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This PDF file contains the front matter associated with SPIE
Proceedings Volume 6972, including the Title Page, Copyright
information, Table of Contents, Introduction (if any), and the
Conference Committee listing.
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The lighting of the underwater environment is constantly changing due to attenuation by water, scattering by
suspended particles, as well as the refraction and reflection caused by the surface waves. These factors pose a great
challenge for marine animals which communicate through visual signals, especially those based on color. To escape this
problem, certain cephalopod mollusks and stomatopod crustaceans utilize the polarization properties of light. While the
mechanisms behind the polarization vision of these two animal groups are similar, several distinctive types of polarizers
(i.e. the structure producing the signal) have been found in these animals. To gain a better knowledge of how these
polarizers function, we studied the relationships between fine structures and optical properties of four types of polarizers
found in cephalopods and stomatopods. Although all the polarizers share a somewhat similar spectral range, around 450-
550 nm, the reflectance properties of the signals and the mechanisms used to produce them have dramatic differences. In
cephalopods, stack-plates polarizers produce the polarization patterns found on the arms and around their eyes. In
stomatopods, we have found one type of beam-splitting polarizer based on photonic structures and two absorptive
polarizer types based on dichroic molecules. These stomatopod polarizers may be found on various appendages, and on
the cuticle covering dorsal or lateral sides of the animal. Since the efficiencies of all these polarizer types are somewhat
sensitive to the change of illumination and viewing angle, how these animals compensate with different behaviors or fine
structural features of the polarizer also varies.
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We investigate the advantages of employing a fiber faceplate in a snapshot polarimetry system. Our previous work at
Sandia National Laboratories indicates that diffraction and propagation between the micropolarizer array, the microwaveplate
array, and the Focal Plane Array (FPA) degrade performance, as quantified by the extinction ratio1,2.
Crosstalk between adjacent pixels due to diffraction increases uncertainty of the measured polarization states in a scene
of interest. These issues are exacerbated in the long-wavelength regime and as FPA pixel dimensions decrease.
One solution, since it minimizes propagation distance, is to construct the micropolarizer and micro-waveplate arrays on a
single substrate surface and to place this combination on the FPA3. This solution is a significant fabrication challenge
and decreases yield due to its serial assembly nature.
An alternative solution that would improve yield is to fabricate the micropolarizer on top of a fiber faceplate, place the
faceplate on the FPA with the micropolarizer facing away, then place the waveplate array on top of the micropolarizer.
The optical field that passes through the plane of the microwaveplate array and the micropolarizer array is guided to the
FPA plane, without suffering diffraction effects associated with free-space propagation. We will quantify the utility of
these proposed configurations with predicted imaging polarimetric system extinction ratios.
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We present a Stokes polarization camera prototype based on an electro-optic ceramic (PLZT) as the key
polarization component. Two pairs of electrodes are used to control the applied electric field and so the retardance and
orientation of the induced waveplate. The active area of the PLZT element is 120x120µm. To increase the effective
active area, a 2D array PLZT is used. Imaging through this 2D array with reduced fill factor is achieved by splitting the
focal plane. The focal plane is split by a microlenses array and interacts with each element of the ceramic array. A
modified focal plane is reconstructed by another microlenses array. Digital image processing is used to recover the prime
focal plane information. The technology used in this device (ceramic element, 2D array, imaging with split focal plane)
as well as characterization of the ceramic element and preliminary results will be presented.
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JDSU has developed a new family of optical retarders based on liquid crystal polymer (LCP) and form birefringent
dielectric thin film technologies. The manufacturing processes are wafer-based, allowing components up to 200mm
diameter to be produced. The component designs allow customization over a wide range of retardance values with
excellent accuracy, uniformity and low transmitted wavefront distortion. Form birefringent components are integrated
monolithically with an LCP-based retarder to create flat retardance response of ±2nm over an incident cone angle of
±30degrees. This paper will present an overview of the technology, measured performance attributes and provide
examples of product applications.
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A new detection system has been designed and constructed that enables remote sensing, recording and archiving of
Electrical Over-Stress (EOS) and Electro Static Discharge (ESD) events, a major cause of electronic device failure in
ruggedized military applications. Advances have been made in the design and manufacture of magneto-optic static event
detection devices and in the ability to perform automatic detection of polarization states of the devices. The combined
automatic reader and next-generation device are providing viable prototypes for insertion into legacy circuit boards for
EOS and ESD monitoring.
