 mm
x-axis
Light
Source
x = 30 mm
z = 30
mm
Fluidic
Lens
Eye
Figure 10-1 Fluidic Auto-Phoropter Prototype Two: The system model shows the dimensions
of the compressed design with the optics shifted out of the line of sight of the user. A natural
view allows for the user to naturally adjust their eyes to targets.
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10.1.1 Design Setup of Fluidic Auto-Phoropter Prototype Two
As a proof of concept, we experimented with a 5 mW HeNe laser at a wavelength of 633
nm. The wavelength length is shorter and the intensity is higher than what will be designed for
actual use with our fluidic auto-phoropter. The choice of this wavelength was to identify if our
optical system functions experimentally and also for comparison to the first prototype and third
prototypes. The alignment of the optical system is again constructed around the beamsplitters.
We applied connection rods to align the telescopic system off axis to the second pellicle
beamsplitter. Light propagates from the source to the first pellicle beamsplitter, which reflects
45% of the propagating light toward the eye model. The fluidic lens would be locked onto the
first beamsplitter as was previously shown in the first prototype. During experimentation we
removed the fluidic phoropter to test the eye model and the defocus wavefront error, similarly to
section 9.1. Showing that we can measure the eye models defocus error identifies that our
system is capable of power variation measurement and thus proves system functionality.
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Figure 10-2 Testing Fluidic Auto-Phoropter Prototype Two: The fluidic phoropter is
removed as to not induce undesired wave distortion. By adjusting the mirror of the model eye
we are replicating power aberration of an eye. We then measure the wavefront power variation
of the full optical system and determine the wavefront variation at a given amount of power error
from the model eye.
After light reflects out of the eye model it propagates through the system. There are two
beamsplitters and a fluidic phoropter in the line of sight of the user. When the fluidic phoropter
is set at zero power, there is no power in the viewer’s line of sight. The wavefront sensor can
measure the prescription required under these conditions. 55% of the laser light that reflects off
of the eye propagates through the first beamsplitter and 45% of the remaining light reflects off
axis toward the telescope system. The propagating light reflected into our telescopic system is
reimaged onto the lenslet array of the wavefront sensor.
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There are two designs with this optical setup that were created. The first design is a table
top version of the optical system. The second design has the capability of becoming mobile.
The difference between the two designs is very slight. The first design has a Shack-Hartmann
wavefront sensor that is disconnected, making the system discontinuous. By combining the
sensor to the connection rods off of the second pellicle beamsplitter, we were able to produce
one mobile optical setup that did not require to be set on a table top. The sensor was combined
to the connection rods through c-mounts and adaptors.
Figure 10-3 Mobile Fluidic Auto-Phoropter Prototype Two: Prototype Two is assembled so
that it has become small and mobile with the light source and sensor locked onto cage rods.
10.1.2 Modeling and Testing of Fluidic Auto-Phoropter Prototype Two
As we no longer observe one to one conjugation between the pupil plane and lenslet array
we begin to see cropping of the wavefront and magnification effects of the measured slope.
There will also be an increased amount of light loss as we are no longer matching pupil planes to
the lenslet array. The goal is to identify if under these new optical design conditions we can
extract data and correlate prescriptions. The system was modeled in ZEMAX to identify the
amount of error that the fluidic auto-phoropter can measure and the range. The exact positions
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of the fluidic auto-phoropter and optics were placed into the design. The eye model was adjusted
in the ZEMAX model to replicate 50 micron increments, identifying power variation observed in
the system with the new physical positions of the optical lenses. The amount of error that the
system was capable of measuring was from the range of -15 to + 15 D for our system stopped
down to 3 mm.
The results for the dynamic range showed that there was variation in the slope of the
second prototype. In order to verify the model, we experimentally replicated power variations of
the model eye by shifting the mirror relative to the eye lens of our eye model. We include values
of -5 to + 5 D in our experimentation as to compare the results of the second prototype with the
results of the first prototype. As shown in Figure 10-4, the wavefront measurement of the second
prototype shows a very gradual slope relative to the first prototype. For plus or minus five
Diopters of defocus the slope of the second prototype is within 0.3 Diopters of zero. This
suggests that as we can achieve more accurate measurements with the first phoropter design as
the slope sensitivity is less. With smaller slope sensitivity a reading of 1 wave of defocus error
for example clearly indicates our model eye with defocus power. Whereas, it is harder to
identify 0.2 waves of defocus error from prototype two as the slope is gradual. It is noted that the
testing of the first phoropter was operating at 785 nm and the testing of the second phoropter was
operating at 633 nm. The wavefront sensor was adjusted and calibrated to test for the proper
wavelengths.
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Eye Error Measured by Fluidic Auto-Phoropter
Designs
Wavefront Measurement (Waves)
3
2
AutoPhoropter
Prototype 2
1
0
AutoPhoropter
Prototoype 1
-1
-2
-3
-4
-5
-4
-3
-2
-1
0
1
2
3
4
5
Error in the Model Eye (Diopters)
Figure 10-4 Comparing Wavefront Error of Prototypes One and Two Relative to Defocus
Power of the Model Eye: The larger slope variation of prototype one allows for clearer defocus
measurements as there is higher differentiation between power variation in the model eye.
Figure 10-5 shows further examination of the second prototype’s wavefront measurement
relative to defocus power of the model eye. This wavefront measurement shows that there is in
fact a slope that is differentiable with the setup of prototype two. Although not as steep of a slope
as prototype one, we are able to extract model eye measurements and differentiate between
various amounts of power at the eye location. As was discussed in Chapter 9, what is necessary
is the identification of a linear change in wavefront error relative to the amount of error identified
by both the model eye and the fluidic phoropter to compensate for that error for a functional
system. Showing that there is a linear variation of the model eye readings in the fluidic
phoropter proves that error correction is achievable with this second prototype.
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Wavefront Measurement (Waves)
Defocus Error of Model Eye Relative to Measured
Wavefront of Prototype Two
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
Auto-Phoropter
Prototype Two
-5
-4
-3
-2
-1
0
1
2
3
4
5
Error in Model Eye (Diopters)
Figure 10-5 Wavefront Error of Prototype Two Relative to Defocus Power of the Model
Eye: The slope variation of the model eye’s defocus measurements proves that fluidic autophoropter two can functionally measure power variation induced by either the fluidic phoropter
or the eye model.
