Texas Instruments | DMD Optical Efficiency for Visible Wavelengths (Rev. A) | Application notes | Texas Instruments DMD Optical Efficiency for Visible Wavelengths (Rev. A) Application notes

Texas Instruments DMD Optical Efficiency for Visible Wavelengths (Rev. A) Application notes
DMD Optical Efficiency for Visible Wavelengths
Application Report
Literature Number: DLPA083A
June 2018 – Revised May 2019
Contents
1
Purpose and Scope .............................................................................................................. 4
1.1
1.2
2
On-State Fill Factor .............................................................................................................. 5
2.1
3
Window Properties........................................................................................................... 6
Mirror Diffraction Efficiency
4.1
4.2
5
On-State Fill Factor .......................................................................................................... 5
Window Properties ............................................................................................................... 6
3.1
4
Purpose and Scope ......................................................................................................... 4
Limitations .................................................................................................................... 4
.................................................................................................. 7
Mirror Flatness ............................................................................................................... 7
Mirror Diffraction Efficiency ................................................................................................. 7
Mirror Reflectivity ............................................................................................................... 14
5.1
Mirror Reflectivity ........................................................................................................... 14
6
Estimating Overall DMD Efficiency ....................................................................................... 15
7
Terms and Abbreviations .................................................................................................... 16
6.1
7.1
8
Terms and Abbreviations .................................................................................................. 16
References ........................................................................................................................ 17
8.1
2
Estimating Overall DMD Efficiency....................................................................................... 15
References .................................................................................................................. 17
Contents
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Copyright © 2018–2019, Texas Instruments Incorporated
www.ti.com
List of Figures
4-1.
Simulated 5.4 µm Pitch DMD Far Field Radiance Image; Dashed Circle Shows Outline of Projection
Lens Aperture Edge ......................................................................................................... 8
4-2.
Summary of Calculated Photopic Diffraction Efficiencies for Different Pixel Sizes (400 nm–700 nm
wavelength) ................................................................................................................... 9
4-3.
13.6 µm Pitch DMD Mirror Calculated Diffraction Efficiency
10
4-4.
10.8 µm Pitch DMD Mirror Calculated Diffraction Efficiency
11
4-5.
4-6.
.........................................................
.........................................................
7.6 µm Pitch DMD Mirror Calculated Diffraction Efficiency ...........................................................
5.4 µm Pitch DMD Mirror Calculated Diffraction Efficiency ..........................................................
12
13
List of Tables
2-1.
DMD On-State Fill Factor ................................................................................................... 5
6-1.
Total Photopic Efficiency Calculation .................................................................................... 15
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
List of Figures
Copyright © 2018–2019, Texas Instruments Incorporated
3
Chapter 1
DLPA083A – June 2018 – Revised May 2019
Purpose and Scope
1.1
Purpose and Scope
The purpose of this document is to summarize the optical properties that are most important in estimating
the efficiency of a Digital Micromirror Device (DMD) in a projection system. The next three sections
discuss the fill factor, window optical properties, and the active mirror array properties, respectively. This
report concludes with a discussion on calculating the overall efficiency.
As discussed in more detail in Chapter 6, overall optical efficiency can be estimated using
Equation 1.
EfficiencyDMD = transmissionwindow × efficiencyfillfactor × efficiencydiffraction × reflectivitymirror × transmissionwindow
where
•
•
•
•
transmissionwindow is single-pass window transmission including two anti-reflection surfaces. This term is
accounted for twice because light travels through the window twice.
efficiencyfillfactor is the fractional mirror coverage (on-state mirrors) as viewed from the illumination direction
efficiencydiffraction is the mirror array diffraction efficiency which can include effects of non-flat mirrors
reflectivitymirror is the mirror reflectivity including mirror scatter
(1)
Overall DMD efficiency is generally a product of fill factor, window transmission, diffraction efficiency, and
mirror reflectivity, which are described in more detail in the following sections.
1.2
Limitations
This document does not include system-level efficiency losses such as etendue mismatches, which can
be better assessed using a raytrace model based on the actual optical design. Factors that affect contrast
ratio are also important, however, the interactions are often much more complex requiring rigorous
electromagnetic scattering theory of the optical system, and it would be difficult to summarize all these
factors in this type of report.