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Many natural materials produce polarization signatures, but man-made objects, typically having more planar or smoother
surfaces, tend to produce relatively strong polarization signatures. These signatures, when used in combination with
other means, can significantly aid in the detection of man-made objects. To explore the utility of polarization signatures
for target detection applications we have developed a new type of polarimetric imaging sensor based on tunable liquid
crystal components. Current state-of-the-art polarimetric sensors employ numerous types of imaging polarimeters, the
most common of which are aperture division, micropolarizer, and rotating polarizer/analyzer. Our design uses an
electronically tunable device that rotates the polarization of incoming light followed by a single fixed oriented linear
polarizer. Its unique features include: 1) sub-millisecond response time switching speed, 2) ~75% transmission
throughput, 3) no loss of sensor resolution, 4) zero mechanical moving parts, 5) broadband (~75% of center wavelength),
6) ~100:1 contrast ratio, 7) wide acceptance angle (±10°), and 8) compact and monolithic architecture (~10 inch3). This
paper summarizes our tunable liquid crystal polarimetric imaging sensor architecture, benefits of our design, analysis of
laboratory and field data, and the applicability of polarization signatures in target detection applications.
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We present a linear Stokes polarization camera working at visible wavelength. The camera is both compact and
robust for use in field experiments and outdoor conditions. It is based on fast polarization modulator. Four polarization
states images are acquired successively. Processing software allows live calculation, visualization and measurement of
polarization images deduced from the acquired images. The architecture of the hardware, calibration results and
sensitivity measurements is presented. Polarization image processing including polarization parameters computed are
proposed. These parameters include linear Stokes parameters (S0, S1 and S2), usual polarization parameters (intensity,
degree of linear polarization, and angle of polarization) and other polarization based parameters (polarized image,
depolarized image, virtual polarizer, polarization difference). Color data fusion and vector overlay algorithms are
presented. Finally experimental results and observations as well as possible applications are discussed.
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Development of robust compact spectropolarimetric imagers that can acquire spectral, spatial and polarization features
from a scene of interest is of utmost importance for efficient detection of targets and backgrounds. Spectral features arise
due to the material properties of objects as a result of the emission, reflection, and absorption of light while the
polarization features arise from the physical nature of the object surfaces and edges that influence the polarization
properties of the reflected, scattered, or emitted light. Using a hyperspectral imager one can acquire images with narrow
spectral bands and take advantage of the characteristic spectral signatures of different materials making up objects and
backgrounds. By combining both polarization and hyperspectral detection capabilities in one single imager, we can
perform much better object detection and identification than by using either polarization or hyperspectral detection
capability. Spectropolarimetrc imagers designed using an acousto-optic tunable filter (AOTF) are ideally suited to
provide both agile spectral and polarization signatures. At the U.S. Army Research Laboratory (ARL), we are
developing small, vibration-insensitive, robust, remotely controlled, and programmable hyperspectral imagers from the
ultraviolet to the long wave infrared. We have also demonstrated a full Stokes polarization imager using an AOTF with
two liquid crystal retarders. Here, we will discuss our imager designs and present results from our experiments.
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Two imaging systems have been designed and built to function as snapshot imaging spectropolarimeters; one system
made to operate in the visible part of the spectrum, the other for the long wavelength infrared, 8 to 12 microns. The
devices are based on computed tomographic imaging channeled spectropolarimetry (CTICS), a unique technology that
allows both the spectra and the polarization state for all of the wavelength bands in the spectra to be simultaneously
recorded from every spatial position in an image with a single integration period of the imaging system. The devices
contain no moving parts and require no scanning, allowing them to acquire data without the artifacts normally associated
with scanning spectropolarimeters. Details of the two imaging systems will be presented.
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Polarimetric Lidar has been recently proposed as a method for remote detection of aerosolized biological warfare
agents. Accurate characterization of the optical signatures for both biological agents and environmental interferents is a
critical first step toward successful sensor deployment.
