Master Thesis
Assembly and proving of a wave front
sensing confocal Scanning Laser
Ophthalmoscope
Christina Schwarz
Supervisors: Prof. Dr. Frederick W. Fitzke, University College London (UK)
Prof. Dr. Josef F. Bille, Universität Heidelberg (Germany)
March 29, 2007
Abstract:
Confocal Scanning Laser Ophthalmoscopy is used to image the
fundus of the living eye. In theory, this technique can be used to
observe single cells of the retina. Unfortunately, vision of most eyes
is decreased by higher-order aberrations, that cannot be corrected
by glasses or contact lenses. This is also the reason why resolution in
confocal Scanning Laser Ophthalmoscopy is not as high as expected.
By the use of adaptive optics (AO) resolution can be dramatically
increased. Implementing a wave front sensor into a conventional
confocal Scanning Laser Ophthalmoscope (cSLO), therefore, is the
first step to set up a compact adaptive-optical cSLO. In this work a
Shack-Hartmann wave front sensor was implemented into a slightly
modified Heidelberg Retina Tomograph (HRT) and aberrations of
model eyes were measured. Results show that this system is now
ready for testing on living eyes.
Zusammenfassung:
Um den Augenhintergrund des lebendigen Auges abzubilden
bedient man sich der konfokalen Scanning Laser Ophthalmoskopie.
Theoretisch kann diese Technik genutzt werden, um einzelne Zellen
der Retina zu beobachten. In der Praxis ist das Sehvermögen
des Auges jedoch im Allgemeinen durch Aberrationen höherer
Ordnungen beeinträchtigt, die weder mit Brille noch mit Kontaktlinsen korrigiert werden können. Aus demselben Grund ist die
Auflösung eines konfokalen Scanning Laser Ophthalmoskops (cSLO)
in in-vivo-Anwendung am Auge schlechter als erwartet. Durch das
Prinzip der adaptiven Optik (AO) kann die Auflösung erheblich
verbessert werden. Der Einbau eines Wellenfrontsensors in ein
handelsübliches cSLO ist daher der erste Schritt, um ein kompaktes
adaptiv-optisches cSLO zu entwickeln. In dieser Arbeit wurde ein
Hartmannn-Shack-Wellenfrontsensor in einen leicht veränderten
Heidelberg Retina Tomographen (HRT) eingebaut und Aberrationen
von Modellaugen gemessen. Die Ergebnisse haben gezeigt, dass
dieser Aufbau nun bereit ist, an lebenden Augen getestet zu werden.
Contents
1 Introduction
1
2 The Human Eye
2.1 Anatomy . . . . . . . . . . . . . . . . . . .
2.2 Ametropia . . . . . . . . . . . . . . . . . .
2.2.1 Myopia . . . . . . . . . . . . . . .
2.2.2 Hyperopia . . . . . . . . . . . . . .
2.2.3 Astigmatism . . . . . . . . . . . . .
2.2.4 Irregular Astigmatism . . . . . . .
2.3 Dynamics of the Eye . . . . . . . . . . . .
2.4 Pathology . . . . . . . . . . . . . . . . . .
2.4.1 Age-related Macular Degeneration .
2.4.2 Glaucoma . . . . . . . . . . . . . .
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3 Confocal Scanning Laser Ophthalmoscopy
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3.1 Principle of the cSLO . . . . . . . . . . . . . . . . 12
3.2 Resolution of Confocal Images . . . . . . . . . . . 14
3.3 The Heidelberg Retina Tomograph . . . . . . . . 15
4 Adaptive Optics
4.1 The Wave Front and Wave
4.2 Wave Front Sensors . . . .
4.3 Phase Modulators . . . . .
4.4 The Control Algorithm . .
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Aberrations
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Contents
5 Setup
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5.1 Hardware . . . . . . . . . . . . . . . . . . . . . . 27
5.2 Software . . . . . . . . . . . . . . . . . . . . . . . 31
6 Results
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6.1 Measurement and Evaluation . . . . . . . . . . . 32
6.2 Discussion and Future Prospect . . . . . . . . . . 36
Bibliography
38
ii
Chapter 1
Introduction
Adaptive correction has its origin in astronomy. Horace Babcock was the first
one who proposed solution to the problem of imaging stars with ground-based
telescopes [1], which lies in the turbulent, rapidly changing atmosphere that
significantly degrades image quality. As the technique of measuring atmospheric aberrations and building and controlling deformable mirrors is very
complex, it took several years until the first successful demonstration. Most
of the ground-based telescopes around the world are now equipped with this
technique and therefore can sometimes achieve images with even higher resolution than those obtained by the Hubble space telescope [2].
The use of AO is not limited to astronomical imaging, and in the past few
decades there has been a rapid expansion in the applications for which adaptive optics has proven valuable. Vision scientists and ophthalmologists have
long been interested in imaging cellular structures in the living retina to examine photoreceptor properties in vivo, and to more precisely characterize
retinal disease. Unfortunately, nearly every human eye suffers from higher
order aberrations induced mainly by the lens and cornea that degrade retinal image quality (like the turbulent atmosphere degrades image quality in
astronomy) and limit spatial vision. So a promising application of AO is the
imaging of the living retina at high resolution, which became possible in the
meantime.
One of the pathfinders of adaptive optics in vision science was Smirnov who
employed a subjective vernier task to measure the retinal misalignment of
rays entering through different parts of the pupil. He recognized that this
method could theoretically allow for the fabrication of contact lenses that
corrected higher order aberrations in the eye but thought that the lengthy
calculations required to compute the wave aberration made his approach
impractical. He could not foresee the rapid development of computer technology that would eventually make it possible to do these calculations in a
matter of milliseconds.
1
1. Introduction
The headstone for clinical adoption of adaptive optics in vision science was
laid when Junzhong Liang demonstrated at the University of Heidelberg,
that it was possible to adapt the Shack-Hartmann wave front sensor, typically used in optical metrology, to measure the eye’s wave aberration [3].
This proved to be the key development that paved the way to closed-loop
AO systems for the eye. The simplicity of the Shack-Hartmann method and
the fact that it is the wave front sensor used in most astronomical AO systems made it easier to translate adaptive optics to the eye. This method was
also amenable to automation and the wave aberration could be measured
and corrected in real-time [4].
It was also at the University of Heidelberg the first attempt of using a deformable mirror to improve retinal images in a scanning laser ophthalmoscope
was made. Thus they were able to correct the astigmatism in one subject’s
eye by use of a deformable mirror [5].
The application of AO to increase the resolution of retinal images promises
to greatly extend the information that can be obtained from the living retina.
Adaptive optics now allows the routine examination of single cells in the eye
such as photoreceptors and leucocytes, providing a microscopic view of the
retina that could previously only be obtained in excited tissue. The ability to see these structures in vivo provides the opportunity to noninvasively
monitor normal retinal function, the progression of retinal disease, and the
efficacy of therapies for disease at a microscopic spatial scale.
In this work a compact wave front sensing confocal Scanning Laser Ophthalmoscope is built out of a conventional Heidelberg Retina Tomograph and
tested in order to set up an adaptive-optical confocal Scanning Laser Ophthalmoscope later on.
This work is organized as follows:
In chapter 2 the necessary medical background for this work is given, including ametropia, aberrations, and the major diseases of the eye. The technical
background of confocal Scanning Laser Ophthalmoscopes is given in chapter 3. Theory for adaptive optics is explained in chapter 4, as well as all
technical components of an adaptive-optical closed-loop system. In chapter 5 I will describe the setup for this work in detail. Finally, results are
presented and discussed in chapter 6. Here also a future prospect is given.
2
Chapter 2
The Human Eye
This chapter will give a brief review on the anatomical structure and basic
function of the eye [6, 7, 8]. As there are many diseases that deteriorate
vision quality and for which retinal imaging is advantageous only two major
diseases are presented here [9].
2.1
Anatomy
Although the eye is commonly referred to as the globe, it is not really a true
sphere but a composition of two spheres with different radii, one set into the
other as shown in Figure 2.1. The anterior sphere is the smaller and more
curved of the two and is called the cornea, which is a completely transparent
structure. The posterior sphere is a white opaque fibrous structure called the
sclera. The cornea and the sclera encase the eye and form a protective shell
for all the delicate tissues within. The human eye measures approximately
