Simulation of practical single-pixel wire

Simulation of practical single-pixel wiregrid polarizers for superpixel stokes
vector imaging arrays
Alan D. Raisanen
Michael D. Presnar
Zoran Ninkov
Kenneth Fourspring
Lingfei Meng
John P. Kerekes
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Optical Engineering 51(1), 016201 (January 2012)
Simulation of practical single-pixel wire-grid polarizers
for superpixel stokes vector imaging arrays
Alan D. Raisanen
Michael D. Presnar
Rochester Institute of Technology
Semiconductor and Microsystems Laboratory
82 Lomb Memorial Drive
Rochester, New York 14551
E-mail: [email protected]
Zoran Ninkov
Kenneth Fourspring
Lingfei Meng
John P. Kerekes
Rochester Institute of Technology
Chester F. Carlson Center for Imaging Science
54 Lomb Memorial Drive
Rochester, New York 14551
Abstract. An optical tracking sensor that produces images containing the
state of polarization of each pixel can be implemented using individual
wire-grid micropolarizers on each detector element of a solid-state focal
plane array. These sensors can significantly improve identification and
tracking of various man-made targets in cluttered, dynamic scenes such
as urban and suburban environments. We present electromagnetic simulation results for wire-grid polarizers that can be fabricated on standard
imaging arrays at three different technology nodes (an 80-, 250-, and
500-nm pitch) for use in polarization-sensitive detector arrays. The degradation in polarizer performance with the larger pitch grids is quantified.
We also present results suggesting the performance degradation is not
significant enough to affect performance in a man-made vehicle-tracking
application. © 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI:
10.1117/1.OE.51.1.016201]
Subject terms: hyperspectral imaging; polarimetry; polarizers; hybrid imaging arrays.
Paper 110580 received May 26, 2011; revised manuscript received Oct. 15, 2011;
accepted for publication Nov. 2, 2011; published online Feb. 7, 2012.
1 Introduction
Optically locating and following a moving target through a
cluttered environment is a challenging task. Target detection
and tracking can be made much more robust by exploiting
specific signatures of an artificial target relative to a natural
background, such as spectral characteristics1 (via multispectral and hyperspectral imaging) or polarization state.2–4 A single linear polarizing element in the input optics of a detector
system can be rotated to enable collection of the complete
Stokes vector describing the polarization state of each pixel
in an image, but this is only practical for slow-moving or static
scenes.2,5 For rapid data collection of fast-moving scenes at
video rates, the Stokes vector of the entire scene must be collected coincidentally. This can be accomplished by simultaneously collecting three polarization images for each pixel
at 0, 60, and 120 deg linear polarization, for example.6
These polarimetric images may be produced by imaging a
scene with multiple cameras, each with a suitable polarizer in
the input optics, but this process can be complicated by the
need to accurately register each camera relative to the others.
A more robust solution may be obtained by permanently
integrating the polarizer or polarizer array with the imaging
detector in a hybridized configuration. The full Stokes vector can be obtained with this approach by segmenting the
polarizer plus imager array into superpixels composed of
2 × 2 pixels, each with a linear polarizer element at a different
angle, as illustrated in Fig. 1(a). This proposed array contains
superpixels with individually polarized elements at 0, 60, and
120 deg linear polarization, plus a single unpolarized pixel
element. These arrays can be fabricated by affixing an array
of wire-grid polarizer elements on an optical element to the
imaging array. An alternative approach proposed here avoids
introducing another set of optical surfaces and avoids the
challenge of aligning and securing the polarizer array on the
0091-3286/2012/$25.00 © 2012 SPIE
Optical Engineering
imaging array by fabricating a set of pixel-sized wire-grid
polarizer elements directly on each element of the imaging
array. If there is sufficient demand for these devices it is
straightforward to fabricate these hybridized arrays during
the microfabrication process, but for low-volume and research
purposes it may be necessary to create the polarizer arrays on
an unpackaged commercial imager array.