MIT Lincoln Laboratory has developed the Standoff Aerosol Active Signature Testbed (SAAST) as a tool for
characterizing aerosol elastic scattering cross sections.1 The spectral coverage of the SAAST includes both the nearinfrared
(1-1.6 μm) and mid-infrared (3-4 μm) spectral regions. The SAAST source optics are capable of generating all
six classic optical polarization states, while the polarization-sensitive receiver is able to reconstruct the full Stokes
vector of the scattered wave. All scattering angles, including those near direct backscatter, can be investigated. The
SAAST also includes an aerosol generation system capable of producing biological and inert samples with various size
distributions.
This paper discusses the underlying scattering phenomenology, SAAST design details, and presents some representative
data.
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1991 STS-43 Shuttle polarimetric imagery was used to calculate a degree of linear polarization (DoLP) image, registered
to a 1994 NW Madagascar Landsat 5 scene. The Jeffries-Matusita (J-M) distance and Transformed Divergence (TD)
were calculated for every class-pair of a 13-class ISODATA classification, using 6 TM (Thematic Mapper) bands, and
TM bands plus DoLP. Separabilities were also calculated using just TM bands 7, 4, and 2 and compared against them
plus DoLP. There was a small, consistent increase in spectral separability for all class-pairs with the addition of DoLP.
A similar experiment was done using 1999 Landsat 7 imagery covering the area of the 1994 NASA BOREAS
experiment. The separabilities were calculated for just a 742 combination and 742 plus DoLP created from the airborne
POLDER sensor. The maximum increase in separability provided by DoLP was nearly 5-fold greater than for the
Madagascar imagery. The separabilities were compared also for bands 742 plus DoLP with 742 plus band 1 and 742
plus band 5. As with band 1, band 5 improved more class-pair separabilities than DoLP, but the average amount of
improvement was more than 4-times greater for DoLP for those class-pairs that saw improvement, versus those that were
better separated by band 5. The J-M distance predicts better classification performance for DoLP compared to bands 1
and 5, while the TD suggests slightly better performance for band 5 over DoLP or band 1.
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An imaging spectro-polarimeter was used to measure polarization signatures in five visible and near infrared channels
(450, 490, 530, 630, 700 nm) from four painted steel plates throughout the day as the solar angle and sky conditions
changed. The primary objective of this study was to characterize the influence of variable sky conditions on the observed
polarization signatures. Smooth plates exhibited higher degree of polarization than rough plates and black plates
generally exhibited higher degree of polarization than tan plates. Changes in cloudiness caused large variations in the
polarization, usually reducing the observed degree of polarization.
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Polarimetry has been used by astronomers to explore diverse objects such as stars in formation, primordial discs around
stars that could provide the birthplace of planets, magnetic fields in stars and interactions of black holes with their
environments and host galaxies. In recent years, telescopes with primary mirrors of 8-10m have been commissioned,
and a new era of airborne astronomy is imminent, enabling more detailed observations of fainter and more distant
objects as well as offering an increasing diversity of wavelength coverage and techniques. Significant technological
progress in polarizing components and methodologies has also been realized in recent years. Together these
developments afford astrophysical polarimetry with considerable advances across all wavelengths. I review the
astronomical drivers for such progress and the instrumentation/methodologies at optical, mid-IR and mm wavelengths
required to realize such progress.
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A four camera Stokes imaging polarimeter operating in the visible at 60 frames
per second will be presented. The polarimeter makes use of a beam splitter design which
allows the measurement of a full Stokes vector image (S0, S1, S2, and S3). The system
measures four images of a scene simultaneously. The polarimeter design, calibration
procedures, and initial data from the instrument are presented.
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A 2-Cam micro-bolometer imaging polarimeter operating in the LWIR is presented. The system is capable of snapshot
imaging Stokes polarimetry in any one channel (S1, S2, or S3) by taking two simultaneous measurements of a scene. For
measurements of S1 or S2, the instrument relies on a specially optimized wire-grid beam-splitter. For measurements of
S3, a form birefringent quarter-wave retarder is inserted into the optical path. Specifics associated with the design of the
wire-grid beam-splitter and the form birefringent quarter-wave retarder will be overviewed, with inclusion of RCWA
simulations. Calibration and simulation procedures, as well as calibration targets, will be highlighted, and initial data
from the instrument are presented.