24 mm in all its main diameters in normal adults.
Most of the refraction of the eye takes place through the cornea having a
convex surface, that acts as a powerful lens. Thereby, the refraction of the
anterior side of the cornea is responsible for 49 dpt of the refraction1 and
the posterior side of the cornea again detracts 6 dpt from it2 . As the cornea
has a thickness of less than 1 mm at its periphery the lens-maker’s formula
(which says that for a thin lens, the power is approximately the sum of the
surface powers) can be used and in doing so this yields a refractive power of
Dcornea = 43 dpt altogether [8].
The opaque sclera forms the posterior five sixths of the eye’s protective coat.
At its most posterior portion, the site of attachment of the optic nerve, the
−nair )
Dant = (ncornea
= (1.377−1)
rant
0.0077 m ≈ 49 dpt
(n
−ncornea )
2
Dpost = aeq rpost
= (1.336−1.377)
≈ −6 dpt
0.0065 m
1
3
2. The Human Eye
sclera becomes a thin, sieve like structure called the lamina cribrosa. It is
through this sieve that the retinal fibers leave the eye to form the optic nerve.
The pigmented iris is perforated at its center by a circular aperture called
the pupil and therefore has the physical meaning of a pinhole. Contraction
of the iris, which occurs in response to bright light, is accomplished by the
activity of a flat, washer like muscle buried in its substance just surrounding
the pupil opening. Between the iris and the cornea the anterior chamber of
the eye is located that is filled by a clear fluid called the aqueous humor.
The ciliary muscle within the ciliary body releases the tension of the zonular fibers, controlling the size and shape of the lens. This in turn allows
the lens of the eye to bulge and increase its power. Therefore, this muscle
directly controls the focusing ability of the eye, a process which is called
accommodation.
Figure 2.1: This figure shows the sagittal section of the human eye [7].
The lens of the eye is a transparent biconvex structure situated right behind the iris and therefore about 5 mm behind the cornea. The diameter
of the lens is about 9 to 10 mm and its refractive power is about 19 dpt in
the emmetropic eye. To calculate the refractive power of the eye in total
Gullstrand’s formula3 is used and equals approximately 59 dpt.
The choroid’s main function is to provide nourishment for the outer layers
of the retina. The retina varies in thickness and elevation, according to key
anatomical features, pathological conditions, and changes with age. It contains all the sensory receptors for the transmission of light which are divided
3
d
m
2
D = Dcornea +Dlens − naeq
Dcornea Dlens = 43 dpt+19 dpt− 0.005
1.336 ·43·19 dpt ≈ 59 dpt
4
2. The Human Eye
Figure 2.2: This figure shows a simplistic scheme of a human retina [7].
into two main populations - the rods (∼ 125 million) and the three different
types of cones (∼ 6 million). Rods function best in dim light whereas the
cones function best under daylight conditions. They enable us to see small
visual details with great acuity. Vision with the rods is relatively poor but
they detect movement. Color vision is totally dependent on the integrity of
the cones which show different spectral sensitivities. According to their maximal spectral reflectivity at 565 nm, 535 nm, and 440 nm respectively, they
are assigned to the fundamental colors red, green and blue. The cones form
a concentrated area in the retina known as the fovea, which lies in the center
of the macula lutea, usually less than 10° from the optical axis of the eye.
Damage to this area can severely reduce the ability to see directly ahead.
When we see an object the following process takes place: Light rays enter
the eye through the cornea, move through the pupil, which is surrounded by
Iris to keep out extra light, the crystalline lens and the vitreous humor and
fall onto the retina, which processes and converts incident light to neuron
signals. The neuron signals finally are transmitted through the optic nerve
towards the brain, where the images are interpreted.
2.2
Ametropia
More than half of the world’s population is affected by any kind of ametropia.
Among the monochromatic aberrations the most frequently are defocus (myopia and hyperopia, respectively) and astigmatism. The amount of aberra-
5
2. The Human Eye
tion for the complete eye arises from the amount of aberration of the cornea
and the amount of aberrations of the internal optics and was found to be
smaller than the sum of the last-mentioned. Indeed this fact indicates that
the first surface of the cornea and internal optics partially compensate for
each others aberrations and produce an improved retinal image [10] but in
general it is still far from perfect. Nowadays these aberrations can be corrected in most instances by spectacles or contact lenses.
2.2.1
Myopia
Myopia or nearsightedness is a refractive defect of the eye in which collimated
light produces image focus in front of the retina when accommodation is
relaxed. This occurs from the eye being too long for its optical power or
optically too powerful for its axial length. People with myopia typically can
see nearby objects clearly but distant objects appear blurred. Myopia can
be corrected by a concave lens placed in front of the eye.
2.2.2
Hyperopia
Hyperopia, also known as hypermetropia or colloquially as farsightedness, is
a defect of vision caused by the eyeball being too short or the lens not being
able to become round enough. People affected by hyperopia are unable to
focus on near objects, and in extreme cases unable to focus on objects at
any distance. As an object moves towards the eye, the eye must increase
its power to keep the image on the retina. If the power of the cornea and
(a) Myopia
(b) Hyperopia
Figure 2.3: In this figure both types of defocus and their correction methods are
illustrated. Myopia [11] is corrected by a diverging or concave lens whereas Hyperopia [12] is corrected by a converging or convex lens.
6
2. The Human Eye
lens is insufficient, as in hypermetropia, the image will appear blurred. Minor amounts of hyperopia are sometimes left uncorrected, however, larger
amounts may be corrected with convex lenses in eyeglasses or contact lenses.
One particular type of hyperopia is presbyopia which specifies the eye’s diminished power of accommodation that occurs with aging. The most widely
held theory is that it arises from the loss of elasticity of the crystalline lens,
although changes in the lens’s curvature from continual growth and loss of
power of the ciliary muscles have also been postulated as its cause. Presbyopia is not a disease as such, but a condition that affects everyone at a
certain age. The first symptoms are usually noticed between the ages of 40
and 50.
2.2.3
Astigmatism
Astigmatism is a refractive error of the eye in which there is a difference
in degree of refraction in different meridians. It is typically characterized
by an aspherical, non-figure of revolution cornea in which the corneal profile slope and refractive power in one meridian is greater than that of the
perpendicular axis. For example, the image may be clearly focused on the
retina in the horizontal (sagittal) plane, but not in front of the retina in the
vertical (tangential) plane as it is shown in Figure 2.4. Astigmatism causes
difficulties in seeing fine detail, and can often be corrected by glasses with a
cylindrical lens (i.e. a lens that has different radii of curvature in different
planes), contact lenses, or refractive surgery.
Figure 2.4: In an astigmatic eye sagittal and horizontal image plane do not coincide. To correct astigmatism cylindrical lenses are used.
7
2. The Human Eye
2.2.4
Irregular Astigmatism
Any other aberration as the above mentioned, the clinician summarizes as
irregular astigmatism. Usually, those aberrations cannot be corrected. One
case irregular astigmatism can be corrected is the appearance of scars on
the cornea. If so correction is possible with hard contact lenses as tear
liquid concentrates between the cornea and the contact lens. The lower
difference between the refractive indexes of the liquid and the cornea reduces
the aberrations the cornea’s irregular shaped surface causes.
2.3
Dynamics of the Eye
The eye is not a static system but moves incessantly [13]. This uncontrollable
action makes it reasonable to not correct the eyes aberrations statically but
rather dynamically or adaptive-optically [4]. Responsible for these movements are several muscles as illustrated in Figure 2.5. The medial rectus
muscle moves the eye toward the nose, or adducts the eye, the lateral rectus
muscle moves the eye horizontally to outer side, or abducts the eye and the
superior rectus muscle elevates the eye primarily, whereas the inferior rectus
Figure 2.5: This figure shows the six ocular muscles, that keep the eye moving
incessantly [7].
8
2. The Human Eye
muscle depresses the eye. The superior oblique muscle functions primarily
as an intorter by rotating the vertical and horizontal axis of the eye toward
