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Contrast Analysis for DMD-Based IR Scene Projector
Julia Rentz Dupuis and David Mansur
OPTRA, Inc.
461 Boston St., Topsfield, MA 01983
phone: (978) 887-6600 fax: (978) 887-0022
[email protected]
www.optra.com
ABSTRACT
OPTRA has developed a two-band midwave infrared (MWIR) scene projector based on digital micromirror device
(DMD) technology; the projector is intended for training various IR tracking systems that exploit the relative intensities
of two separate MWIR spectral bands. Next generation tracking systems have increasing dynamic range requirements
(on the order of 12-bits) which current DMD-based projector test equipment is not capable of meeting. While sufficient
grayscale digitization can be achieved with drive electronics, commensurate contrast is not currently available. In this
paper we present a detailed analysis of the contrast of our MWIR DMD-based scene projector. A series of factors which
affect the overall contrast are modeled and design approaches to address the worst offenders are presented. In addition,
we present methods for meeting the grayscale digitization requirements through the drive electronics.
Key Words: Two-band infrared scene projector, digital micromirror device
1. INTRODUCTION
Under a U.S. NAVY SBIR Phase II program, OPTRA developed a two-band midwave infrared (MWIR) scene projector
based on digital micromirror device (DMD) technology.1 The system employs two miniature thermal sources, a series of
MWIR lenses and spectral filters, and two DMDs – one for each spectral band. Spectrally separated MWIR images
projected by each DMD are fused and projected onto a unit under test (UUT). This technology was developed as
advanced threat detection test equipment with the unique ability to vary the relative intensity of simulated threats in the
two MWIR bands – loosely called “red” and “blue” – via pulse width modulation of each spatial resolution element of
each DMD. The overall system supports realistic simulation of the spectral, spatial, temporal, and radiant intensity
properties of a host of threats for exercising and testing MWIR threat detection systems.
Under the Phase II program a point design was generated and a prototype system was built, integrated, and tested. The
initial application envisioned was flightline testing at a standoff range of about one meter. Figures 1a and 1b are
photographs of the integrated system; Figure 1c shows a simulated and projected image recorded using a FLIR SC6000
indium antimonide camera with a 250 mm focal length lens. The original image was visible grayscale but was projected
in the MWIR by our system. Table 1 gives the performance specifications.
Table 1: Prototype Performance Specifications
QUANTITY
VALUE
Spectral Bands*
3.4-4.2 m (blue), 4.2-5.0 m (red)
Maximum Radiant Intensity in Red Band*
≥ 1 W/ster
Apparent Temperature
785 K
Grayscale Resolution
10-bits
Maximum Update Rate at 10-bits
40 Hz
Pixel Count
768 diameter
Maximum Scene Duration
54 s
Angular Resolution
225 rad
Image Registration
One Angular Resolution Element
Contrast Ratio
250:1
*
Maximum radiant intensity is specified for the 4.5-4.7 m spectral range, which is a representative band for a UUT.
Copyright 2011 Society of Photo-Optical Instrumentation Engineers.
This paper was published in The Proceedings of Technologies for Synthetic Environments: Hardware-in-the-Loop Testing XVI and
is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use
only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any
material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
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Figure 1a: Two-Band Projector Prototype
(Cover On)
Figure 1b: Two-Band Projector Prototype
(Cover off)
Dichroic Beam
Combiner
Projector
Lenses
Projector
Lenses
“Blue” DMD
Blue
Illumination
Module
“Red” DMD
Power
Supplies
Figure 1c: Simulated Projected MWIR Image
In the process of identifying a suitable Navy platform for this promising technology, it became apparent that the dynamic
range of current DMD-based scene projectors (ours included) was limiting their utility for testing advanced IR tracking
technology. More specifically, the Navy is looking for 12-bits of grayscale resolution which applies to not just our
ability to digitize the grayscale range but also the contrast of the scene projector. DMD-based scene projectors in all
wavelength bands can already digitize beyond 16-bits, depending on the required frame rate and integration time,
however, the contrast, particularly in the MWIR spectral region, has been limited to around 250:1 or about 8-bits.
OPTRA has since been presented with the opportunity to improve the contrast of our two-band DMD-based scene
projector thereby expanding the testing capabilities of this technology. The following paper details an analytical model
which predicts the overall contrast and can be used to identify approaches to improve the overall contrast. This paper
also treats grayscale digitization.