10.2 Nulling Error with Prototype Two Fluidic Auto-Phoropter
In section 10.1 we proved through shifting the mirror position of the model eye that our
wavefront sensor is capable of measuring wavefront error variation in the functional second
prototype. To further verify that our second prototype can in fact correct for wavefront error we
tested the second prototype with our fluidic lens. For both the null test and the model eye test of
prototype two we set the auto-phoropter so that it was stopped down to 3 mm. The eye model
mirror was shifted relative to the eye model lens so that -5 D of defocus power error was induced
and measured in the system with -.275 waves of defocus aberration. We then adjusted the power
of the defocus fluidic lens to null this measured error until the wavefront sensor identified zero
defocus error. Figure 10-6 shows the setup with both the fluidic defocus lens and the model eye
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represented in the setup. Figure 10-7 shows the nulled out wavefront that was outputted by the
Shack-Hartmann wavefront sensor.
Figure 10-6 Nulling Power Error with Fluidic Auto-Phoropter Prototype Two The defocus
component of the fluidic phoropter was inserted into the system. The eye model is adjusted to 5D of defocus and nulled out with the fluidic defocus lens in the setup of fluidic auto-phoropter
prototype two.
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Figure 10-7 Nulling Power Observed for Fluidic Auto-Phoropter Prototype Two from
Shack-Hartmann Wavefront Sensor: The Shack-Hartmann image of when the -5 D of eye
model error is nulled by the fluidic phoropter’s defocus lens
10.3 Limits of Optical Design
Fluidic auto-phoropter prototype two was designed with the motivation of proof of
concept. We proved that we are capable of taking the optics off axis and achieve measurable
results. The advantage of a natural scene for the user is very significant and more off-axis
designs must be tested. This specific design does have shortfalls that are significant: 1) Lack of
4f imaging and 2) Field of View.
The field of view was meant to be increased by taking the optics off-axis. For this
specific design we doubled two beamsplitters in the line of sight of the user while applying the
same pellicle beamsplitters with a 17.8 mm lateral width in order to take the optics off axis. By
having two sequential beamsplitters have added 30 mm along the optical axis relative to a one
beamsplitter setup as discussed in section 9.4. This reduces the field of view from 11.8 o with a
single beamsplitter to 8.8o with two beamsplitters. Prototype one had a field of view of 10o and
so this second prototype exhibits a worse field of view then our first prototype.
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Transitioning to 4F imaging, the first shortfall in losing 4f imaging is that our throughput
has decreased. Depending on how far adjusted we are from 4f imaging we can determine what
percentage of the light is lost. We were able to achieve measurable results with our HeNe laser
as the intensity of the light was at 5 mW. If this intensity of light was placed into an eye it would
create severe damage. The power range that our light source functions is between 10-15 W or
almost 3 orders of magnitude less than the power we tested with.
A second approach in increasing throughput was in how we designed the eye model.
Prior to discussing the eye model, we will discuss the other locations where light loss occurs.
The light propagates through our 45:55 beamsplitters once and then reflects through the
beamsplitters once after exiting the eye, giving approximately 75% light loss after exiting the
eye. We pass through the fluidic phoropter twice where we have two uncoated glass plates that
give 4% light loss every time we pass. The remaining 24.75 % of light will drop to 21.0 % after
the four passes through the optical flats of the fluidic phoropter. When we designed the eye
model we placed a flat mirror and a power lens which produce negligible light loss. This allowed
for the 21.0 % of light coming from the 5 mW laser at 633 nm to reach the Shack-Hartmann
wavefront sensor, or 1.05 mW of energy. In actuality, an eye will only reflect approximately 510% of the light back through the system. This amount of light loss would bring the throughput
of the 1.05 mW to 105 W reaching the detector plane. This means that about 2.1 % of the light
exiting the laser source reaches the detector plane when dealing with a real eye. The 2.1 % of
power that would be transmitted through the system is relative to only the transmission of the
optics and not the physical placement of the optics. The physical position and lack of 4F imaging
further decreases the throughput of the system.
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The second shortfall in the factor of losing 4F imaging is the physical magnification
induced within the system. As was mentioned earlier, we are no longer producing 1:1 angular
magnification as we have shifted our conjugate planes to compress the system. The shift in
physical position of the optics causes cropping of the wavefront, induces aberrations and shifts
the amount of vigneting. There are shifts in the measured error as is observed from Figure 10-4
between the two systems. Even though we nulled the eye model error with the defocus lens we
were not necessarily placing the correct power for the user. We were nulling the error of the
whole auto-phoropter system with the relative position of the eye model relative to the ShackHartmann wavefront sensor. The nulling power for the eye coupled with the fluidic lenses may
not produce the desired results.
The best approach in verifying whether prototype two can measure accurately on a
human eye is to adjust the system and to compare the model to a 4F imaging system that is off
axis. The adjustment with prototype two is to remove the laser source and insert our NIR source
that operates at 15 W reaching the eye position. It is significant to note that the output of the
NIR source is not 15 W but the amount of light reaching the eye location is 15 W as to
maximize the amount of light that is used at the eye location. The second adjustment to prototype
two is in the eye model. Instead of using a plane mirror we can replace the mirror with a Tums.
Tums have advantages beyond heart burn in that they also have similar scatter effects as
observed by light propagating through an eye. We can replicate the 10% light loss at the eye
experimentally with this approach.
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Figure 10-8 Modified Fluidic Auto-Phoropter Prototype Two: The light source and eye
model are modified to produce a better representation of a real time examination.
An additional system, which we will call prototype three is designed, but not yet tested,
to improve on the system limitations of prototype two. In the line of sight of the user, it is
preferred to have one beamsplitter rather than two beamsplitters. This will give us a field of
view of 11.8o for the user, rather than the 8.8o viewed in prototype two and the 10o field of view
from prototype one. Again, we set the NIR light source with its power output is 10-15 W at the
location of the model eye. Also the model eye applies a Tums rather than a flat mirror to
replicate the energy loss at the eye. This optical systems primary modification relative to both
prototype one and prototype two is that of the telescopic system. We would like to compare a 4F
imaging system with off-axis optics to both prototype one and prototype two. This will give a
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clear indication on whether prototype one is realizable without a 4F imaging system and also if
4f imaging systems different focal lengths produce variable results.
The third prototype requires longer focal lengths. We shifted the optics in front of the 1 st
doublet relative to prototype one so that there are two beamsplitters on the front side of the
optical system. If we also include tolerance of the beamsplitters, eye relief, and fluidic lenses
then a focal length of 125 to 150 mm would be optimal. With this alteration, the 2f separation
between our optical doublets with the same focal length is required to be between 250 to 300
mm. We will require our folded optical system, but we must adjust the dimensions of the
separations in a fashion similar to the calculations for the size of the prisms and locations of the
separations as we have shown in Figure 7-10 in section 7.1.3. Once we have remodeled the
system and chosen a focal length for the doublets we can match the length behind the telescope
to the Shack-Hartmann wavefront sensor with a distance of F.