the nose. The inferior oblique muscle acts to extort the eye and also serves
to elevate the eye.
Humans do not look at a scene in a steady way. Instead, the eyes move
around, locating interesting parts of the scene. Saccades are quick, simultaneous movements of both eyes in the same direction. The saccade is the
fastest movement of an external part of the human body. The peak angular
speed of the eye during a saccade reaches up to 500°/s. One reason for saccades of the human eye is that only the central part of the retina, the fovea,
can image fine details. Microsaccades are a kind of fixational eye movement and typically occur during prolonged visual fixation. Microsaccades
are also simultaneous movements, have amplitudes of 2-5’ and last for 10-20
ms, whereas Microtremor occurs independently in both eyes, has amplitudes
of 5-15” and appears with a frequency of up to 90 Hz.
2.4
Pathology
Laser Scanning Ophthalmoscopy is an important imaging technique to diagnose
diseases of the eye’s fundus. The color of
the fundus is characterized by the mixture of reflected wavelengths determined
by the amount of light reflected at various surfaces in the eye. Different retinal structures are more easily viewed at
different wavelengths of light [14]. Light
of short wavelengths is predominantly reflected by the retinal layers and used to
view macular pigmentation and arcuate
Figure 2.6: Healthy retina as it is
fiber bundles. As wavelength increases,
seen through an ophthalmoscope [7].
seeing retinal and choroidal vessels in eyes
without heavy pigmentation becomes easier. With wavelengths of 600 nm or
above, there is a large increase in light penetration, and the choroidal vasculature becomes apparent in darkly pigmented fundi. Near-infrared imaging
is well suited for investigating sub-retinal structures.
9
2. The Human Eye
2.4.1
Age-related Macular Degeneration
Age-related macular degeneration (AMD) is
a common retinal problem of the aging eye
and a leading cause of blindness in the industrialized world [15]. Both types of AMD
affect the macula, the part of the eye that
allows to see fine detail. Wet AMD occurs when abnormal blood vessels behind
the retina start to grow under the macula.
These new blood vessels tend to be very
fragile and often leak blood and fluid. The
blood and fluid raise the macula from its
normal place at the back of the eye. In this
case damage to the macula occurs rapidly Figure 2.7: Retina affected by
and so loss of central vision can occur quickly. AMD as it is seen through an
ophthalmoscope [7].
Dry age-related macular degeneration occurs when the light-sensitive cells in the macula slowly break down, blurring
central vision in the affected eye. As less of the macula functions, central
vision is gradually lost in the affected eye. Dry AMD generally affects both
eyes. One of the most common early signs is drusen. Drusen were initially described by the Dutch physiologist Donders who named them for the German
word for geode, based on their glittering appearance. Drusen are tiny yellow
or white accumulations of extracellular material that build up in Bruch’s
membrane of the eye.
Still scientists are unclear about the connection between drusen and AMD,
but they do know that an increase in the size or number of drusen raises a
person’s risk of developing either advanced dry AMD or wet AMD. However,
the presence of a few small drusen is normal with advancing age, and most
people over 40 have some drusen.
10
2. The Human Eye
2.4.2
Glaucoma
Glaucoma is not only one but a group of diseases of the optic nerve involving loss of retinal ganglion cells in a characteristic pattern
of optic neuropathy [9]. Although raised intra ocular pressure is a significant risk factor for developing glaucoma, there is no set
threshold that causes glaucoma. Untreated
glaucoma leads to permanent damage of the
optic nerve and resultant visual field loss,
which can progress to blindness. A fact is,
that Glaucoma is the second leading cause
of blindness in the world. The two main
Figure 2.8: Retina affected by types of glaucoma are primary open angle
Glaucoma as it is seen through an glaucoma (POAG), and primary angle cloophthalmoscope [7].
sure glaucoma (PACG). Primary open angle glaucoma also called chronic glaucoma is the most common type. This
develops slowly so that any damage to the nerve and loss of sight is gradual.
The term ’open angle’ refers to the angle between the iris and sclera which
is normal, in contrast to primary angle closure glaucoma where the angle is
narrowed. In this condition there is a sudden increase in the pressure within
one eye and the eye quickly becomes painful and red.
Figure 2.9: To distinguish between different forms of Glaucoma it is important to
measure the chamber angles of the patient’s eyes [16].
11
Chapter 3
Confocal Scanning Laser
Ophthalmoscopy
Confocal scanning laser tomography is currently the most widespread nonphotographic technique for imaging the optic disc and peripapillary retina in
glaucoma. Although there are several available instruments, that use scanning laser tomography, almost all the published clinical and experimental
work, like this one on hand as well, is based on the Heidelberg Retina Tomograph (HRT) produced by Heidelberg Engineering GmbH in Germany.
3.1
Principle of the cSLO
With the introduction of the ophthalmoscope by Hermann von Helmholtz in
1850 in vivo visualisation of the human fundus was enabled, and therefore
had a major impact in the understanding of many eye conditions. In 1980,
Webb’s group from Boston created a device that used a laser light source to
illuminate the fundus and produce an image of it on a television monitor [17].
The scanning laser ophthalmoscope (SLO), as it was termed later on, provides
a high quality image of the fundus using less than 1% of the light necessary to
illuminate the fundus with conventional light ophthalmoscopy. At any instant
only one small area of the retina is illuminated, and the light returned from
this point through the whole pupil is collected by a photomultiplier tube,
which drives a TV monitor. Each pixel on the monitor corresponds directly
to a pixel of the fundus. As the illuminating spot scans the fundus, the
electron beam scans in synchrony the TV screen, and a picture is built up.
To improve the contrast and resolution of the SLO, the confocal mode is
used. In this mode, only light which is reflected from the focal plane of the
12
3. Confocal Scanning Laser Ophthalmoscopy
laser is detected by the photodetector. Light reflected or scattered by other
retinal layers is ignored. Confocality of the system is achieved by placing
a pinhole in front of the detector, which is conjugate to the laser focus.1
The size of the pinhole determines the degree of confocality, so that a small
pinhole aperture will give a highly confocal image.
1
Conjugate points are defined as any pair of points such that all rays from one point
are imaged on the other within the limits of validity of Gaussian optics. This applies
accordingly to conjugate planes.
Figure 3.1: The optical path in confocal microscopes: Light emitted by a laser
source (1) illuminates via a beam splitter (2) and an objective (3) the specimen
(4). Reflected light transmits the objective and the beam splitter again, passes
the ocular lens and falls onto a confocal pinhole. This aperture allows light to
transmit, if it arises out of the focal plane, whereas light arising out of another
plane below or above the focal plane is blocked by the pinhole. A detector (6)
passes the information on to a PC, which can progress the images.
13
3. Confocal Scanning Laser Ophthalmoscopy
3.2
Resolution of Confocal Images
(a) I(u) = I0 · sinc2 ( u4 )
(b) I(u) = I0 · sinc4 ( u4 )
Figure 3.2: These figures show an intensity distribution of a spot imaged by a
widefield microscope (a) and by a confocal microscope (b) in comparison.
In Figure 3.2 axial intensity distributions of a point source imaged by a
widefield microscope and confocal microscope are compared [18, 19]. In
widefield microscopy the distribution determined as I(u) = I0 · sinc2 ( u4 )
has side maxima that can be seen clearly. The variable u stands here for
a
u = 2π
z with the aperture radius a, the illuminating wavelength λ, and the
λ f
focal length f. In confocal microscopy the shown distribution is described
by I(u) = I0 · sinc4 ( u4 ). It is slimmer than the former mentioned and side
maximums can hardly be recognized. This becomes important if two object
points of very different intensity and small distance between each other are
imaged. In the case of widefield microscopy it is possible that the darker spot
14
3. Confocal Scanning Laser Ophthalmoscopy
lies in a side maximum of the brighter one and therefore cannot be seen. In
the case of confocal microscopy in contrast side maxima are less significant
and the darker spot can be identified.
3.3
The Heidelberg Retina Tomograph
The Heidelberg Retina Tomograph (HRT) is a confocal laser scanning system for acquisition and analysis of the posterior segment of the eye [20]. This