Some authors have already reported successful integration
of pixel-sized polarizer arrays on optical detectors using
aluminum wire grids fabricated with electron-beam lithography.7 Very-high-efficiency micropolarizer elements can be
fabricated using the fine linewidths achievable with e-beam
lithography processes. Unfortunately, this process is expensive, low throughput, and can potentially degrade optical
detectors via radiation damage effects. Low-impact optical or
nanoimprint lithography can produce a suitable grid pattern
on each pixel of an imaging array, but the linewidths and spacing produced will be tend to be wider than that achievable
by an electron-beam lithography process. The advantage is
that the more conventional optical lithography processes
will have much higher throughput and be much cheaper.
The study of lower-cost fabrication processes was part of
an effort looking at MEMS-based adaptive sensors for urban
surveillance applications.8 Simulation of imaging systems
and target tracking algorithms9 using the Rochester Institute
of Technology (RIT)’s digital imaging and remote-sensing
image generation (DIRSIG) model was used to investigate
whether target-detection probability and tracking-path accuracy can be significantly improved by using polarimetric
imaging with even relatively low-efficiency large-spacing
polarizer elements. Detailed optical performance parameters
for these low-efficiency polarizing elements were unavailable
in the literature, so we selected three example technology
nodes that could realistically produce integrated or add-on
single-pixel polarizer elements without destroying an existing
imaging detector array. We simulated polarizer elements at a
500-nm pitch (readily fabricated using high-NA i-line or
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Raisanen et al.: Simulation of practical single-pixel wire-grid polarizers for superpixel stokes vector imaging arrays
Table 1 Geometrical design parameters for the simulated wiregrid polarizers.
Pitch (nm)
Fig. 1 (a) Superpixel detector geometry including three single-pixel
wire-grid polarizer elements at 0-, 60-, and 120-deg orientation, and
a single unpolarized pixel. (b) Two-dimensional (2-D) electromagnetic
simulation geometry illustrating location and dimensions of the aluminum wire grid, the pixel frame, and perfectly matched layer boundaries.
deep-UV optical lithography), a 250-nm pitch (fabricated
using advanced deep-UV optical lithography), and an 80-nm
pitch (achievable using advanced nanoimprint or state-of-theart immersion optical lithographic processes). The simulated
optical throughput of these devices was then used to postprocess hyperspectral polarization-resolved DIRSIG video
simulations in Mathworks Corporation (Natick, MA, USA)
MATLAB analysis software to assess the ability of a tracking
algorithm9 to monitor the position of a number of moving
vehicular targets in a simulated cluttered urban scene.
This paper describes the geometry and electromagnetic
wave propagation modeling of the wire-grid polarizers, the
resulting polarization performance, and the impact of that
performance on the vehicle-tracking application.
2 Geometry and Analysis
Wire-grid polarizer arrays were simulated using COMSOL
Multiphysics (COMSOL Inc., Burlington, MA) finite
element modeling software release 3.5a using the twodimensional (2-D) in-plane hybrid electromagnetic wave
Optical Engineering
Linewidth (nm)
Gap spacing (nm)
Thickness (nm)
500
100
400
100
250
50
200
50
80
20
60
20
application mode of the radio frequency (RF) modeling
module. Three different wire-grid geometries were modeled
as described in Table 1.
A relatively coarse 500-nm-period grid with 100-nmwide lines 100 nm thick was simulated as a geometry that
could be fabricated in our microelectronics lab on high-NA
i-line lithography equipment with a moderate amount of
effort. A more aggressive 250-nm-pitch grid, which would
require more complex and expensive deep ultraviolet lithographic techniques was simulated. An 80-nm-period grid
with 20-nm lines 20 nm thick was chosen as a candidate
geometry that we could fabricate using more aggressive
immersion lithographic techniques.