4
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Chapter 2
DLPA083A – June 2018 – Revised May 2019
On-State Fill Factor
2.1
On-State Fill Factor
Table 2-1 shows typical on-state fill factor based on DMD micromirror pitch.
• Tilt angle - Nominal mirror tilt angle is listed. Each DMD datasheet specifies the actual tilt angle and
how much it can vary.
• Fill Factor - Calculated from viewpoint of nominal illumination angle from DMD die surface. Typically
twice the mirror tilt angle (for example, 24 degrees for a 12 degree tilt). These numbers can be
calculated using ray tracing, however as the pixel structures get smaller with respect to the wavelength
more rigorous methods are required for better accuracy. See Section 4.2 for a description of scalar
diffraction methods. More rigorous methods such as Finite Difference Time Domain (FDTD) can be
used for even greater accuracy.
Table 2-1. DMD On-State Fill Factor
(1)
(2)
DMD EXAMPLES (1)
MICROMIRROR PITCH
(µm)
TILT ANGLE (deg.)
TYPICAL ON-STATE
FILL FACTOR (2)
DLP7000
13.6
12
92%
DLP650LE
10.8
12
92%
DLP303X-Q1
DLP553X-Q1
DLP4501
DLP9000
7.6
12
94%
DLP3010
5.4
17
93%
DMD example list is not comprehensive and other devices may be available within each micromirror pitch category.
On state fill factor values are approximate. Refer to DMD data sheet for device-specific values.
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
5
Chapter 3
DLPA083A – June 2018 – Revised May 2019
Window Properties
3.1
Window Properties
The two main types of DMD windows are directly related to the packaging types:
• Type A uses Corning 7056 glass (typically about 3 mm thick).
• Wafer Level Packaging (WLP, often referred to as Sxxx package) uses Eagle XG glass (typically about
1 mm thick or less).
Both the WLP window and the Type A window have an anti-reflective thin film coating to reduce reflections
and increase transmission efficiency. Depending on the application, either the visible, UV, or IR coating is
used.
The values below describe a single pass of visible light (420 nm–680 nm) with random polarization
through the window, and accounting for two surface coatings.
• Minimum transmittance, Tmin ≥ 97% at all angles 0–30° AOI,
• Average transmittance, Tave ≥ 99% at all angles 0–30° AOI,
• Average transmittance, Tave ≥ 97% at all angles 30–45° AOI
All transmittance values are the total transmittance of the window (through both surfaces and glass). A
transmission number of 96% is used in the Table 6-1 calculation representing a double pass through the
window with approximately 99% transmission at each coated surface.
See the Window Transmittance Considerations for DLP® DMD Window Application Report (DLPA031) for
more information on window transmittance, .
6
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Chapter 4
DLPA083A – June 2018 – Revised May 2019
Mirror Diffraction Efficiency
4.1
Mirror Flatness
The semiconductor processing required to build the mirror structure can result in the mirrors deviating
from a perfectly flat plane. However, the processing is designed and controlled to minimize the nonflatness or non-planarity of the mirror. Diffraction modeling described below can be used to predict losses
due to non-flat mirrors. Typically, the mirror is sufficiently flat that light losses in a visible light, F/2.4
projector is less than 1%. This loss is included in the diffraction efficiency calculation.
4.2
Mirror Diffraction Efficiency
The active array area consists of a large rectangular array of aluminum-based mirrors which can tilt to one
of two stable angles. For the 13.6 μm, 10.8 μm, and 7.6 μm micromirror sizes, this is typically +12 and –12
degrees around the diagonal. The 5.4 µm micromirror devices are different in that they tilt approximately
17 degrees about the orthogonal direction.
The illumination and projection f-numbers are typically matched to obtain the tradeoff of efficiency and
contrast ratio. However, even under these conditions, there is some loss of light due to clipping of the
diffracted light at the projection lens aperture stop. Because the size of the mirrors is not large with
respect to the wavelength, the mirror reflected light diffracts into a larger cone angle which results in a loss
of light.
The longer wavelengths (red) are clipped more than the shorter wavelengths (blue), resulting in a
diffraction efficiency loss that increases for longer wavelengths.
In order to more accurately model the complex diffraction pattern that arises, use the fact that the array of
tilted mirrors behaves similarly to a classic blazed optical diffraction grating. Conceptually, the best way to
approach broadband source diffraction is to consider it as a combination of a large number of plane waves
varying in wavelength and direction. All of these plane wave sources can be combined incoherently to
assess the final diffraction pattern.