instrument consists of a camera head mounted on a slit-lamp-type stand, a
control panel for operation, and a computer for control and for the display,
acquisition, processing, and storage of data. The camera head contains a
diode laser, emitting light at a wavelength of 670 nm, and a confocal optical
system, which contains a pinhole situated in front of the detector, and a photodiode, that detects the intensity of the light reflected from the fundus.
By scanning both horizontally and vertically
in one focal plane, the instruments acquires a
two-dimensional confocal image. Varying the
depth of the focal plane allows acquisition of
images from other planes along the z-axis (perpendicular to the optical axis). The image
resolution on each plane is 256×256 picture
elements (pixels), resulting in 65,536 measurements per image. An entire scan contains 32
confocal section images that are equally spaced
along the z-axis, whereas the operator can vary
the total scan depth and scan area, depending
on the size of the optic disc and depth of the
Figure 3.3: HRT as it is avail- optic cup. Because of the relatively long acable for doctor’s practices
quisition time and the high resolution of these
devices, the confocal section images must be aligned to correct for any horizontal or vertical eye movements during image acquisition. This alignment
procedure ensures that each pixel location in all of the section images corresponds to the same transverse location on the fundus, allowing a graphical
representation of the intensity values for that location (the intensity, or zprofile) over all image depths. Using the intensity and depth values of each
pixel, the software generates a topography and reflectivity image. The primary utility of any optic disc imaging technique is to determine whether there
is abnormality (detection), like glaucoma for instance, and whether there is
a change (progression) in the optic disc.
15
Chapter 4
Adaptive Optics
In astronomy adaptive optics (AO) is used to overcome the blurring effects
of atmospheric turbulence, the fundamental limitation on the resolution of
ground-based telescopes. More recently, AO has found applications in other
areas, most notably vision science, where it is used to correct for the eyes’
wave aberration [21].
Since adaptive-optical systems are control systems, they consist of at least
four items: A control variable, in our case the wave front, is needed, which
should be corrected onto a setpoint value. A sensor determines the actual
value of the variable to be controlled. In adaptive optics this device is known
as a wave front sensor. An actuator is able to modulate the control variable.
In case of a wave front as control variable the actuator is a phase modulator.
A control system (including a specific control algorithm) can convert the
wave aberration measurements made by the wave front sensor into a set of
actuator commands that are applied to the wave front corrector.
4.1
The Wave Front and Wave Aberrations
In geometrical optics a wave front is the set of all points with same optical
path length away from a particular object point. In the wave picture the
wave front is a plane of constant phase which is always perpendicular to
light rays.
The image-forming properties of any optical system, in particular the eye,
can be described completely by the wave aberration. It is defined as the
difference between the perfect (spherical) and the actual wave front for every
point over the eye’s pupil. A perfect eye (without aberrations) forms a perfect
retinal image of point source (Airy disc). In reality, however, imperfections
in the refracting ocular surfaces generate aberrations that produce a larger
16
4. Adaptive Optics
and, in general, asymmetric retinal image. As in this work a monochromatic
light source is used only monochromatic aberrations are discussed below.
The aberrations of the complete eye can be measured using a variety of different subjective and objective techniques, for instance the Shack-Hartmann
wave front sensor like in this work. By using the Zernike representation (according to the Optical Society of America’s Standards for reporting Optical
Aberrations [22]), the wave aberration W (r, Θ) can be represented with a
Zernike polynomials expansion
W (r, Θ) =
∞ X
n
X
m
cm
n Zn (r, Θ)
≈
N
n
X
X
m
cm
n Zn (r, Θ)
,
(4.1)
n=0 m=−n
n=0 m=−n
m
where cm
n are scalars and Zn are the Zernike polynomials, a set of functions
that are orthonormal over the continuous unit circle. These functions are
usually defined in polar coordinates (ρ, Θ), where ρ is the radial coordinate
ranging from 0 to 1 and Θ is the azimuthal component ranging
p from 0 to
2π. The conventional definition of polar coordinates ρ =
x2 + y 2 and
−1
Θ = tan (y/x) is used here.
Each of the Zernike polynomials consists of three components: a normalization factor, a radial-dependent component and an azimuthal-dependent
component. In this work the double indexing scheme is used for unambiguously describing these functions, with the index n describing the highest
power (order) of the radial polynomial and the index m describing the azimuthal frequency of the sinusoidal component. So the Zernike polynomials
are defined mathematically by
(
|m|
Nnm Rn (ρ) cos (mΘ)
for m ≥ 0,
m
Zn (ρ, Θ) =
,
(4.2)
m |m|
−Nn Rn (ρ) sin (mΘ) for m < 0
where Nnm is the normalization factor described in more detail below and the
|m|
radial component Rn (ρ) is given by
(n−|m|)/2
Rn|m| (ρ)
=
X
(−1)s (n − s)!
i h
i ρn−2s
n+|m|−s
n−|m|−s
s!
!
!
2
2
h
s=0
.
(4.3)
The normalization is given by
s
Nnm =
2(n + 1)
1 + δm0
,
(4.4)
where δm0 is the Kronecker delta function. The values of both n and m are
always integers or zero. In addition, n can only take on positive values and
17
4. Adaptive Optics
Term
Zernike polynomials
in spherical coordinates
Name
Z00
1
Piston
Z1−1
2ρ sin Θ
Tilt in y-direction
2ρ cos Θ
Tilt in x-direction
6 ρ2 sin (2Θ)
√
3 (2ρ2 − 1)
√ 2
6 ρ cos (2Θ)
√ 3
8 ρ sin (3Θ)
Astigmatism ±45°
Z11
√
Z2−2
Z20
Z22
Z3−3
√
Z3−1
√
Z31
Z33
Z4−4
Z4−2
Z40
Z4−2
Z4−4
√
√
Defocus
Astigmatism 0°/90°
8 (3ρ3 − 2ρ) sin Θ
Coma in x-direction
8 (3ρ3 − 2ρ) cos Θ
√ 3
8 ρ cos (3Θ)
√
10 ρ4 sin (4Θ)
Coma in y-direction
10 (4ρ4 − 3ρ2 ) sin (2Θ)
√
5 (6ρ4 − 6ρ2 + 1)
Spherical aberration
10 (4ρ4 − 3ρ2 ) cos (2Θ)
√
10 ρ4 cos (4Θ)
Table 4.1: This table contains all Zernike polynomials up to 4th order (15 terms)
in spherical coordinates.
for a given n, m can only take on values −n, −n + 2, −n + 4, ...n. The first
15 Zernike polynomials are listed in Table 4.1 and illustrated in Figure 4.1.
Since the Zernike polynomials are orthogonal over the continuous unit circle
and the lower-order terms represent familiar corneal shapes such as sphere
and cylinder, the Zernike polynomials appear to be an ideal set of functions
for decomposing and analyzing aberrations. Wave front sensors measure
the aberrations only at a discrete number of points, and unfortunately the
Zernike polynomials are not orthogonal over a discrete set of points. A
technique known as GramSchmidt orthogonalization [23], however, allows
the discrete set of aberration data to be expanded in terms of the Zernike
polynomials and still keep the advantages of an orthogonal expansion.
18
4. Adaptive Optics
(a) Z00
(b) Z1−1
(d) Z2−2
(g) Z3−3
(k) Z4−4
(c) Z11
(e) Z20
(h) Z3−1
(l) Z42
(f) Z22
(j) Z3−3
(i) Z31
(m) Z40
(n) Z42
(o) Z44
Figure 4.1: This Figure illustrates all Zernike polynomials up to 4th order.
4.2
Wave Front Sensors
For the eye various wave front sensing techniques have been developed. Wave
front sensors measure the aberrations of the entire eye generated by both
corneal surfaces and the crystalline lens and can be categorized by whether
the measurement is based on a subjective or objective method and whether
the wave front sensor measures the light going into the eye or coming out of
the eye.
The most commonly used wave front sensors are the spatially resolved refractometer (subjective method measuring the ingoing light) [24], the laser ray
tracing technique (objective method measuring the ingoing light) [25], and
the Shack-Hartmann wave front sensor (objective method measuring the out19
4. Adaptive Optics
going light) [3] as it is used in this work. However, all wave front sensors
developed for vision science and ophthalmology are based on the same principle, which is an indirect measurement of local wave front slopes and the
reconstruction of the complete wave front by integrating these slopes.
The Shack-Hartmann wave front sensor contains a lenslet array that consists
of a two-dimensional array of a few hundred lenslets, all with the same focal
length (∼ 5 mm − 30 mm) and the same diameter (∼ 100 µm − 600 µm). The
light reflected from the laser beacon projected on the retina is distorted by
the wave aberration of the eye. The reflected light is then spatially sampled
into many individual beams by the lenslet array and forms multiple spots in