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Circular
Eye Chart
IR
Source
50
mm
Doublet 2
Folding
Design Right
Angle Prisms
5 mm
Dia = 25 mm
F = 125-150 mm
35 mm
12.5 mm
12.5 mm
Collimation
Optics
Dia = 25 mm
F = 125-150 mm
Doublet 1
Mirror
30 mm
IR BS
55:45
Fluidic
Phoropter
30 mm
Eye Relief
25 mm
Eye Model
Doublet
30 mm
IR BS
55:45
Lenslet
Array
CCD
Array
Scattering
Screen
Figure 10-9 Fluidic Auto-Phoropter Prototype Three: This design will give us a 4f imaging
system with a wider field of view and a natural viewing in front of the user. Prototype three is a
modification of the first two prototypes.
This system will produce a 4f imaging system for an off-axis optical system. It will not
reduce the size of prototype one, but will geometrically verify the significance of 4F imaging. In
addition, we increase the field of view by removing a beamsplitter in the line of sight of the user
who is observing a clear view in front of them. We can replicate the amount of light that
propagates through the system. An additional advantage of prototype three and prototype two
are that we can place additional optics between the beamsplitter next to the doublet and the
doublet of the telescopic system. If we are not able to produce enough light to reach the detector
plane a signal amplification method can be inserted in front of the telescopic system. Signal
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amplification was not possible with the telescope in the line of sight of the user as it would block
the viewer from seeing though the optical system. By placing the optics off axis we can insert a
signal amplifier to improve the signal at the sensor plane. This of course would require further
experimentation.
Figure 10-10 Image of Fluidic Auto-Phoropter Prototype Three: Prototype three is built
here to show the functional form of the optics. This system was a model and was not tested with.
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11.0 FLUIDIC AUTO-PHOROPTERS: OFF-AXIS OPTICAL DESIGNS
WITH HOLOGRAPHIC OPTICAL ELEMENTS
Our previous systems have taken advantage of traditional optical lenses in reimaging of
the wavefront. The telescopic system and the lenslet array of the Shack-Hartmann wavefront
sensor are composed of standard optical lenses. There are many advantages to shifting from
traditional optics to holographic optical elements (HOE’s).
HOE’s are lighter, quickly
repeatable, and cost much less than traditional optics. Adding HOE technology to our existing
fluidic auto-phoropter design will also assist in miniaturizing our optical design as single HOE
elements can become transparent in certain wavelengths, act as a lens in other wavelengths, and
also act as beamsplitters. We will show the advancement and progression of the fluidic autophoropter with the use of HOE’s for the telescopic system with an off-axis design. As a proof of
concept, in the same way we proved prototype two, we will show a nulled image of the fluidic
auto-phoropter and its functioning results with a model eye.
Functionally, the produced system is similar to the previous design with the exception of
the modification to the telescopic system as coupled HOE’s.
The compact systems are
comprised of three modules: our fluidic phoropter with any sphere, cylinder, and axis
combination, a holographic relay telescope and a Shack-Hartmann sensor. This fluidic autophoropter system will concurrently measure refractive error by: (1) Shining infrared light that
scatters off the retina. (2) The scattered light exits the eyes as an emerging wavefront that is
relayed to the Shack-Hartmann wavefront sensor. (3) The sensor reconstructs the wavefront and
extracts the sphero-cylindrical refractive error. (4) This prescription is applied to adjust the fluid
volume, nulling out each eye's refractive error while the user views an eye chart. The users’ field
of view is drastically enhanced with the HOE in the line of sight of the user as we can produce
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large substrates. This allows for the system field of view to be limited by the fluidic phoropter
and no longer by the auto-phoropter design. The HOE’s can be designed to be transparent in the
visible wavelengths, allowing for the subject to view external targets such as an eye chart with
ease. The HOE’s additional desired capabilities are to direct infrared light toward the eye and to
act as a lens at the 785 nm wavelength. When the HOE acts as a lens, it is at a designed
wavelength and that wavelength range is towards an off axis location where a second HOE is
placed for the telescopic system. The exiting light of the off-axis holographic telescopic system
reaches the final module: a Shack-Hartmann wavefront sensor. The holographic telescope
applies volume holograms operating at Bragg's Regime to drastically reduce the system size. The
desired wavelength of the holographic optical elements operates in the infrared and produce
direct geometry optical lens replication. The adaptive phoropter prototype fits in a 60 mm long
by 240 mm wide area.
It was mentioned a few times in this section that our desired wavelength was at 785 nm
for reading and writing. There were no HOE’s available that operating at this wavelength. For
testing purposes, the standard wavelength of 633 nm was applied into our fluidic auto-phoropter.
This design with this wavelength will not be tested on humans, but rather it was to develop a
proof of concept for the combination of fluidic adaptive optics, wavefront sensing and
holographic optical elements into an advanced fluidic auto-phoropter. If the system operates at
633 nm for reading and writing then it should operate at 785 nm once the technology for this
wavelength becomes available. In this chapter, we will be assessing the physical capabilities of
the holographic phoropter relative to prototype two of our fluidic auto-phoropter with off-axis
traditional lenses from Chapter 10.
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11.1 Holography and Holographic Lenses
Holography has evolved over the years in a progression that has shifted holograms from
static 3D imaging to mobile 3D image replication. In 1947, Gabor proposed a holographic
theory which recorded the light field’s amplitude and phase [94]. Stationary 3D replicas of
written objects are observed when the recorded information is properly illuminated in traditional
holograms at a designed writing and reading wavelength.
In-line transmission holography
produced lenses that are on axis such as "Gabor" zone plates (CGH's). This type of HOE
operates on-axis for large holograms with wide-band illumination. Unfortunately, Gabor
geometry based holograms produced large amounts of background noise as the 0,-1, and higher
order diffraction orders were reimaged onto the writing material. There had been a large focus in
holography in the late 1960’s and 1970’s in the expansion of holographic technology. For a
further background in holographic theory one should read Chapter 9 of Goodman’s “Introduction
to Fourier Optics”.
The desire of our research was in the progression of HOE’s as optical lenses. Beyond
Gabor zone plates, Fresnel lenses and volume hologram lenses were two options for the creation
of HOE optical lenses. Fresnel lenses work efficiently with profiled grooves when refraction and
diffraction angles of these grooves are matched. However groove profiling drops lens resolution
and there is a degradation of image quality.
The best viable option was the use of volume
holograms in the design of our holographic lenses under designed conditions. In the past couple
of years there has been a progression of polymer based volume holograms.
Our volume
holograms apply the Bayer photopolymer, which is a new holographic recording material
developed in the past half decade, in the creation of our volume holograms [95].