For a two-dimensional array of mirrors illuminated by a single wavelength, collimated laser beam, the far
field appears as an array of bright points (diffraction orders) which are spaced approximately by λ/pitch in
angle, where λ is the wavelength. Scalar diffraction theory which can be approximated using the fast
Fourier transform algorithm (FFT) can generally be used for this calculation with reasonably good
accuracy. The amplitude of the array of bright points is modulated by the far-field pattern of an individual
mirror which is generally close to a sin(x)/x shape. The far-field radiance function can be calculated as a
function of direction cosines α and β using the Fourier transform as described in Equation 2.
(2)
Here, the quantity
represents the EM field (magnitude and phase) as it leaves the surface of
the DMD mirror array. The calculated radiance profile,
, can then be mathematically truncated
corresponding to the acceptance angle defined by the projection lens aperture. By integrating the radiance
over incident angle and wavelength and keeping track of the power inside the aperture relative to the total
power, you can calculate the diffraction efficiency.
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
7
Mirror Diffraction Efficiency
www.ti.com
The resulting far-field radiance pattern for a white-light incoherent source has radiating arms of alternating
color as shown in Figure 4-1. The energy in the outer arms is lost as only the central part of the beam is
collected by the projection lens. The calculated diffraction efficiency varies with mirror pitch, mirror tilt, and
wavelength.
Because the far-field diffraction pattern (or image at the projection pupil) depends upon illumination angle,
mirror pitch, mirror tilt angle, and wavelength, the far-field diffraction from white light has a significant
amount of color variation. The most important factors in determining diffraction-induced color variation are
mirror pitch and mirror tilt angle, the illumination angle being less of a factor. This color variation causes
the diffraction efficiency to vary approximately as a sinusoid as a function of wavelength as shown in
Figure 4-3 through Figure 4-6. A spectral plot of diffraction efficiency shows periodic oscillations in
wavelength, and the period of those oscillations generally depends on the pitch of the mirrors—the smaller
pitch mirrors showing a longer period. As a result, the diffraction efficiency can change significantly as a
function of wavelength. Also, variation in tilt angle from device to device causes the spectral peaks to shift
in wavelength.
Figure 4-2 shows the calculated nominal diffraction efficiency for the various pixel types as a function of
pixel pitch. As expected, there is a general reduction in diffraction efficiency as the pixel is scaled down in
pitch.
Figure 4-3 through Figure 4-6 show the spectral diffraction efficiencies for different f-numbers matched
between illumination and projection, and nominal design tilt angles. Note that the 13.6 µm, 10.8 µm, and
7.6 µm mirrors land at 12 degrees, while the 5.4 µm mirrors tilt at 17 degrees.
Diffracted
light
Projection aperture
Figure 4-1. Simulated 5.4 µm Pitch DMD Far Field Radiance Image; Dashed Circle Shows Outline of
Projection Lens Aperture Edge
8
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Mirror Diffraction Efficiency
www.ti.com
Figure 4-2. Summary of Calculated Photopic Diffraction Efficiencies for Different Pixel Sizes (400 nm–700
nm wavelength)
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
9
Mirror Diffraction Efficiency
www.ti.com
Figure 4-3. 13.6 µm Pitch DMD Mirror Calculated Diffraction Efficiency
10
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Mirror Diffraction Efficiency
www.ti.com
Figure 4-4. 10.8 µm Pitch DMD Mirror Calculated Diffraction Efficiency
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
11
Mirror Diffraction Efficiency
www.ti.com
Figure 4-5. 7.6 µm Pitch DMD Mirror Calculated Diffraction Efficiency
12
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Mirror Diffraction Efficiency
www.ti.com
Figure 4-6. 5.4 µm Pitch DMD Mirror Calculated Diffraction Efficiency
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
13
Chapter 5
DLPA083A – June 2018 – Revised May 2019
Mirror Reflectivity
5.1
Mirror Reflectivity
The active array area consists of a large rectangular array of aluminum based mirrors. The mirrors are
nominally 89% reflective in the visible range.
14
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Chapter 6
DLPA083A – June 2018 – Revised May 2019
Estimating Overall DMD Efficiency
6.1
Estimating Overall DMD Efficiency
Overall optical efficiency can be estimated using Equation 3.