the focal plane of the lenslet. The relationship between wave front slope and
the spot displacement, ∆xs and ∆ys with respect to the x and y directions,
can be expressed as
∆xs
∂W (x, y)
=
(4.5)
∂x
F
∂W (x, y)
∆ys
=
(4.6)
∂y
F
where F is the focal length of the focusing optics. A CCD-Camera placed
in the focal plane of the lenslet array records the spot array of pattern for
wave front calculation. With the measured spot displacements in the x and
y directions at each sampling point, the original wave front can be calculated
using different reconstruction algorithms.
For a perfect eye light reflected from the retina emerges from the pupil as a
collimated beam, and the Shack-Hartmann spots are formed along the op-
Figure 4.2: This figure shows the principle of the Shack Hartmann Sensor. Spots
of a perfect wave front are indicated green, spots of an aberrated wave front are
indicated red.
20
4. Adaptive Optics
tical axis of each lenslet, resulting in a regularly spaced grid of spots in the
focal plane of the lenslet array. In contrast, individual spots formed by an
aberrated eye, which distorts the wave front of the light passing through the
eye’s optics, are displaced from the optical axis of each lenslet. This displacement of each spot is proportional to the wave front slope at the location of
that lenslet in the pupil and is used to reconstruct the wave aberration of
the eye.
Figure 4.3: This figure shows the Shack Hartmann spots as they are obtained by a
Shack Hartmann sensor. Spots of a perfect wave front are indicated green, spots
of an aberrated wave front are indicated red.
However, the major disadvantage of the Shack-Hartmann device is its relatively small dynamic range that is limited by the lenslet spacing or number
of lenslets across the pupil and the focal length of the lenslet array. The
relationship between the wave front slope Θ and the spot displacement ∆s
can be expressed as
∆s = F · tan(Θ) ≈ F · sin(Θ) ≈ F · Θ
(4.7)
where F is the focal length of the lenslet. Larger wave front slopes will cause
larger displacements of the spot.
Measurement accuracy of the wave front sensor is directly related to the precision of the centroid algorithm, that is, to the measurement precision of ∆s.
A conventional centroid algorithm will fail to find the correct centres of the
spots if the spots partially overlap or fall outside of the virtual subaperture
(located directly behind the lenslet) on the photodetector array unless a special algorithm is implemented.
The dynamic range of Θmax is the wave front slope when the Shack-Hartmann
spot is displaced by the maximum distance ∆smax within the subaperture,
which is equal to one-half of the lenslet diameter for a given focal length
lenslet array (when ignoring spot size). So the dynamic range can be rewrit21
4. Adaptive Optics
ten as
∆smax
d
=
(4.8)
F
2F
Assuming that the lenslet diameter is determined by the required number of
Zernike coefficients, the only way to increase the dynamic range is to shorten
the focal length of the lenslet. However, if the focal length is too short,
this causes a decrease in measurement sensitivity (that is the minimum wave
front slope Θmin that can be measured). The measurement sensitivity can
be written as
∆smin
(4.9)
Θmin =
F
where ∆smin is the minimum detectable spot displacement, which is normally
determined by the pixel size of the photodetector, the accuracy of the centroid
algorithm and the signal-to-noise ratio of the sensor. The dynamic range and
the measurement sensitivity are inversely related. So increasing the dynamic
range of the wave front sensor results in a decrease in its sensitivity and vice
versa for a constant lenslet spacing d.
Θmax =
(a) Perfect
front
wave
(b) Defocus
(c) Astigmatism
(d) Coma
Figure 4.4: These figures show Shack Hartmann Sensor spot pattern of wave fronts
distorted by the aberrations named above. All images were generated by the simulation software of Michael Schottner [26].
4.3
Phase Modulators
Phase modulators or wave front correctors alter the phase profile of the incident wave front by changing the physical length over which the wave front
propagates or the refractive index of the medium through which the wave
front passes. Most wave front correctors are based on mirror technology and
impart phase changes by adjusting their surface shape. Several types of wave
front correctors have been used in vision science AO systems for the correction of ocular aberrations.
22
4. Adaptive Optics
Figure 4.5: These figures show the principle of different types of deformable mirrors
as they are us in adaptive optics: A discrete actuator deformable mirror is pictured
in (a), (b) shows a piston-only segmented mirror, and in (c) a membrane mirror
is illustrated.
Three types of wave front correctors are illustrated in Figure 4.5: Discrete
actuator deformable mirrors consist of a continuous, reflective surface and
an array of actuators, each capable of producing a local deformation in the
surface. Piston-only segmented correctors consist of an array of small planar
mirrors whose axial motion is independently controlled. Membrane mirrors
consist of a grounded, flexible reflective membrane sandwiched between a
transparent top electrode and an underlying array of patterned electrodes,
each of which is capable of producing a global deformation in the surface.
4.4
The Control Algorithm
The vital link between the wave front sensor and the wave front corrector in
an adaptive optics system is the control algorithm. To improve resolution the
set of actuator commands that are applied to the wave front corrector should
minimize the residual wave aberrations. The control algorithm’s task is to
convert the wave aberration measurements made by the wave front sensor
into a set of actuator commands. Basically the software has to fulfill these
steps:
• acquire an image of the lenslet array spots,
• find the centre of the spots and measure their displacements from a fixed
reference,
• find the Zernike coefficients as a compact description of the wave front in
order to completely correct aberrations that have visual significance, and
• repeat until the residual wave front error is minimized by deforming the
mirror.
Regarding image acquisition it is important that the camera’s frame rate is
high enough. A good update target for a realtime AO loop in vision science
research is 30 frames per second (fps) [21].
Once a spots image is grabbed any image processing that needs to be done
is performed first. For instance, subtracting a background image, averaging
23
4. Adaptive Optics
(a) search boxes
(b) centroid
Figure 4.6: This figure illustrates the proceeding of the spot finding algorithm. It
uses iterative search boxes (a), in each one searching the centre of mass (b).
frames, thresholding or flat fielding improve the likelihood of finding good
spot centres.
Afterwards the software has to find the spots. One can take advantage of the
fact that each spot comes from a corresponding lenslet, assuming that the
optics of the system are designed so that spots lie in their lenslet’s region of
interest, or search box, which does not overlap the box of any other lenslet.
Search boxes can be constructed initially so that they centre on a theoretical
reference, a point where the spots would appear in an aberration-free system.
When the set of search boxes has been determined, it is time to find each
spot centre, or centroid.
The centroid algorithm normally used is an iterative one. It simply performs
a standard centre-of-mass centroiding operation (which weights pixel position
by intensity) but does so recursively, shrinking the box from the original size
down to the size of a box that would just contain the diffraction limited spot.
Each new smaller box is formed by reducing both its width and height by
one pixel, and by centring it on the centroid found in the previous step.
Once all centroids are found spot displacements can be calculated. This
can be done by Singular Value Decomposition, for instance, as shown below.
Samples of the wave front derivative, ∂W (x, y)/∂x and ∂W (x, y)/∂y , with
respect to both x and y, are in the form of measured spot displacements in
the wave front image, scaled by the lenslet focal length (see Equation 4.5 and
Equation 4.6, respectively). When we switch to the single indexing scheme
and cartesian coordinates as shown in Table 4.2 we can write Equation 4.1
24
4. Adaptive Optics
as
W (x, y) =
∞
X
cj Zj (x, y)
.
(4.10)
j=0
Derived by x and y, respectively, this yields
∞
∂W (x, y) X ∂Zj (x, y)
cj
=
∂x
∂x
j=0
and
(4.11)
∞
∂W (x, y) X ∂Zj (x, y)
=
cj
∂y
∂y
j=0
.
(4.12)
Assuming we have data for K lenses, the derivatives have to be averaged over
the K subapertures and Equation 4.13 and Equation 4.14 change to
∞
X
∂Zj (x, y) ∂W (xm , ym )
=
cj
(4.13)
∂x
∂x j=0
and
m
∞
X
∂Zj (x, y) ∂W (xm , ym )
=
cj
∂y
∂y
j=0
.
(4.14)
m
Doing the approximation J ≈ ∞ these equations can also be written as one
vector equation
s(2K×1) = Z(2K×J) c(J×1)
(4.15)
or in detail when the piston
 ∆x1   1 0 2x
1
F