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There are several advantages in applying Bayer photopolymer based volume holograms
as our lenses. From a design stand point, the Bayer material does not require chemical or
thermal treatment, which makes them cheap and easily replicable. From an optical standpoint,
under certain conditions these HOE’s exhibit high optical qualities. The main restrictions of the
HOE’s for our fluidic holographic auto-phoropter is that the HOEs geometry can be designed as
a lens for only a particular wavelength because (1) focal length of the holographic lenses is
roughly proportional to the operating wavelength and (2) HOEs work efficiently in only off-axis
geometries known as Bragg’s angle and this diffraction angle is also wavelength dependant.
In our approach we are using volume holograms as our holographic lenses operating in
the Bragg regime, which requires off axis geometry when operable. Standard HOE’s are
designed in the visible wavelength where our HOE’s was designed at 633 nm for testing
purposes. After proof of concept, which will be shown in this chapter, the next generation
HOE’s will be designed for a band at 785 nm and will be transparent in the visible. The HOE’s
appear on 2.3 mm thick glass substrates with a rectangular shape and have a 2 inch diameter size.
HOEs recorded in such a regime can achieve more than 90% diffraction efficiency, less than 1%
background noise, a transparency in wavelength ranges from 350 nm to 1500 nm, and high
angular selectivity.
These qualities of the holographic lens are desirable in our final HOE design. The high
angular sensitivity allows for almost no diffraction outside of the controlled angular range. This
allows for the rest of the range between 350 nm to 1500 nm to be transparent. Thus when we
design at 785 nm, the HOE will act as a clear window in the visible where the viewer looks
through while at the same time acts as a lens at our testing wavelength of 785 nm off axis. As
these HOE’s function as a lens off axis, we have now replaced the need for a beamsplitter as the
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HOE lens functions as a lens at our operating wavelength, but simultaneously acts as a
beamsplitter with a clear window in the rest of the visible spectrum.
At our operating
wavelength, we have high diffraction efficiency of over 90% with negligible amounts of
background noise. Instead of losing approximately half the operating light every interaction with
the beamsplitters, we now lose less than 10 % of the light from each of the holographic lenses.
11.2 Design of Fluidic Holographic Auto-Phoropter with Holographic Optical Elements as
Lenses
As was stated, the first motivation was to prove the functionality of the HOE’s as a
telescopic system in our fluidic auto-phoropter in the creation of a fluidic holographic autophoropter. Our comparison of the functionality of the HOE based auto-phoropter was relative to
prototype two. Prototype two applied two 35 mm focal length doublets as the telescope design
in an off axis setup. We therefore replicated these two 35 mm focal length lenses as HOE lenses.
Both HOE’s were positive powered lenses that were exactly of those used in the design of
prototype two. The combination of the two HOE lenses at a 2F separation produced a Keplerian
holographic telescope with an afocal design. As we were replicating prototype two, there was a
loss of 4F imaging in which the telescopic system would produce 1:1 angular magnification at
the lenslet array relative to the pupil plane. We will describe a correction for this later on. The
operating wavelength for the HOE prototype was at a HeNe wavelength of 633 nm, the same
wavelength as that of prototype two. The system was drastically compressed and efficiency
improved by removing the beamsplitters in the optical setup. The length in front of the user is
still 3.5” in the z-axis for the line of sight. The width of the optical system was compressed to
100 mm or roughly 4”. The Shack-Hartmann wavefront sensor in this design is described with a
position vertically above the second HOE lens in the telescopic system.
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Figure 11-1 Fluidic Holographic Auto-Phoropter: The HOE lenses replace the telescope
lenses and a beamsplitter in prototype one of our fluidic holographic auto-phoropter.
11.3 Modeling Fluidic Holographic Auto-Phoropter Prototype One
We modeled the holographic auto-phoropter in ZEMAX prior to building the system.
We used the same approach in proving the functionality of the fluidic holographic autophoropter by testing the slope variation of the model eye as we did in the previous systems. The
holographic auto-phoropter was modeled so that the two holographic elements were set in a
position relative to each other to produce a telescope. After the HOE’s were set to produce a
holographic telescopic system we began adding components of the holographic auto-phoropter.
The light source enters from off axis onto a beamsplitter and half the light reflects toward the eye
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model. The fluidic phoropter was set at zero power as again we were testing to verify if there
was a power variation due to the shifting of the mirror position in the eye model and what range
is achievable. Figure 11-2 shows the holographic telescope in alignment with the model eye.
This optical path is a representation that the testing light follows through the system and not the
path that the user observes through the system.
Figure 11-2 Fluidic Holographic Auto-Phoropter ZEMAX Model: The fluidic holographic
auto-phoropter was designed so the fluidic phoropter applied zero power into the system. The
system is aligned for a corrected eye model before power variation in the model testing occurred.
Once our model was fully aligned we tested power variation of the model eye caused by
shifting the mirror position. The ZEMAX model identified the physical range in which our
holographic auto-phoropter functions. The lower limit, as seen in Figure 11-3, was observed as
the lenslet points began focusing on a single point location. The dynamic range that was
observed in the physical model was down to about -16 D of power. With the specified optical
separations that we modeled in ZEMAX, we were able to model powers that ranged between -15
D to + 15 D.
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Figure 11-3 Fluidic Holographic Auto-Phoropter Power Range: We measured the power
range for our designed separations. The images above show the point separation and shifts
relative to mirror position in the model eye. As the points focused closer to the detector plane,
the resolution between points diminished.
11.4 Design and Setup of the Fluidic Holographic Auto-Phoropter
As a proof of concept, we experimented with a 5 mW HeNe laser at a wavelength of 633
nm as was used in prototype two. The wavelength length is shorter and the intensity is higher
than what will be designed for actual use with our fluidic holographic auto-phoropter. The
choice of wavelength was defined by the available HOE lenses. The testing with these HOE
lenses and wavelength gave us the opportunity to verify if the systems produced meaningful
results experimentally. These results would then be compared to prototype two as both systems
used the same focal length lenses and telescope setups.
The alignment of the optical system is no longer constructed around the beamsplitters
like previous fluidic auto-phoropter designs but rather centered around the two HOE lenses. The
alignment of the two HOE lenses relative to each other is achieved by taking advantage of two
lasers, both operating at the HeNe 633 nm wavelength. Each HOE is aligned individually so that
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the maximum intensity reaches the focal location of that HOE lens. The HOE’s are aligned
relative to each other so that the focal location of the two HOE lenses is at the exact same
location. The direction of the optical axis for both HOE lenses must be exact. Once the HOE’s
are aligned with the two lasers entering the system from both sides, the telescopic HOE system is
ready for use.