2. CONTRAST MODEL
The DMD community has two definitions of contrast:
Full-on:Full-off (or FO:FO) which is the ratio of lumens (or watts) projected with all micromirrors turned on
(full white screen) to the lumens projected with all of the micromirrors turned off (full black screen). In general,
the FO:FO contrast is roughly an order of magnitude below what you could expect by replacing the DMD with a
mirror; this is due to the various device-related factors that will be discussed below.
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ANSI checkerboard contrast which is measured by projecting a checkerboard pattern of black and white squares.
This measure of contrast includes the effects of the projection lens(es) and coating.
The model described below predicts the FO:FO contrast.
Figure 2: Geometry Convention
Figure 2 shows the geometry convention used for this analysis. Our
system uses a 0.7 XGA DMD chip with 13.7 m micromirrors and a 12°
tilt angle. Energy from the illumination source is directed through the
projector and out to the UUT when the micromirrors are in their on
position and to the off state when the micromirrors are in their off
position. From the perspective of the UUT, it is “looking” at the source
when the micromirrors are in their on position and at the flat state when
the micromirrors are in their off position. The flat state is also where
source light is directed when the micromirrors are not powered up and are
parallel with the substrate datum. This convention applies to each
individual micromirror.
The following sources of background light which have the effect of
degrading contrast have been analyzed:
1.
Self emission and reflection of the flat state,
2.
Source light diffracted onto the flat state by the micromirrors,
3.
Source light reflected onto the flat state by the DMD window,
4.
Source light illuminating the flat state in transit between on and off states,
5.
Scattered light from the DMD substrate (beneath the micromirrors) illuminating the projector,
6.
Source light diffracted onto the projector by the micromirrors,
7.
Self emission of the DMD chip, and
8.
Reflection of the projector optics.
Each source of background light is treated below. All projections are given for the red band (approximately 4.2 to 5 m)
because at least in the case of diffraction, the red channel represents the worst case scenario.
1.
Self emission and reflection of the flat state
Because the UUT “looks” at the flat state when the micromirrors are in their off position, any energy originating from or
reflecting off the flat state increases the lowest achievable light level (i.e. the projector’s ability to simulate “black” in
this spectral range).
The projected power due to the self emission and reflection of the flat state is given by


Pser _ fs  proj   DMD   fs   N(, Tfs )  d  (1   fs )   N(, Tinst )  d  [] W
red
red


(1)
proj is the radiometric efficiency of the projector optics, DMD is the total etendue of the system (detailed below), fs is
the flat state emissivity, N(,T) is Planck’s blackbody function, Tfs is the temperature of the flat state, and Tinst is the
temperature of the instrument. The first integral inside the parentheses represents the self emission of the flat state as a
graybody emitter at the flat state temperature; the second integral inside the parentheses represents the reflection of
instrument radiance by the flat state.
The etendue is given by
 DMD  A DMD   DMD  (0.785)  (0.085)  0.067 cm 2  ster
(2)
ADMD is the illuminated area of the DMD (an approximately 1 cm diameter circle), and DMD is the solid angle
associated with f/3 illumination and collection (i.e. the fastest practical f/3 given the 12° tilt angle).
 DMD  2  1  cos(u )   0.085 ster
where
u  a tan 1 /( 2  f /# )   0.165 rad
(3a and 3b)
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Etendue is conserved throughout the system.
2.
Source light diffracting onto the flat state by the micromirrors
The model for this contribution is of a two-dimensional diffraction pattern due to a two-dimensional array of square
apertures (i.e. the micromirrors). The issue is that when the micromirrors are in their off position and the source light is
being steered to the off state, some of it will illuminate the flat state because of diffraction. The equation for the
diffraction intensity pattern due to a single rectangular aperture is given by
 sin  
I( x , y )  I o  

  
2
 sin  

 
  
2
(4)
where

k a x
2R
and

kby
2R
(5a) and (5b)
k is given by 2 and R(x,y,z) = √(x2+y2+z2). Figure 3 shows the coordinate convention.