∆y
 1   0 1 2y1
 ∆x
 
F
2


1 0 2x2
 F  
 ∆y2  
0 1 2y2
 F =
 ..
 
.. .. ..

 .

. . .
 ∆x  

K 

 1 0 2xK
F
∆yK
F
0 1 2yK
is out of interest
4x1
4y1
4x2
4y2
..
.
2x1
−2y1
2x2
−2y2
..
.
4xK 2xK
4yK −2yK
1 ,y1 )
. . . ∂ZJ (x
∂x
1 ,y1 )
. . . ∂ZJ (x
∂y
2 ,y2 )
. . . ∂ZJ (x
∂x
2 ,y2 )
. . . ∂ZJ (x
∂y
..
..
.
.
. . . ∂ZJ (x∂xK ,yK )
. . . ∂ZJ (x∂yK ,yK )
 
 
 
 
 
 
·
 
 
 
 

c1
c2
c3
c4
c5
..
.






 (4.16)




cJ
J indicates the number of Zernike coefficients that we want to recover, and
2K is twice the number of lenslets for which we have data because we have
derivatives with respect to both x and y. For c one can solve via
c = Z† s
25
(4.17)
4. Adaptive Optics
Term
Zernike polynomials
in cartesian coordinates
Name
Z00
Z0
1
piston
Z1−1
Z1
x
tilt in y-direction
Z11
Z2
y
tilt in x-direction
Z2−2
Z3
2xy
astigmatism ±45°
Z20
Z4
2x2 + 2y 2 − 1
defocus
Z22
Z5
y 2 − x2
astigmatism 0°/90°
Z3−3
Z6
3xy 2 − x3
Z3−1
Z7
3x3 + 3xy 2 − 2x
coma in x-direction
Z31
Z8
3y 3 + 3x2 y − 2y
coma in y-direction
Z33
Z9
y 3 − 3x2 y
Z4−4
Z10
4xy 3 − 4x3 y
Z4−2
Z11
8x3 y + 8xy 3 − 6xy
Z40
Z12
Z4−2
Z13
4y 4 − 4x4 + 3x2 − 3y 2
Z4−4
Z14
y 4 − 6x2 y 2 + x4
6x4 + 6y 4 + 12x2 y 2 − 6x2 − 6y 2 + 1 spherical aberration
Table 4.2: Zernike polynomials up to 4th order (15 terms)
In the above notation, the elements, z 0 , of the matrix Z are the derivatives
of the basis functions, Z, and the dagger indicates pseudo-inverse. The coefficients of c result from multiplying the pseudo-inverse of the derivative of
the Zernike polynomials, Z† , by the slope vector, s
 ∆x1 
F

  0

0
0
0
0
0
 ∆y1 
z11 z12
z13
z14
. . . z1(2K−1)
z1(2K)
c1
 F 
0
0
0
0
0
0
 c2   z21
  ∆x2 
z
z
z
.
.
.
z
z
22
23
24
2(2K−1)
2(2K)   F


 
0
 c3   z 0 z 0 z 0 z 0 . . . z 0
  ∆y2 
 (4.18)

 =  31 32 33 34
3(2K−1) z3(2K)  ·  F

 ..   .
  ..
.
.
.
.
.
.
..
..
..
..
..
..