EfficiencyDMD = transmissionwindow × efficiencyfillfactor × efficiencydiffraction × reflectivitymirror × transmissionwindow
where
•
•
•
•
efficiencyfillfactor is the fractional mirror coverage (on-state mirrors) as viewed from the illumination direction
transmissionwindow is single-pass window transmission including two anti-reflection surfaces. This term is
accounted for twice because light travels through the window twice.
efficiencydiffraction is the mirror array diffraction efficiency which can include effects of non-flat mirrors
reflectivitymirror is the mirror reflectivity including mirror scatter
(3)
The photopic numbers shown in this table assume a source with a flat power spectrum with wavelengths
of 420 nm–680 nm. More accurate results can be obtained for a given light source by multiplying the
spectral diffraction efficiency by the actual source spectrum.
Table 6-1. Total Photopic Efficiency Calculation (1)
(1)
(2)
DMD PITCH
TILT
ANGLE
(deg)
f/number
DIFF. EFF.
ON-STATE
FILL
WINDOW
TRANSMISSION
(DOUBLE PASS)
MIRROR
REFL.
TOTAL
EFF.
13.6
12
2.4
89%
92%
96%
89%
70%
10.8
12
2.4
87%
92%
96%
89%
68%
7.6
12
1.7 (2)
82%
94%
96%
89%
66%
7.6
12
2.4
84%
94%
96%
89%
67%
5.4
17
1.7
86%
93%
96%
89%
68%
5.4
17
2.4
80%
93%
96%
89%
64%
The values in this table are approximate. Refer to DMD data sheet for device-specific values.
Illumination angle of 29 degrees used for this case. While this decreases total DMD efficiency, it increases the etendue of the
DMD and therefore allows higher maximum brightness. It is likely that image contrast is reduced when compared to nominal
illumination angle and f-number case.
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
15
Chapter 7
DLPA083A – June 2018 – Revised May 2019
Terms and Abbreviations
7.1
Terms and Abbreviations
ABBREVIATION
DMD
AOI
WLP
16
DESCRIPTION
Digital Micromirror Device
Angle of Incidence
Wafer Level Package
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
Chapter 8
DLPA083A – June 2018 – Revised May 2019
References
8.1
References
1. “Linear systems formulation of non-paraxial scalar diffraction theory”
James E. Harvey, Proc. of SPIE Vol. 8122
DLPA083A – June 2018 – Revised May 2019
Submit Documentation Feedback
DMD Optical Efficiency for Visible Wavelengths
Copyright © 2018–2019, Texas Instruments Incorporated
17
IMPORTANT NOTICE AND DISCLAIMER
TI PROVIDES TECHNICAL AND RELIABILITY DATA (INCLUDING DATASHEETS), DESIGN RESOURCES (INCLUDING REFERENCE
DESIGNS), APPLICATION OR OTHER DESIGN ADVICE, WEB TOOLS, SAFETY INFORMATION, AND OTHER RESOURCES “AS IS”
AND WITH ALL FAULTS, AND DISCLAIMS ALL WARRANTIES, EXPRESS AND IMPLIED, INCLUDING WITHOUT LIMITATION ANY
IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE OR NON-INFRINGEMENT OF THIRD
PARTY INTELLECTUAL PROPERTY RIGHTS.
These resources are intended for skilled developers designing with TI products. You are solely responsible for (1) selecting the appropriate
TI products for your application, (2) designing, validating and testing your application, and (3) ensuring your application meets applicable
standards, and any other safety, security, or other requirements. These resources are subject to change without notice. TI grants you
permission to use these resources only for development of an application that uses the TI products described in the resource. Other
reproduction and display of these resources is prohibited. No license is granted to any other TI intellectual property right or to any third
party intellectual property right. TI disclaims responsibility for, and you will fully indemnify TI and its representatives against, any claims,
damages, costs, losses, and liabilities arising out of your use of these resources.
TI’s products are provided subject to TI’s Terms of Sale (www.ti.com/legal/termsofsale.html) or other applicable terms available either on
ti.com or provided in conjunction with such TI products. TI’s provision of these resources does not expand or otherwise alter TI’s applicable
warranties or warranty disclaimers for TI products.
Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265
Copyright © 2019, Texas Instruments Incorporated
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Related manuals

Download PDF

advertising