Figure 3: Coordinate Convention for Diffraction Calculation
The model (written in Matlab) computes one quadrant of the diffraction pattern in amplitude space (i.e. E-field or
√I(x,y)) for 13.7 m apertures (a = b = 13.7 m) over a 50° half angle in each of x and y directions, which contains
approximately 97% of the total diffracted light (into the quadrant), based on a one-dimensional calculation. The half
angle range was limited based on the computational time required for the program to run, and the 97% was taken into
account when calculating this background contribution. The model calculates this amplitude pattern for a 100 x 100
micromirror array spaced at 13.7 m centers and adds the 10,000 patterns. The program was run for wavelength values
of 4.2 through 5 m in 0.1 m increments, and the resulting nine amplitudes were added. Finally, the intensity was
calculated by taking the square of the amplitude. Figure 4 shows the intensity pattern on a log scale resulting from this
model. In this plot the origin (0°,0°) is the off state.
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Figure 4: Intensity Plot on Log Scale
Diffraction angle (degrees)
10
20
30
40
50
10
20
30
40
50
Diffraction angle (degrees)
The flat state was modeled as a circular aperture offset by 24° with respect to the off state in the diagonal direction and
subtending 19° associated with f/3 operation (Figure 5). The reason the flat state is spaced along the diagonal is because
the DMD is used at a 45° tilt which orients the diffraction pattern as such relative to the spacing between the flat and off
states.
Figure 5: Overlay of Flat State with Intensity Plot on Log Scale
24°
Diffraction angle (degrees)
10
Flat State
20
30
40
50
10
20
30
Diffraction angle (degrees)
40
50
The model calculates the amount of integrated energy that intersects with the flat state aperture and divides this value by
the total integrated energy diffracted into the full quadrant multiplied by four. The result represents the fraction of the
total diffracted source energy (intended for the off-state) that illuminates the flat state. Based on this model and taking
the 97% factor into account, this fraction, diff_fs, is .016.
The total power incident on the flat state when the micromirrors are in the off position is then
Pdiff _ inc _ fs (Ts )  diff _ fs  s _ opt   DMD   N(, Ts )  d [] W
(6)
red
where s_opt is the radiometric efficiency of the source optics (including the source emissivity), and Ts is the source
temperature. The portion of this energy collected by the projector is calculated assuming diffuse reflection off the flat
state.
Pdiff _ refl _ fs (Ts )  fs  proj 
 DMD
 Pdiff _ inc _ fs (Ts ) [] W
2
(7)
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where fs is the flat state diffuse reflectivity given by fs = 1-fs. Pdiff_refl_fs (as well as some of the subsequent
background contributions) is left as a function of Ts because we will ultimately show the total contrast vs. Ts (Figure 9).
3.
Source light reflected onto the flat state by the DMD window
Source light reflected by the window and incident on the flat state is given by
Pwindow _ inc (Ts )   window  s _ opt   DMD   N(, Ts )  d [] W
(8)
red
where window is the Fresnel reflectivity of calcium fluoride at 5 m. The amount of light that diffusely reflects back into
the projector is given by Equation 7 with Pdiff_inc_fs replaced by Pwindow_inc.
4.
Source light illuminating the flat state in transit between on and off states
The optical switching time of the DMD is about 2 s which is about .01% (= transit) of the 25 ms (required) integration
time of our system (i.e. (40 Hz)-1). The total amount of source light reflected onto the flat state by the DMD while in
transit between on and off states is then
Ptransit _ inc (Ts )  transit  s _ opt   DMD   N(, Ts )  d [] W
(9)
red
The amount of light that diffusely reflects back into the projector is again given by Equation 7 with Pdiff_inc_fs replaced by
Ptransit_inc.
5.
Scattered light from the DMD substrate (beneath the micromirrors) illuminating the projector
Lacking a rigorous model of this contribution at this point in time, our calculation relies on a TI model of contrast and
relative intensity projected as a function of illumination angle for one of the older DMD devices (17 m micromirrors,
10° tilt, .8 m mirror gaps, and an f/3 telecentric projector system). Because this model is for the visible spectral range
we can presume that contributions 1, 2, 6, and 7 are effectively zero and contributions 3, 4, and 8 are relatively small for
either wavelength range. Therefore the contrast shown in this figure is dominated by the scattering. Figure 6 shows the
plot.2
Figure 6: TI Contrast and Relative Intensity vs Illumination Angle Plot
This plot illustrates the fact that increasing the illumination angle beyond twice the micromirror tilt angle allows for the
increase in contrast at the expense of brightness since the “on” light will be partially steered off of the projector aperture.
Our Phase II device, however, illuminates at twice the tilt angle or at 24°.