The lasers are then removed and the rest of the system is aligned. One of the HeNe lasers
is placed off axis and lighter enters the system through a beamsplitter. Half the light reflects
toward the fluidic phoropter and the eye model. We have removed the fluidic phoropter as to
test the accuracy of the auto-phoropter system with the eye model. The Shack-Hartmann
wavefront sensor was placed at the proper position off axis to HOE lens 2 in order to focus light
at the center of the sensor plane.
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Figure 11-4 Testing Fluidic Holographic Auto-Phoropter: The fluidic phoropter is removed
as to not induce undesired wave distortion. By adjusting the mirror of the model eye we are
replicating power aberration of an eye. We then measure the wavefront power variation of the
full optical system with the HOE’s and determine the wavefront variation at a given amount of
power error from the model eye.
11.5 Testing Fluidic Holographic Auto-Phoropter
We are replicating prototype two with our holographic fluidic auto-phoropter. This
implies that the shortfalls from prototype two still exist within this holographic auto-phoropter
design. We still no longer observe one to one conjugation between the pupil plane and lenslet
array. This causes a cropping of the wavefront and magnification effects of the measured slope.
There should be a slight slope variation between prototype two and the holographic design as the
physical positions and lens powers are replicated with each other. This suggests that the HOE
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design will have wavefront measurements in the order of magnitude similar to prototype two
rather than the results of prototype one with the 4F imaging design.
There is one less
beamsplitter in the HOE design and we have taken this into account when positioning the
telescope system, model eye, and Shack-Hartmann wavefront sensor. The light loss should be
decreased relative to that of prototype two as the quantum efficiency of the HOE’s are higher
than the 50% loss of light caused by the beamsplitters.
There are a couple of goals to achieve in the comparison of these two systems. The first
is to verify that the holographic fluidic auto-phoropter achieves extractable information. If we
can correlate a slope to prescriptions then we have verified that the volume holograms can be
coupled into a telescopic system that functions actively with the auto-phoropter setup. The
second goal is to determine if the HOE lenses produce the exact same results as the traditional
lens results. The significance of this second goal is from a scientific standpoint in identifying the
affects of change in system design. As long as goal one is achieved, then we have proven that
the holographic fluidic auto-phoropter functions. As was stated earlier, the ZEMAX models
identified that both prototype two and the holographic design operated from -15 D to +15 D. We
adjusted the model eye by 50 microns per measurement and recorded the amount of shift in
defocus error that was observed.
Promising results were achieved through the testing of the HOE auto-phoropter. It was
found that in fact a slope was measurable as we adjusted the defocus power at the model eye
location. The linear change in power was measured with shifts of the mirror position at the eye
model location, verifying that our holographic fluidic auto-phoropter can in fact measure a shift
in power and can compensate for that power. The results also show that there was a slight
variation in the slope of the holographic fluidic auto-phoropter relative to the second prototype.
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The HOE telescope in some fashion has diminished the slope variation as measured by the
wavefront sensor. As shown in Figure 11-5, the wavefront measurement of the HOE design
shows a slightly more gradual slope relative to prototype two. For plus or minus fifteen Diopters
of defocus of the model eye, the slope of the HOE prototype is within .1 waves of zero.
Whereas, the slope variation of the second prototype is within .4 waves of zero at the plus or
minus fifteen Diopters of defocus range of the model eye. This suggests that we can achieve
more accurate measurements with the second phoropter design as the slope sensitivity is less.
Both systems have gradual slopes relative to our first prototype which was a 4F imaging system.
Eye Error Measured by Fluidic Auto-Phoropter
Designs
0.2
Wavefront Measurement (Waves)
0.1
AutoPhoropter
Prototype 2
0
-0.1
HOE AutoPhoropter
-0.2
-0.3
-0.4
-15
-12
-9
-6
-3
0
3
6
9
12
15
Error in the Model Eye (Diopters)
Figure 11-5 Comparing Wavefront Error of Prototypes Two and HOE Designs Relative
Defocus Power of the Model Eye: Functionally prototype two will have a better accuracy due
to larger slope variation. Both designs offer small slope changes at the same order of magnitude.
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Figure 11-6 shows further examination of the wavefront measurement relative to defocus
power of the model eye for the holographic prototype. This wavefront measurement shows that
there is in fact a slope that is differentiable with the setup of the holographic fluidic phoropter.
Although not as steep of a slope as prototype two, we are able to extract model eye
measurements and differentiate between various amounts of power at the eye location. As was
discussed in Chapter 9, what is necessary is the identification of a linear change in wavefront
error relative to the amount of error identified by both the model eye and the fluidic phoropter to
compensate for that error for a functional system. Showing that there is a linear variation of the
model eye readings in the fluidic phoropter proves that error correction is achievable with this
holographic prototype.
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Defocus Error of Model Eye Related to
Holographic Fluidic Auto-Phoropter
Wavefront Measurement (Waves)
0.08
0.06
HOE AutoPhoropter
0.04
0.02
y = 0.0043x + 0.0067
0
-0.02
-0.04
-0.06
-15
-12
-9
-6
-3
0
3
6
Error in the Model Eye (Diopters)
9
12
15
Figure 11-6 Wavefront Error of Prototype Two Relative to Defocus Power of the Model
Eye: The slope variation of the model eye’s defocus measurements proves that holographic
fluidic auto-phoropter can functionally measure power variation induced by either the fluidic
phoropter or the eye model.
11.6 Nulling Error with Fluidic Holographic Auto-Phoropter
In section 11.5 we proved through shifting the mirror position of the model eye that our
wavefront sensor is capable of measuring wavefront error variation in the functional holographic
prototype. To further verify that our holographic prototype can in fact correct for wavefront
error we tested the holographic prototype with our fluidic lens. For both this null test and the
model eye test of prototype two we set the auto-phoropter so that it was stopped down to 3 mm.
The eye model mirror was shifted relative to the eye model lens so that -15 D of defocus power
error was induced and measured in the system with -.057 waves of aberration. We then adjusted
the power of the defocus fluidic lens to null this measured error until the wavefront sensor
identified zero defocus error. Figure 11-7 shows the setup with both the fluidic defocus lens and
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the model eye represented in the setup. Figure 11-8 shows the nulled out wavefront that was
outputted by the Shack-Hartmann wavefront sensor.
Figure 11-7 Nulling Power Error with Holographic Fluidic Auto-Phoropter: The defocus
component of the fluidic phoropter was inserted into the system. The eye model is adjusted to 15 D of defocus and nulled out with the fluidic defocus lens in the holographic fluidic autophoropter setup.
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Figure 11-8 Image Plane of Holographic Fluidic Auto-Phoropter: The Shack-Hartmann
image plane when -15 D of eye model error is nulled by the fluidic phoropter’s defocus lens.