The metal grid was specified to be aluminum with 35.6 ×
106 siemens∕meter conductivity with a center aperture of
10 μm. Literature values10 for the complex permittivity of
aluminum in the visible region were interpolated and extrapolated to the near infrared and entered into the COMSOL
model as a wavelength-dependent function. The modeling
space was defined as 10 μm total perpendicular to the
centered grid, and 15 μm in the plane of the grid, with a
solid metal aperture plate bounding the vertical central
10-μm grid opening of a detector with a 17-μm element
pitch, as shown in Fig. 1. The wire-grid model is infinite
in extent in the direction perpendicular to the plane of the
figure. A 1-μm-thick perfectly matched layer (PML) was
defined surrounding the modeling space, and scattering
boundary conditions were defined at the outer boundary.
Electromagnetic plane waves were excited at the leftmost
boundary of the modeling space before the PML, and transmitted electromagnetic power was extracted by integration of
the Poynting vector at the rightmost boundary after the wave
had propagated through the metal grid. The relative intensity
of in-plane and perpendicular-to-plane electric and magnetic
fields of the incident plane wave were specified to produce
the polarization condition desired. That is, the electric field
(E) was defined as entirely out-of-plane for the s-polarized
(90-deg angle of polarization) case, and the electric field (E)
was defined as entirely in-plane for the p-polarized (0-deg
angle of polarization) case. The in- and out-of-plane incident
fields were thus defined as E in ¼ E 0 cos θ and E out ¼
E 0 sin θ, respectively, where θ is the polarization angle
between the incident electric field and the orientation of
the wire-grid array.
Meshing of the modeling space was refined until the solution obtained converged and was essentially unaffected by
further refinement. Simulations were performed by parametrically stepping through wavelengths from 400 to 2500 nm
by 10-nm increments. The simplified model described here
does not fully account for detailed effects such as polarizer
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Raisanen et al.: Simulation of practical single-pixel wire-grid polarizers for superpixel stokes vector imaging arrays
edge termination,11 the gap between polarizer and detector,12 and diffractive effects from the 2-D frame around
the polarizer. However, the model provides good qualitative
agreement with more sophisticated approaches using finitedifference time domain methods while remaining computationally simple enough to provide polarizer performance
metrics across a broad range of input wavelengths. Patterning
of a wire-grid polarizer array directly on a detector surface
is also expected to potentially excite near-field effects13
that may produce wavelength-dependent enhancements or
suppressions of both s- and p-polarized radiation, leading
to narrow peaks and valleys in the extinction ratio observed
for a given polarizer. These effects are neglected in this
model, but might be utilized to improve device performance
in specific spectral regions of interest in future work.
3 Polarization Performance Results
Figure 2 describes the simulated raw-transmission characteristics on a log scale of the three wire-polarizer geometries
selected in the wavelength range 400 to 2500 nm, plotted
for linear polarization angles from 0 to 90 deg. Transmission
is defined in this case by simply taking the ratio of transmitted electromagnetic power integrated across the right
boundary divided by the incident power integrated across
the left boundary. Results for the 80-nm-pitch polarizer
grid show better than −20 dB attenuation of s-polarized
light throughout the range 450 to 2500 nm, in qualitative
agreement with comparable wire-grid polarizer simulations
using other modeling techniques.11,12,14 Maximum transmission of p-polarized light is approximately 0.7 across the full
wavelength range 400 to 2500 nm. Wire-grid polarizers of
250 nm attain better than −20 dB attenuation of s-polarized
light only for wavelengths 1300 to 2500 nm and at least
−10 dB attenuation down to 600 nm, with performance
decreasing rapidly at shorter wavelengths. In comparison,
500-nm wire-grid polarizers have relatively poor attenuation
performance of s-polarized light at all wavelengths studied,
with −10 dB attenuation or more only at wavelengths greater
than 1300 nm. The 500-nm polarizer becomes ineffective as
the incoming wavelength approaches the pitch of the polarizer. Detailed behavior of the 500-nm polarizer in the 400- to
500-nm wavelength range is sensitive to the size and shape
of the individual wires making up the polarizer.