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Presuming we can extrapolate from this plot an anticipated contrast of 370 owing to this background source we can
project the power by taking the ratio of the total power emitted by the source and coupled into the projector to this
contrast. The power emitted by the source and coupled into the projector is given by
Ps (Ts )  s _ opt   DMD   N(, Ts )  d [] W
(10)
red
The amount of power scattered into the projector due to this background contribution is then given by
Pscattered (Ts )  proj 
6.
Ps (Ts )
[ ] W
370
(11)
Source light diffracted onto the projector by the micromirrors
This source of background light is calculated in the same manner as #2, however, this time the circular aperture
represents the projector rather than the flat state. It is offset along the diagonal by 48° rather than 24°; the aperture still
subtends 19° (associated with f/3 operation). Figure 7 shows the overlay of the projector aperture with the diffraction
pattern (intensity on a log scale).
Figure 7: Overlay of Projector Aperture with Intensity Plot on Log Scale
Projector
Aperture
Diffraction angle (degrees)
10
48°
20
30
40
50
10
20
30
Diffraction angle (degrees)
40
50
The amount of source light steered towards the off state but diffracting into the projector aperture was calculated the
same way as the flat state. The value, diff_proj is 1.16×10-3. The amount of power in this contribution is then given by
Pdiff _ proj (Ts )  diff _ proj  total   DMD   N(, Ts )  d [] W
(12)
red
where total = s_opt·proj.
7.
Self emission of the DMD chip
The published total reflectivity of the DMD is about 85% where the 15% loss is a combination of absorption and
scattering. In this case if we assume that the instrument and DMD chip are in thermal equilibrium, this background
contribution can be modeled as all emission (i.e. DMD = 0.15) because the DMD will be scattering instrument radiance
into the projector that is equivalent to its own self emission. This factor is given by
Pse _ DMD (Ts )   DMD  proj   DMD   N(, TDMD )  d [] W
(13)
red
where TDMD is the DMD temperature.
8.
Reflectivity of the projection optics
This factor is equivalent to the self emission of the projector optics, however, as the AR-coated projector optics will have
little if any absorption, all surface losses are expected to be reflection. This contribution is given by
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Prefl _ proj (Ts )   proj   DMD   N(, Tinst )  d [] W
(14)
red
where proj = 1 – proj.
Comparison of Background Contributions
Figure 8 is a log plot of the eight background contributions assuming the values given in Table 2 and a source
temperature of 1023 K (750°C). Factor 9 is the sum of all background contributions. Scattering by the DMD substrate
(#5) is the largest background contribution, followed by source light diffracted onto the projector (#6) and the self
emission and reflection of the flat state (#1).
Figure 8: Comparison of Background Contributions
3
1 10
1 10
List of Factors
4
9
Watts
5
1 10
5
1 10
6
1 10
7
6
1
7
8
3)
2
1 10
8
1 10
9
3
4
10
1 10
0
2
4
6
8
10
1. Self emission and reflection of the
flat state,
2. Source light diffracted onto the flat
state by the micromirrors,
3. Source light reflected onto the flat
state by the DMD window,
4. Source light illuminating the flat
state in transit between on and off
states,
5. Scattered light from the DMD
substrate (beneath the
micromirrors) illuminating the
projector,
6. Source light diffracted onto the
projector by the micromirrors,
7. Self emission of the DMD chip,
8. Reflection of the projector optics.
9. Total background power
Factor Number
Table 2: Values used for Calculations
VARIABLE
proj
s opt
total
diff fs
diff proj
window
transit
DMD
DMD
fs
fs
Tfs
Tinst
TDMD
Ts
DMD
SR
red
DESCRIPTION
Projector optics radiometric efficiency
Source optics radiometric efficiency
Total radiometric efficiency
Portion of diffracted energy incident on flat state
Portion of diffracted energy incident on projector
Reflectivity of DMD window
Ratio of switching time to observation time
Etendue of system
Solid angle of illumination/collection at DMD
Emissivity of flat state
Diffuse reflectivity of flat state
Temperature of flat state
Temperature of instrument
Temperature of DMD
Source temperature
Emissivity of DMD
Scattering ratio
Red spectral band
VALUE
0.8
0.8
0.64
0.016
0.0012
0.028
0.0001
0.067
0.085
0.98
0.02
300
300
300
1023
0.15
370
4.2 to 5
UNITS
unitless
unitless
unitless
unitless
unitless
unitless
unitless
cm2·ster
ster
unitless
unitless
K
K
K
K
unitless
unitless
m
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Total Contrast
The total contrast is calculated by taking the ratio of the total source power coupled into the projector (Equation 10) to
the sum of all the background contributions. Based on the values given above, Figure 9 shows contrast as a function of
IR source temperature. The model supports published (and our own) MWIR DMD-based scene projector contrast values
on the order of 250:1.