11.7 Limits of Holographic Optical Design
The first holographic fluidic auto-phoropter was designed with the motivation of proof of
concept. We proved that we are capable of replacing the traditional telescope with holographic
optical elements designed as a holographic telescope. The next step is to shift the HOE’s reading
and writing wavelength to the light sources operable wavelength at 785 nm. This will allow for
us to achieve full transmission in the visible with our HOE’s and test in the NIR without
distracting the viewer from the scene in front of them. In the previous chapter we described the
shortfalls of the second prototype which were 1) Lack of 4f Imaging and 2) Field of View. We
will expand on these two topics as this holographic fluidic phoropter is a replication of that work
with a slightly different design in the physical positioning of the optics.
The field of view of the holographic design increased relative to the other auto-phoropter
designs. The size of the substrate that the HOE was embedded in was a 2’ or 50.8 mm glass
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plate. The HOE was set at a 900 angle, giving the lateral width of 36 mm’s perpendicular to the
optical axis. By replicating prototype two we know that the furthest distance of the HOE is 115
mm along the optical axis, giving a field of view of 17.3 o and hence no longer the limiting object
in the line of sight. Again, we calculate the field of view with zero power of the fluidic
phoropter. The limiting factor of the optical system now becomes the first beamsplitter that
brings the system field of view to 11.8o.
Remembering in section 9.4, we calculated the
maximum field passing through the fluidic lens was 14o relative to the 25 mm eye relief distance
between the eye and the flat of the fluidic phoropter. In order to maximize the field of view we
must be able to eliminate the second beamsplitter and bring the HOE to a closer distance of the
fluidic phoropter. This will cause the fluidic phoropter to become the limitations on the field of
view and not the auto-phoropter design.
It is possible to redesign the holographic system so that all beamsplitters are eliminated.
This second holographic design takes advantage of polarization in order to eliminate the last
remaining beamsplitter. The NIR source will be polarized in the p direction by placing a
polarizer in front of the source. The first HOE element will have an embedded layer that
function as a mirror for p-pol light at 785 nm, causing the p-pol light at 785 nm to reflect. As an
aside, there may be stray p-pol light near 785 nm passing through the first HOE to the second
HOE. The second HOE is designed so that p-pol light at 785 nm passes the light through the
element in order to eliminate the stray light from the system. Regressing, the 785 nm light that
reflects off of the first HOE is in the line of sight of the user. This p-pol light propagates through
the fluidic lens to the human eye or the model eye with the scattering screen. The majority of the
light exiting the retina upon reflection is no longer polarized. The unpolarized light propagates
back to HOE Lens 1. HOE Lens 1 is now a lens to the unpolarized light and becomes part of our
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telescopic system. HOE Lens 2 is placed at a proper distance from HOE Lens 1 to produce our
telescopic system. The light exiting the second HOE then propagates to the Shack-Hartman
wavefront sensor, thus eliminating all beamsplitters from the optical system.
HOE Lens 2 passes ppol light and acts as
lens for unpolarized
780 nm light
ShackHartmann
Sensor
Telescopic
HOE System
HOE Lens 1: reflects p-pol
light, transmits visible and
acts as lens for unpolarized
780 nm light
Stray p-pol
light
Unpolarized
780 nm light
Circular
Eye Chart
Eye
Transmitted
visible light
Polarizer
Fluidic
Lens
Reflected
p-pol
light
Source
780nm
Figure 11-9 Polarization Controlled Holographic Fluidic Auto-Phoropter Design: The
beamsplitters were eliminated from the first holographic design by the control of polarization.
Again, as the first holographic phoropter was a matching system to the second prototype,
it has had the same short falls in 4f imaging. We can expand further with our polarization
controlled HOE design in eliminating the shortfall of lacking 4F imaging. The reason we broke
the 4f design was to miniaturize the system. If we were to produce a 4F imaging system with the
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polarization controlled design we would need space for two elements between HOE lens 1 and
the eye for the fluidic phoropter and eye relief. The minimum distance of these two optical
elements is approximately 60 mm when we include tolerance. Therefore, the shortest focal
length for 4f imaging with HOE’s is with the two HOE lenses exhibiting focal lengths of 60 mm
and polarization control.
The length between the two HOE’s would be 120 mm or
approximately 4.7 inches. This size would be small enough to fit on a helmet sized fluidic autophoropter if desired. If we rotate the optical axis instead so we maximize Bragg efficiency the
height in the vertical direction will be less than 4.7 inches, hence making it more suitable for a
helmet sized holographic fluidic auto-phoropter design. Therefore, the next step for advancing
our holographic designs would be to design a table top setup with two HOE lenses designed with
60 mm focal lengths at a wavelength of 785 nm that have polarization control as described in
Figure 11-9.
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12.0 CONCLUSION AND FUTURE WORK
We have covered throughout the course of this dissertation the fundamental advantages
of optofluidic technology. Adaptive optic technology has revolutionized real time correction of
wavefront aberrations and optofluidic technology enabled us to produce real time corrective
lenses.
Fluidic lenses offered superiority relative to their solid lens counterparts in their
capabilities of producing tunable optical systems, that when synchronized produced real time
variable systems with no moving parts.
We have developed optofluidic fluidic lenses for
applications of applied optical devices as well as ophthalmic optic devices. This dissertation has
covered fluidic based devices for astigmatism and defocus correction. We then produced zoom
optical systems with no moving parts by synchronizing these fluidic lenses. The variable power
zoom power system incorporates two singlet fluidic lenses that were synchronized. The coupled
device has no moving parts and produced a magnification range of 0.1 x to 10 x or a 20 x
magnification variation. We further expanded the topics into chromatic aberration correction
with the design of our two fluid based variable focal length chromates.
The second half of this dissertation discusses the production of optofluidic technology in
ophthalmic applications.
We discussed experimental results in the production of a fluidic
phoropter which was produced through the combination of a defocus lens with two cylindrical
fluidic lenses orientated 45° relative to each other. We then coupled this optofluidic phoropter
with relay optics and Shack-Hartmann wavefront sensing technology to produce several designs
of fluidic auto-phoropter devices. The auto-phoropter systems combined a designed ShackHartmann wavefront sensor with the compact refractive fluidic lens phoropter that was reimaged
through various telescope orientations and designs.
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As we have covered several different topics there are many directions in which future
works can expand on. In the following subsections we will describe future work projects that
can advance our research with optofluidic devices. The following suggestions of future work will
be sequential with the order that the projects were discussed in this dissertation.
12.1 Wavefront Comparison of Freely Supported Edge vs. Clamped Edge Designs
It would be advantageous to measure the wavefront of the clamped edge design of fluidic
defocus lens two and compare the results to the freely supported edge of fluidic defocus lens one.