Extinction ratios of the simulated polarizers can be calculated by taking the ratio of transmission at 0 deg polarization
to the transmission at 90 deg polarization. This represents the
relative intensities of p-polarized to s-polarized light from a
randomly polarized input transmitted through the polarizer.
r e ðλÞ ¼
τmax ðλ; θÞ
τðλ; 0 degÞ
:
¼
τmin ðλ; θÞ τðλ; 90 degÞ
(1)
Extinction ratios for all three polarizers simulated are plotted
in Fig. 3 on a log scale as a function of wavelength. For
comparison, commercial macroscopic calcite and nanoparticle polarizers are available with extinction ratios exceeding
105 , and commercial infrared wire-grid polarizers are available with extinction ratios exceeding 102 . The simulated
80-nm wire-grid polarizer provides an extinction ratio
Fig. 2 Transmission characteristics of single-pixel wire-grid polarizers with pitch of (a) 500, (b) 250, and (c) 80 nm for polarization angles
0 to 90 deg.
Optical Engineering
Fig. 3 Extinction ratio versus wavelength plotted for 80-, 250-, and
500-nm-pitch single-pixel polarizers.
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Raisanen et al.: Simulation of practical single-pixel wire-grid polarizers for superpixel stokes vector imaging arrays
greater than 102 for all wavelengths 500 to 2500 nm, while
the 250-nm wire-grid extinction ratio only exceeds 102
above 1600 nm, and exceeds 101 for wavelengths longer
than 650 nm. The 500-nm wire-grid extinction ratio is
relatively poor at all wavelengths investigated, exceeding 101
only for wavelengths above 1500 nm and rapidly dropping to
unity (i.e., no polarization contrast) at shorter wavelengths
approaching 500 nm.
Finally, the diattenuation response of a polarizer is a
measure of the polarizer efficiency, defined as
DðλÞ ¼
¼
τmax ðλ; θÞ − τmin ðλ; θÞ
τmax ðλ; θÞ þ τmin ðλ; θÞ
τðλ; 0 degÞ − τðλ; 90 degÞ
:
τðλ; 0 degÞ þ τðλ; 90 degÞ
(2)
Ideally, the diattenuation response of a polarizer will be relatively flat over the wavelength range of interest, with a value
close to unity. The diattenuation response of all three simulated wire-grid polarizers is plotted in Fig. 4 as a function of
wavelength. The 80-nm-pitch wire-grid polarizers produce a
relatively flat diattenuation response greater than 95%
throughout the wavelength range 400 to 2500 nm, while the
250-nm polarizer achieves this level of diattenuation only at
wavelengths longer than 1000 nm, with a rapid decrease in
performance at shorter wavelengths to a minimum of 0.18 at
400 nm. The 500-nm polarizer grids exhibit relatively poor
diattenuation throughout the wavelength range studied, with
a maximum diattenuation of 0.94 at 2500 nm rapidly
decreasing to zero at 500 nm.
3 2
τ90 ðλÞ þ τ0 ðλÞ
S^ 0
4 S^ 5 ¼ 4
0
1
0
S^ 2
2
32 3
0
0
S0
54 S1 5 :
τ90 ðλÞ − τ0 ðλÞ
0
0
τ90 ðλÞ − τ0 ðλÞ
S2 input
For each simulated wavelength, spectral video imagery from
DIRSIG was processed with the polarizer transmission
results to simulate the output from the 2 × 2-superpixel
Stokes vector detector [assuming a constant detector
signal-to-noise ratio (SNR) of 200], and the processed
video was input to Numerica’s algorithm simulator for
tracking and observations (ALTO),9 a hyperspectral target
tracking algorithm to assess target detection and tracking
performance. The ALTO algorithm with video-processing
examples is described fully elsewhere.9 It employs measurement of target features (e.g., spectral radiance, polarization
state) to aid in identifying, classifying, and distinguishing
between multiple targets. Two of the key metrics associated
with the ALTO tracking algorithm9,15 are track completeness,
which is a normalized measure of the probability of correctly
identifying a moving target vehicle, and Track Purity, which
is a normalized measure of how long a track retains the
Track Purity ¼
4 Impact on Tracking Performance
Sequences of at-sensor polarized spectral radiance images of
an urban scene with moving vehicles were generated to study
the effect on tracking performance of the various wire-grid
designs.15 The model was created in DIRSIG16 using the
“MegaScene”17 large-area suburban model containing a
large number of buildings, trees, and other topographical
clutter. Polarization-dependent DIRSIG video simulations
in the wavelength range 400 nm to 2.5 μm were generated
to account for the polarizing properties of surfaces in the
scene, the effect of the atmosphere, and the geometry of the
solar illumination and off-nadir downward viewing-sensor
position. A large number of moving vehicles were defined
and simulated throughout the scene using the simulation
of urban mobility (SUMO)18 simulation tool.