Figure 9: Total Contrast vs. IR Source Temperature
300
Contrast (unitless)
250
200
150
100
50
0
400
600
800
1000
1200
1400
1600
IR Source Temperature (K)
Improving the Contrast
OPTRA is in the process of initiating a development effort to significantly improve the contrast of this DMD-based
MIWR scene projector. Improving the contrast will require steps to decrease the worst offender background
contributions – scattered light (#5), source light diffracted into the projector (#6), and the self-emission and reflection of
the flat state (#1). Concepts for improving both scattered and diffracted light include strategically positioned and shaped
aperture and field stops,3 increasing the illumination angle beyond twice the tilt angle (Figure 6), and polarizing the
illuminating and reflecting light off the DMD since scattered light tends to be largely depolarized. The model presented
in Figure 6 is also for an older DMD chip; improvements in DMD contrast for visible operation have since been made,
including the increase in tilt angle (12° from 10°) and the blackening of the substrate,4 although we do not yet know how
the latter will affect the performance in the MWIR without knowing the MWIR emissivity of the blackened surface.
Addressing the flat state emission and reflectivity will involve thermo-electrically (TE) cooling and possibly increasing
the emissivity even further beyond 0.98. A 2-stage TE cooler can lower the flat state temperature to 233 K or less which
will render this background contribution almost negligible.
Once factors 5, 6, and 1 have been addressed, the next largest background source is the projector optics’ reflectivity (# 8)
which in theory can be lowered with better AR coating and/or fewer surfaces, if possible.
3. GRAYSCALE DIGITIZATION
Grayscale digitization is limited by the drive electronics of the DMD and ultimately the fastest rate at which the
individual micromirrors can be flipped. The next generation OPTRA system will use a Digital Light Innovations (DLi)
D2D DVI interface daughter card which supports 24-bit color images at a 60 Hz update rate. This solution will be
customized for 10-bit grayscale (non-color) resolution at a minimal 100 Hz update rate. Part of the development effort
will be to examine the upper grayscale limit for a 100 Hz frame rate. An additional 2-bits of grayscale can then be
achieved in the spatial domain. Our next generation system projections show a 2 mrad internal field of view (i.e. the
field of view per micromirror) with an optical resolution of about 5 mrad. We propose to exploit this difference and the
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fact that a single micromirror will be unresolved by projecting images with 2×2 micromirror “superpixels” where each
superpixel can be modulated with the additional 2-bits of grayscale resolution via the intensity of each of the four
micromirrors that compose the superpixel. In other words, each superpixel can be further digitized into four levels by
the state of each of the four micromirrors which compose it. The overall result is a 12-bit grayscale image updating at
a 100 Hz frame rate.
4. CONCLUSIONS
We have presented a detailed analytical model predicting the total contrast of our MWIR DMD-based scene projector.
The worst offenders in order starting with the largest background contribution are scattering by the DMD substrate,
diffraction of off state light into the projector aperture, and self emission and reflectivity of the flat state. Concepts have
been presented to improve each of these as well as the next largest background source, the reflectivity of the projector
optics. We have also presented a scheme to achieve 12-bits of grayscale resolution at a 100 Hz frame rate. The next
steps will be the analysis, design, and implementation of these contrast improving concepts.
ACKNOWLEDGEMENTS
This research was conducted under a Small Business Innovation Research Phase II contract funded by the U.S. Navy.
REFERENCES
1
J.R. Dupuis, D.J. Mansur, R. Vaillancourt, T. Evans, D. Carlson, and E. Schundler, “Two-band DMD-Based Infrared
Scene Simulator,” Proc. SPIE Vol. 7663 (2010).
2
TI Application Report, “Single-Panel DLPTM Projection System Optics, Discovery DLPA002-March 2005.
3
Y. Meuret and P. De Visschere, “Contrast-improving methods for Digital Micromirror Device projectors,” Opt. Eng.,
Vol. 42, No. 3 (2003).
4
D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE
Vol. 4985 (2003).