We have built two different designed fluidic defocus lenses. The majority of our systems have
applied the freely supported edge design in our optical designs, with the exception of our zoom
optical system and the future work of the double fluidic achromat. We analyzed the wavefront
measurements of the freely supported edge lens or defocus lens one to identify the outputted
wavefront. There was additional astigmatism in addition to defocus as we increased the defocus
power of the lens. Through our optimization approach described in Chapter 6 we are able to
correct for both astigmatism and defocus by stacking our two astigmatism and one defocus lens
together.
There are advantageous in knowing the wavefront of defocus lens two. One, we verify
the optical control that is achievable with clamped edge designs. It gives a clearer picture on
identifying the optimal clamping mechanism in the creation of our fluidic lenses. Secondly, if
the clamped edge design produces less astigmatism then the freely supported edge design,
assuming all other aberrations except defocus are negligible, we have decreased the amount of
time required for all fluidic auto-phoropter systems to correct for ocular aberrations. The amount
of iterations for compensation between the three lenses for astigmatism and defocus will be
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decreased, which causes for faster readings. It addition, by creating a larger spread between the
defocus and astigmatism wavefront measurements, we can improve on the physical control of the
lens and thus improve on the accuracy of our corrections.
12.2 Improving Fluidic Zoom with a Redesigned Terrestrial Keplerian Telescope
The zoom optical system showed a magnification range of 20 x but there are
improvements that can be done to the system to increase this range. We found that a loss of
throughput as caused by vigneting, reducing the resolvability of the image at larger
magnifications. Theoretically, the ranges of the two lens Keplerian system should have had a
greater magnification range then 20 x, but the image was unresolvable due to loss of light.
We can alter the traditional Keplerian telescope to a Terrestrial Keplerian telescope, also
known as a Relayed Keplerian Telescope, to increase the magnification range of our zoom
system. The input of a relay telescope will inverse the orientation of the image but will also
increase the amount of throughput through the optical system. This is significant as our system
should produce a larger magnification range with only increased throughput. By making the
relay lens into a fluidic lens, we now have three fluidic lenses in our new proposed system.
Syncing three fluidic lenses will also offer the advantage of increasing the magnification range of
the Keplerian Zoom system as we have brought more focal length control to the system. This
will most likely cause the system to increase in size but may be worth the tradeoff for the
advancement in magnifying power. This Keplerian design still requires the fixed lens to focus
the magnified power exiting the Keplerian telescope to the CCD plane.
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Fluidic
Objective
Lens
Fluid
Relay
Lens
fobj
zR
Fluid
Eye
Lens
z‘R
Fixed
Lens
CCD
-f eye
Figure 12-1 Terrestrial Keplerian Telescope in Zoom System: The modification to our Zoom
system that will improve throughput and magnification range.
12.3 Progression of Fluidic Achromat
The two membrane fluidic achromat has been explained in functionality but has not yet
been experimented, as not all parts have been completely machined. The next step for the
advancement in this project is in the testing of the two synced surfaces synced to produce an
achromatic lens. The testing has been explained in Chapter 5 and so we will add one additional
suggestion for the fluidic achromat. An even greater advancement for the fluidic achromat
would be to create a GUI that interfaces the achromat with the user. If the user can identify
the two fluids in a given achromat and the focal length that is desired, then we have in a sense
designed a digital achromatic lens. The GUI can cover multiple achromatic lenses and would
allow for control of multiple achromatic lenses at the same time. This will assist in the zoom
optical system designs as well as any other accommodating optical design one is interested in
creating. This will increase the research on producing synced microscopes, telescopes, and
other optical devices. An additional test that can be expanded on is to set the fluidic lenses in
the vertical direction and verify how gravity affects our membrane suspension with time.
12.4
Progression of the Fluidic Auto-Phoropter Systems
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There is much advancement that is achievable for the progression of this research. In
section 10.4 we discussed the next step in the testing process in verification of the 4f imaging
system of prototype three. This should be the next step to identify how the 4f imaging system
compares to prototype two. The compensation of the fluidic lenses for a given correction must
be compared after full correction is achieved for both systems. If the fluidic lenses are not
approximately the same magnitude from both results, then we have identified that we have
corrected for the optical systems and not for the users prescription with prototype two. In
addition, we will verify the amount of light loss that occurs with the two designs and if we need
to maintain 4f imaging. Light loss for a system with less than 15 W of power may require
signal amplification. It is possible to place a signal amplifier between the second beamsplitter
and the telescopic system of the off-axis designs. Signal amplification should also be examined
as a future direction of the work.
Once we established that our off-axis 4F imaging system
works, we should perform studies on the fluidic auto-phoropter accuracy to user prescriptions
and also the repeatability of the system.
To examine the fluidic auto-phoropter accuracy and repeatability, we must move onto the
next phase of testing, which is human testing. Here we will give an example of data collection
and what kind of future work can be covered through these examinations. A procedure for
testing would be to require two testing sessions per individual with a separation of about 6
months. Each testing session should last for less than 10 minutes. The individual will offer the
prescription that was given to them by their eye doctor so that we have reference points for each
user. If the individual has 20/20 vision then they will notify us of their 20/20 vision, as a control
group is required. The individual then looks into our binocular auto-phoropter systems. We
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should test as many systems as possible with each individual to identify variation between
optical designs and their relative prescription defined by the doctors. At least four targets at four
measured distances should be set so we can identify the accommodation of the user relative to
targeted planes. Both eyes should be measured with the device separately and then concurrently.
The sample size and age of the tested population is important in maximizing our test
results. The minimum population of subjects to be tested on should be at least 210 and we will
continue with this population size for explanation purposes. From these 210 subjects, we should
break the grouping down to 7 larger population groups spanning from 18 to 74 years of age with
each group spanning a range of 8 years. Each group will have three sub-populations. A subpopulation will occur of 10 subjects that offer 20/20 vision, 10 subjects that require corrective
eye wear, and 10 subjects with corrective eye surgery for each subgroup. This means that ever
population will have three sub-populations where there are a total of 21 sub-groups for this
research: 1) a group with 20/20 Vision, 2) a group with corrective eye wear, and 3) a group with
corrective eye surgery. While we run the experiments, the users in the corrective eye subgroup
must not wear contact lenses or other corrective eye wear. Thus, the people excluded from this
research are those who are under the age of 18 and over the age of 75 years of age.
Data from this experiment allows for us to extract information from both our system and
the human populations. The results measured will be analyzed to determine the quality of the
system and the accuracy of our objective vs. subjective eye examinations. Also, the relation of
age to the accuracy of the test results is also measured. The purpose of the second test 6 months
following the initial testing is to ensure the repeatability of the auto-phoropter. This testing
approach enables us to identify the effects of Presbiopia for various populations as we have
identified sub-groups at different ages. These subgroups will identify how accurately our system
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measures visual performance of age related changes. In addition, we would have data for
corrective eye surgery and for healthy eyes. In essence, with at least 210 subjects we can verify
accommodation in addition to prescription and their effects for different eye correction groups
and healthy groups. The separation of data into 21 sub-groups will allow for information that
can test for additional concepts in the future.