 .   ..
  .
 ∆x 
0
0
0
0
0
0
K


cJ
zJ1 zJ2 zJ3 zJ4 . . . z
z
J(2K−1)
26
J(2K)
F
∆yK
F
Chapter 5
Setup
5.1
Hardware
For this work a conventional Heidelberg Retina Tomograph as it is described
in section 3.3 was modified. The optical path of the whole aperture is
schematically shown in Figure 5.1 and a photo of the original setup is shown
in Figure 5.3.
The illuminating laser beam is injected into the model eye via the HRT.
Thereby it is necessary to set up a telescope to image the scan pupil onto
the pupil of the model eye. This telescope also serves as defocus correction
so that it is even possible to get a rather sharp image of an aberrated eye’s
fundus. The laser beam then is focused onto the surface of the model eye
retina by the model eye lens. The light scattered back from the point source
on the retina exits the eye through the pupil.
The beamsplitter cube B1 is designed to provide a 50:50 split ratio and to
work over a broad wavelength range from 700 nm to 1100 nm. The entrance
and exit faces are antireflection coated while the diagonal internal surface
has the broadband beam splitting coating. It divides the outgoing beam into
one leading to the Shack-Hartmann sensor and another one leading to the
diode of the HRT. This diode is connected to a personal computer that runs
the conventional HRT software, which is called the Heidelberg Eye Explorer.
The telescope consisting of lens L1 and L2 serves to telecentrically image
the pupil plane (and the scan pupil, respectively) onto the lens array. Here
a ratio of 2:1 was used to halve the beam diameter so that all the ShackHartmann spots of the microlenses, that are illuminated by the laser source,
fit onto the CCD camera. The wave front in the plane of the SHS lenslet
array is sampled by the central part of the lenslet array and focused directly
onto the CCD camera to form the 2-D focal spot image. This CCD camera is
27
5. Setup
connected to another personal computer, which is used for grabbing, storing
and preprocessing the Shack Hartmann images. The frame grabber in this
PC is able to grab 30 pictures per second.
Figure 5.1: This is a drawing of the optical path in the setup. Conjugate pupils are
here the lens of the model eye, the scan pupil, and the lenslet array of the Shack
Hartmann Sensor.
The Laser Diode The original illumination source of the HRT was replaced by a wavelength division multiplexer (ozoptics) with an output wavelength of 830 nm. This wavelength was chosen because of mainly two reasons.
The first reason is that several studies proved near infrared light providing
better visibility than visible light for sub-retinal features [14, 27]. Contrast
and visibility of features increases with increasing wavelength, at least in
the range from 795 to 895 nm. The second reason is that in living eyes it
is possible to illuminate the retina for a longer period with light of longer
wavelengths without causing damage to the retina cells than with light of
shorter wavelengths.1 The laser power was tunable and a maximal power of
3.25 mW could be reached.
1
This fact results from the power equation P =
28
h·c
t·λ .
5. Setup
The femtosecond Laser In addition to the diode laser source a Nd:Glass
laser of 1054 nm wavelength could be injected into the optical path. To
switch between the two light sources easily, a fold-away beamsplitter was
implemented into the optical path. If it was situated into the course of
beam, it blocked the laser diode beam whereas it reflected the femtosecond
laser beam into the HRT. The femtosecond laser was not used for wavefront
measuring purpose.
The Scanner The scanning system of the HRT consists of a galvanometer
scanner for the slow (horizontal) and a resonant scanner for the fast (vertical)
scan direction. Recording one image lasts 32 ms but due to a dead time of
the photo diode in the HRT of 16 ms image acquisition frequency shrinks to
20,83 images per second. By automatically shifting the confocal pinhole also
a depth scan is made. Recording a whole z-scan of 32 single images is possible
in 1.54 s. In our setup x-y-scan angles could be chosen between 1°, 5°and 10°.
With these scan angles it was also possible to take ophthalmoscope images
as shown in Figure 5.2. Furthermore, the scanner could operate in the freeze
modus, so the scanner was only scanning over 0.5°and the scanner could be
switched off completely. Using these modi no ophthalmoscope images could
be gained.
(a) 10°
(b) 5°
(c) 1°
Figure 5.2: Opthalmoscope images with different scan angles.
The Model Eye As model eyes a human model eye and a rat model eye,
respectively, were used. A model eye consists of a lens and a piece of printed
paper located in the focal plane of the lens. In case of the human model
eye a lens with a focal length of 17 mm and a diameter of 8 mm was used.
The lens diameter corresponds to the achievable dilated pupil size of a real
29
5. Setup
human eye. In case of the rat model eye a lens with a focal length of 9 mm
and a diameter 5 mm was used.
The Sensor The Shack-Hartmann-Sensor was realized by placing a lenslet
array of Adaptive Optics Associates in front of a cooled CCD-Camera of SACimaging (SAC9). The CCD image resolution is 640 × 480 pixels with each
pixel size of 8.6 µm × 8.6 µm and a 10 bit dynamic range. This corresponds
to 1024 grey scales. With the SAC9 camera it was possible to grab 30 frames
per second in full resolution. The microlenses of the chosen lenslet array
have a distance of 400 µm between each other (also called pitch) and a focal
length of 53 mm. Each lenslet of the Shack Hartmann Sensor covers an area
of 46.5 × 46.5 pixels in the CCD plane. Because the telescope between model
eye and sensor caused a demagnification of 2, the beam diameter was halved
and therefore the slope was doubled. These considerations are paid attention
to in the evaluation software.
Figure 5.3: This figure shows the original setup with illustrated light path of the
fs-laser (yellow) and the laser diode (red).
30
5. Setup
5.2
Software
To grab and store images I used the software that belongs with the camera
SAC9. As this camera is in general used for astronomical imaging, it is called
AstroVideo.
To preprocess the images I used the free ImageJ software available on http:
//rsb.info.nih.gov/ij/. For improving image quality, all images were averaged and afterwards the also averaged background was subtracted. Finally,
I enhanced contrast so that 0.01% of all pixels were saturated. As it is proved
in Figure 5.4 a saturation of 0.01% of the pixel still ensures a reliable spot
finding algorithm. The surface plot of gray values shows the 9 brightest spots
lying in the central area of the Shack-Hartmann spots image.
Preprocessed images were stored as bitmap-files (*.bmp) and then evaluated
by the software HSS written by Michael Schottner and explained in detail
in his dissertation [26]. The software calculates the Zernike coefficients out
of spot displacements, while all necessary parameter like sublens diameter,
pixel size of the ccd camera and magnifying telescopes, for example, are
considered.
Figure 5.4: These plots shows a surface plot of gray values. As this curve is
smooth a saturation of 0.01% of the pixels enhances the reliability of the centroiding
algorithm.
31
Chapter 6
Results
6.1
Measurement and Evaluation
To test this wave front sensing Scanning Laser Ophthalmoscope with living
eyes it is important that the laser power is not too high. Therefore the power
of the laser diode at the model eye’s pupil was always kept at 6 µW or less
for wave front measurements or fundus imaging. This is more than 100 times
smaller than the maximum permissible exposure for continuous viewing at
this wavelength [28].
To take Shack Hartmann spot images, there were basically two ways to do