The output of the DIRSIG simulation consists of a set of
Stokes vectors for each pixel and wavelength in the scene as
viewed from the observation optical system. These Stokes
vectors incorporate all of the polarizing effects included in
the scene, including reflection from flat or curved surfaces,
or depolarization from scattering in atmospheric haze or
aerosols. Modifications to these polarized images originating
from the optical viewing system are applied by postprocessing in MATLAB to produce an “effective” Stokes vector for
each pixel after the idealized at-sensor radiance from the
scene passes through our imperfect polarizer array, adding
in s-polarized light leaking past an imperfect polarizing
element, or removing p-polarized light being absorbed by
an element. This “effective” Stokes vector is computed from
the input DIRSIG Stokes vector and the transmission coefficients obtained in Fig. 2 by the matrix
(3)
correct vehicle without losing the target (due to clutter,
for example) or incorrectly switching to a different nearby
vehicle. Perfect tracking performance gives a unity track
completeness and Track Purity measure. Track completeness
is defined as
Track Completeness¼
of Valid-Tracks
:
of Should-Tracks
Valid-Tracks are defined as detected targets that are confirmed to be within a 4-m radial distance to its known position output by SUMO, while Should-Tracks is the total
number of targets that have been placed in the field of
view. This parameter can also be described as the “probability of target detection,” which is a primary figure of merit for
any target-tracking algorithm. The Track Purity parameter is
defined as
of epochs a valid tracks followed the same truth vehicle
totalof epochs in a valid track
Optical Engineering
(4)
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Raisanen et al.: Simulation of practical single-pixel wire-grid polarizers for superpixel stokes vector imaging arrays
moves into different illumination conditions or changes
direction, so ALTO has to compensate for this changing
target profile without misidentifying an altered target as a
completely new target. Although both the 80- and 500-nm
polarizer arrays provide for improved target detection, we
believe that in at least this case the higher performance of
the 80-nm polarizers produces a large enough change in target signature to confuse the tracking algorithm for some
tracks, while the lower-performance 500-nm polarizer sensor
do not produce sufficient change in the target signature under
the same motion and illumination conditions to break the
target-tracking lock.
Fig. 4 Diattenuation versus wavelength plotted for 80-, 250-, and
500-nm-pitch single-pixel polarizers.
Track Purity is a measure of how accurately the tracking
algorithm can follow a target when it is occluded by an
object, such as an overhanging tree, or when it encounters
an ambiguous situation, such as two targets meeting at an
intersection. If the predicted target track jumps between
two closely spaced vehicles, or fails to positively reacquire
a previously tracked target after an occlusion, it reduces the
Track Purity parameter. Table 2 illustrates some of the initial
tracking results for two video sets that were generated15 for
both the 80-nm polarizer and the 500-nm polarizer models. It
should be noted that addition of polarization dependence
does not improve tracking performance in all simulations
over plain panchromatic tracking simulations, especially
in the presence of atmospheric haze and other interference.
Also, in general, simulations of the 80-nm polarizer sensors
are superior to those generated by 500-nm polarizer sensors.