In addition, we can develop an approach for the correction of convergence and
misalignment of the eye. There are conditions such as Esotropia, Exotropia, Hypertropia and
Hypotropia that can be corrected for by designing a fluidic prism. By inserting fluid into the
prism, we can adjust the wedge and thus the prism power. This fluidic prism would be a great
tool in the correction of individuals with a lack of control for the convergence of their eyes.
12.5
Progression of the Fluidic Holographic Auto-Phoropter Systems
We can further expand on the advancements found in section 11.7 in the discussion of
the next steps for the holographic fluidic auto-phoropter project. The next steps are to shift the
HOE’s so that the system operates at 785 nm and shows a functioning system with low intensity
light. After this step is achieved, the following step as described in section 11.7 is to eliminate
the beamsplitters in the optical system through the use of polarization control. With the
elimination of the beamsplitters we can compress the system further through eliminating space
needed for the beamsplitter, but also through the shorter focal length required of the
holographic lenses for 4F imaging. The distance between holographic lens 1 and the eye
location is reduced to 60 mm for the fluidic lens separation and eye relief. This suggests that
with 60 mm focal length holographic lenses, we can produce a 4F based holographic fluidic
auto-phoropter. We can further this design with a couple more advancements beyond section
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11.7. We can change the lenticular array for the Shack-Hartmann wavefront sensor so that it is
replaced with HOE based lenses. It would be interesting to identify how the system compares
between a traditional lenslet array and an HOE based lenslet array. A second additional system
advancement that can be applied to all of our fluidic auto-phoropter systems would be an off
axis pupil imaging device. In the second half of the dissertation we have identified the
significance of pupil size to our optical system. By adding an off axis imaging system we can
verify the iris size as we test the users prescription, giving us further data about the
accommodation of the user as he naturally views various depths. Figure 12-2 shows the
combination of the HOE based holographic fluidic auto-phoropter with polarization control
combined with an imaging system to measure the pupil size and also a HOE lenslet array for the
Shack-Hartmann wavefront sensor. Figure 12-3 further expands the system with the same
features as Figure 12-2 except now we have added dimensions to produce the proper
geometrical positioning of our optics to produce a 4f imaging system in addition to our desired
features. This last holographic fluidic auto-phoropter has the same polarization features for the
HOE’s as Figure 12-2, geometrically has 4f imaging, applies our fluidic based adaptive optics
fluidic technology, offers off axis imaging to identify pupil size, and also proposes an advanced
wavefront technology where the Shack-Hartman wavefront sensor takes advantage of
holographic optical technology. The 4f advanced holographic fluidic auto-phoropter is also very
small in size, with approximately a 3” by 6” area offering us the opportunity to make this device
mobile. If the HOE wavefront sensor does not function properly we can revert back to the
traditional Shack-Hartmann wavefront sensor.
242
ShackHartmann
Sensor
HOE
Based
Lenslet
Array
HOE Lens 2 passes ppol light and acts as
lens for unpolarized
780 nm light
Telescopic
HOE System
HOE Lens 1: reflects p-pol
light, transmits visible and
acts as lens for unpolarized
780 nm light
Stray p-pol
light
Eye
Circular
Eye Chart
Transmitted
visible light
Unpolarized
780 nm light
Polarizer
Fluidic
Lens
Source
780nm
Reflected
p-pol
light
Off-Axis Pupil
Imaging
Figure 12-2 Advanced Holographic Fluidic Auto-Phoropter with Pupil Imaging: Expansion
on system described in Figure 11-8. We have modified the auto-phoropter system in this design
so that the lenslet array of the Shack-Hartmann Sensor is designed with holographic optical
elements. In addition, we added an off axis imaging system to identify the iris size and thus the
pupil size. This system again takes advantage of polarization control and our holographic
telescope coupled with our fluidic phoropter.
243
ShackHartmann
Sensor
HOE Lens 2
F = 60 mm
Substrate Size = 2"
HOE
Based
Lenslet
Array
2f = 120 mm
or 4.725"
Telescopic
HOE System
HOE Lens 1
F = 60 mm
Substrate Size = 2"
1f = 60 mm
Circular
Eye Chart
Eye
Transmitted
visible light
Polarizer
Fluidic
Lens
Source
780nm
Off-Axis Pupil
Imaging
Figure 12-3 4F Advanced Holographic Fluidic Auto-Phoropter With Pupil Imaging: With
the above defined distances and focal lengths we have designed a 4f imaging system with our
fluidic phoropter, pupil imaging system, advance holographic based wavefront technology and a
polarization controlled holographic telescope.
12.6 Mobile Holographic Fluidic Auto-Phoropter
There are many disadvantaged regions in the world that do not have access to phoropters
and eye care. It would be highly advantageous for a phoropter system to become mobile. As is
seen in Figure 12-3, the size of our 4F advanced holographic fluidic auto-phoropter can fit within
244
a helmet. This helmet can hold two of these optical systems next to each other. The next step
after testing and verifying that this system functionally measures and corrects for prescriptions is
to set the system into a helmet and make it mobile. The following figures show a system without
pupil imaging but modifications can be made to add this feature to our binocular system / helmet
display. The helmet display was modeled in SolidWorks to identify the coupling of the two
holographic auto-phoropters into a single system. The actuators for the fluid pump controls
would be inside the periphery of the casing. The inter-pupilary distance is taken into account by
adjusting the separation on the helmet with a knob between the two monocular setups. We can
make advancements into interfacing with other mobile devices to read out prescriptions and
further the advancement of these research projects.
245
ShackHartmann
Sensor
Telescopic
HOE System
Circular
Eye Chart
Eye
Polarizer
Fluidic
Lens
Source
780nm
ShackHartmann
Sensor
Telescopic
HOE System
Circular
Eye Chart
Eye
Polarizer
Fluidic
Lens
Source
780nm
Figure 12-4 Binocular Advanced 4F Holographic Fluidic Auto-Phoropter Without Pupil
Imaging: This binocular setup is set in sequence next to each other. Both systems are in the
north south direction relative or perpendicular to the line of sight of the users. This binocular
system fits inside a helmet for a mobile eye exam.
246
Figure 12-5 Mobile Binocular Helmet With Two Advanced 4F Holographic Fluidic AutoPhoropter Designs: The helmet is applied to combine two monocular setups and account for
inter-pupilary separation between the users eyes.
247
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