this: As the scanner was very fast and only needed 32 ms for one whole
single scan and the framegrabber’s limit was to grab one image in 33 ms,
spots became too blurred when taking spot images during a scan with a big
scan angle. So the first possibility was to switch the scanner to the freezemode where it was only scanning over an angle of 0.5 × 0.5°.
The second possibility was to switch off the scanner completely. Although
this step usually results in bad quality images as speckles1 appear in the
image, this turned out to be the better way. The laser diode I used has a
short coherence length resulting in less speckles in the Shack Hartmann spots
than when using a coherent laser source. Still one can see speckles in the
images, but the software was able to reliably gain the Zernike coefficients.
Some taken images on a human model eye are shown below. Figure 6.1 (a)
shows the Shack-Hartmann spot pattern of an unaberrated model eye. Spots
are still not perfectly equidistant because of system aberrations. This image
is used as reference image. Figure 6.1 (b) shows the Shack-Hartmann spot
1
Speckles are spatially random intensity distributions produced from the coherent interference of light that reflects from an optically rough surface or propagates through a
turbulent medium.
32
6. Results
pattern of a model eye aberrated by an astigmatic lens and Figure 6.1 (c) a
model eye aberrated by a defocal lens.
(a) unaberrated model eye
(b) astigmatic model eye
(c) defocal model eye
Figure 6.1: Shack Hartmann spots of a model eye without aberration (a) and aberrated by astigmatism (b) and defocus (c), respectively.
33
6. Results
Table 6.1 contains the first 4 orders of Zernike coefficients without units, that
is, not standardized onto the pupil. As the piston Z0 cannot be calculated it
is not considered here. Having gained Zernike coefficients, the best correction
by astigmatic and confocal lenses can also be calculated by the software. In
case of the spot images shown in Figure 6.1, we get for the astigmatic model
eye a defocus of -0.19587 DS and an astigmatism of -2.4066 DC with an axis
of 165.975°. For the defocal eye a defocus of -0.41254 DS and an astigmatism
of -0.7545 DC with an axis of 171.283°was calculated. This seems to be
reasonable as I used an astigmatic lens of -2.5 DC and a defocal lens of -0.5
DS for the test measurements presented here. In Table 6.1 and Figure 6.1
the 14 Zernike coefficients are illustrated in diagrams.
Term Zernike polynomials
of an astigmatic lens
Zernike polynomials
of a defocal lens
Name
Z1
-0.000894463
0.001782818
Tilt in y
Z2
-0.000441715
0.000346664
Tilt in x
Z3
0.000369128
0.001848045
Astigmatism ±45°
Z4
0.001823945
0.003231278
Defocus
Z5
-0.001175501
-0.003468369
Astigmatism 0°/90°
Z6
-0.000249881
-0.001183771
Z7
-0.000155659
-0.000198111
Coma in x
Z8
-0.000151466
-0.000569209
Coma in y
Z9
0.000305387
0.000621058
Z10
-0.000057627
-0.000362092
Z11
0.000126923
0.000333755
Z12
0.000000033
0.000401334
Z13
0.000052089
-0.000846666
Z14
0.000039092
0.001576040
Spherical aberration
Table 6.1: This table contains all Zernike polynomials gained by the spot images
shown above up to 4th order in spherical coordinates. Tilt is not considered in the
evaluation.
34
6. Results
Figure 6.2: In this figure the Zernike coefficients calculated out of the spot pattern
shown in Figure 6.1 (b) are illustrated. For this measurement the model eye was
aberrated by an astigmatic lens of -2.5 DC.
Figure 6.3: Here the Zernike coefficients calculated out of the spot pattern shown
in Figure 6.1 (c) are illustrated. For this measurement the model eye was aberrated
by a defocal lens of -0.5 DC.
35
6. Results
6.2
Discussion and Future Prospect
In this work a wave front sensing confocal Scanning Laser Opthtalmoscope
was built and tested. The confocal Scanning Laser Opthtalmoscope that was
modified for this purpose is known as a Heidelberg Retina Tomograph built
by Heidelberg Engineering. As this Opthtalmoscope is compact, manipulations were limited. By measuring the wave front in between scanner and
model eye, I was forced to stop the scanner while taking a spot image. By
a trigger this stopping procedure could be as short as 50 ms. Considering
that the operating power of the laser was kept far under the permitted power
this would not be of any harm to the patient, but keeping in mind to build a
real-time closed loop adaptive-optical system this is very unhandy. Besides
stopping and starting the scanner over and over will show signs of wear by
the time. Although the wave front sensor was working properly, this setup
should be modified in future. One setup improving the setup presented in
this work will be built at the Ruprecht-Karls-Universität in Heidelberg and
is explained below.
AO-cSLO
For setting up a new adaptive-optical confocal Scanning Laser Ophthalmoscope the layout shown in 6.2 was chosen. The AO-cSLO occupies approximately a 1.5 m × 1 m area on an optical table. Here the light beam of a laser
diode is measuring about 3mm in diameter. To use the deformable mirror
(DM) ideally, this beam is expanded by a 1:3 telescope. The 9 mm laser beam
then passes a polarizing beam splitter (PBS) and, thus, is linearly polarized.
Afterwards it is reflected by a mirror (M) onto the deformable mirror and
demagnified again by a 3:1 telescope. The scanner is still the conventional
one of the HRT. It scans the beam over the pupil of the model eye. The
telescope between scanner and eye functions as a relay telescope without any
magnification. In front of the eye a λ/4-retarder causes light entering the eye
to be circularly polarized. The lens of the model eye focusses the beam onto
a point on the retina. Due to the varying directions out of which light enters
the eye, also the retina is scanned. Light reflected by the retina exits the eye
again, is caused to be linearly polarized (but perpendicular to the incoming
light) by the wave-retarder and descanned by the scanner. Because velocity
of light is much higher than the velocity of the scanner this consideration is
justified. After the scanner the beam is expanded again and reflected by the
deformable mirror and the mirror. Because polarization is rotated by 90°,
light is now reflected by the polarizing beamsplitter. In this arm the ophthalmoscope image is gained by the photodiode (APD) and the spot image
36
6. Results
by the Shack-Hartmann sensor (SHS). Aberrations measured by the SHS are
corrected by the deformable mirror in a closed loop circuit.
Figure 6.4: This outline shows an AO-cSLO as it will be set up in Heidelberg.
Because of the scanning and descanning principle as it is explained in the text
image quality of the Shack-Hartmann spot images is expected to be much higher.
37
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39
Acknowledgments
Here I would like to express my gratitude to all those people who helped me in completing
this Master Thesis.
In particular thanks to
• Prof. Dr. Frederick Fitzke
for giving me the opportunity to work on this interesting topic and for his support
and professional scientific advice during my time in his group in the Department for
Visual Science.
• Prof. Dr. Josef Bille
for offering me to take part in this Master Program.
• Vy Luong
for his appreciated advice in and around the world of computers and electronics and
his helpfulness to organize all the equipment needed.
• Dr. Nina Korablinova
for her advice and for helping me with the image evaluation.
• Olivier La Schiazza and Mikael Agopov
for their support and advice via telephone and email.
• Felix Frank
for sharing numberless hours in and out the lab.
• My family
for their encouragement and support throughout my years of study.
Furthermore, I would like to thank the ”Landesstiftung Baden-Württemberg” for financially supporting my stay in London.
40