This data set consisted of 151 frames at 10 Hz simulated for a
50-deg oblique viewing angle with 1120 × 1760 pixels and
13 spectral bands from 400 to 2500 nm and four Stokes
bands, with 32 vehicles to track. It is interesting to note
that tracking metrics for the 500-nm polarizer were comparable to those obtained for the 80-nm polarizer, implying that
at least for some conditions of target, illumination, clutter,
and atmospherics, the low-performance polarizer elements
provide sufficient contrast in the near infrared to be effective
in improving target tracking in cluttered urban environments.
Also interesting is the higher Track Purity metric for the
500-nm polarizer sensor compared with the 80-nm polarizer
sensor. The ALTO target-tracking algorithm uses the spectral
and polarization signature of a target to distinguish it from
other nearby targets. This signature can vary as a target
Table 2 Comparison of tracking metrics generated by alto for
the same cluttered urban scene using Stokes vector polarizer
detectors with80- and 500-nm line pitch.
Polarizer pitch (nm)
Track completeness
Track Purity
500
0.805
0.766
80
0.868
0.655
Optical Engineering
5 Conclusions
Optical performance metrics for three single-pixel wire-grid
polarizer elements using three fabrication technology nodes
are described. As anticipated, a wire-grid polarizer fabricated
with an 80-nm pitch provides good diattenuation and extinction ratio performance across the design wavelength range
400 to 2500 nm. Wire-grid polarizers fabricated with lowcost technology at a 500-nm pitch provide relatively poor
optical performance in terms of diattenuation and extinction
ratio, but are shown to still enable good target-tracking capability in urban scenes under specific circumstances. These
results offer the potential of fabricating highly integrated
Stokes vector detectors at relatively low cost and high
volume using moderate resolution microlithography.
Acknowledgments
This research was supported by the Air Force Office of
Scientific Research (AFOSR) under agreement number
FA9550-08-1-0028 (AFOSR-BAA-2007-8). OSLO optical
modeling software used in this research was donated by
Lambda Research Corporation under their University Gratis
program. The authors gratefully acknowledge use of RIT’s
Research Computing and Center for Imaging Science
computing resources to accomplish this project.
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Alan D. Raisanen received his BS degree in
physics from Drake University, Des Moines,
Iowa, in 1985 and his PhD in materials
science and engineering in 1992. He joined
Rochester Institute of Technology as a technical staff member in 2001. His current
research focuses on use of microfabrication
techniques to implement microsystems
for imaging, detection, and biomedical
applications.
Michael D. Presnar received a BS in chemical engineering together with a BS in electrical engineering from Michigan Technological
University, Houghton, Michigan, in 1995; an
MS in electrical engineering together with
an MS in applied mathematics from the Air
Force Institute of Technology, Dayton, Ohio,
in 2000; and his PhD in imaging science
from the Rochester Institute of Technology,
Rochester, New York, in 2010. He is currently
an officer in the United States Air Force.
Optical Engineering
Zoran Ninkov is a professor in the Center
for Imaging Science (CIS) at the Rochester
Institute of Technology. He completed his
BSc in physics at the University of Western
Australia, MS in chemistry at Monash
University, and his PhD in astronomy at the
University of British Columbia. He was a
postdoctoral fellow at the University of
Rochester working on infrared detector
array for the Spitzer Space Telescope. He
subsequently spent time at the DSTO in
Adelaide, Australia, and at ISTS in Toronto before joining CIS. His
research interests are in detectors and instrumentation.
Lingfei Meng received his BS degree in
electrical engineering from the Tianjin University, China, in 2007. He is currently pursuing
his PhD degree in imaging science at the
Rochester Institute of Technology, New
York. His research interests include imaging
system modeling, digital image processing,
and computer vision.
John P. Kerekes received a BS, MS, and
PhD in electrical engineering from Purdue
University, West Lafayette, Indiana, in 1983,
1986, and 1989, respectively. From 1989
until 2004 he was a technical staff member
at MIT Lincoln Laboratory in Lexington,
Massachusetts. Since 2004 he has been an
associate professor at the Chester F. Carlson
Center for Imaging Science at the Rochester
Institute of Technology. His research interests include pattern recognition, image
processing, and remote-sensing system modeling.
Biographies and photographs of the other authors are not available.
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