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Analysis: Polarization Mathematics, Algorithms, and Processing I
Division of focal plane (DoFP) polarimeters are a particular class of imaging device that consists of an array
of micropolarizers integrated upon a focal plane array sensor (FPA). Such devices are also called microgrid
polarimeters and have been studied over the past decade with systems being designed and built in all regions
of the optical spectrum. These systems are advantageous due to their rugged, compact design and ability to
obtain a complete set of polarimetric measurements during a single frame capture. One inherent disadvantage
of DoFP systems is that each pixel of the FPA sensor makes a polarized intensity measurement of a different
scene point. These spatial measurements are then used to estimate the Stokes vectors across the scene. Since
each polarized intensity measurement has a different instantaneous field-of-view (IFOV), artifacts are introduced
that can degrade the quality of estimated polarization imagery. Here we develop and demonstrate a visual
enhancement technique that is able to reduce false polarization caused by IFOV error while preserving true
polarization content within the Stokes parameter images. The technique is straight-forward conceptually and is
computationally efficient. All results are presented using data acquired from an actual LWIR microgrid sensor.
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We revisit the theoretical model for emission polarization from rough surfaces to improve previous models.
Previous models treat the directional emissivity σs as 1- rs where rs is directional reflectivity and s stands for
perpendicular or parallel component to the incident surface. The directional emissivity is based on the Kirchhoff's law
and the energy conservation between incident, reflected and transmitted light. This emission model considers only linear
polarization as it does not allow the cross term of parallel and perpendicular components of Fresnel reflection
coefficients.
In this paper, we formulate the four emission Stokes parameters with emission wave amplitudes to describe the
complete emission polarization content of dielectric as well as conduction media. The emission wave amplitudes are
derived from the energy conservation and are functions of Fresnel transmission coefficients and incident and refraction
angles. For a conducting medium which has a complex indices of refraction, the refraction angle is redefined to avoid the
physically unreasonable complex angle. The emission Stokes parameters are averaged over time and then over the
roughness of the surface. The time average of the cross terms of the perpendicular and parallel emission electric fields is
assumed to be zero as the emission is an incoherent process.
It is found that the emission S2 is zero for a smooth surface or a surface with isotropic roughness and S3 is zero
regardless of surface roughness if the time average of the cross terms is assumed to be zero. Our results are compared
with previous theoretical models and lab measurements and reasonable agreement is found.
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Polarimetry sensor development has been in work for some time to determine the best use of polarimetry to differentiate
between manmade objects and objects made by nature. Both MWIR and LWIR Focal Plane Arrays (FPAs) have been
built at Raytheon Vision Systems each with exceedingly higher extinction ratios. This paper compares field imagery
between MWIR and LWIR micro-grid polarimetric sensors independently and during simultaneous image collects.
LWIR polarimetry has the largest polarimetric signal level and an emissive polarimetric signature which allows
detection at thermal crossover and is less dependent on sun angles. Polished angled glass and metal objects are easily
detected using LWIR polarimetry. While LWIR
polarimetry has many advantages its resolution is not as
good as MWIR.
MWIR polarimetry has higher resolution than LWIR. With
good sun angles plastic drums, and wet surfaces provide
good polarization signatures. With poor sun angles
detection can be challenging.
To gain acceptance polarimetric sensors must provide
intelligence signatures that are better than existing nonpolarimetric
Infrared sensors. This paper shows several
examples of images without polarimetric processing and
identical images with MWIR and/or LWIR polarimetric
fusion onto the non-polarized images to show the
improvement of detection using polarimetric sensors. It is
the author's belief that the fastest way to gain acceptance of
polarimetric remote sensing is through field demonstration
as shown in Figure 1.
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Analysis: Polarization Mathematics, Algorithms, and Processing II
Efficient surface and subsurface land mine detection is still one of the several important tasks in the
civilian and military areas. Often information derived from multiple sensors are fused together to lead a
net gain in probability of detection of these land mines. Some drawbacks of this approach are the different
sensor output formats and the overall processing efficiency of the system. To overcome some of the
aforementioned concerns we propose a simple and efficient image fusion using logical operators. The
proposed technique uses logical operators to fuse multiple images derived from a single sensor. The
logical fusion operation is applied to the output of the sensor to lead a logically fused image. This image
serves as an input to the detection algorithm. The proposed technique is shown to improve the probability
of detection of land mines. This improvement is shown using the ROC curve approach.
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The polarimeter we developed is composed of a single commercial CCD camera with a bistable ferroelectric liquid
crystal modulator as a polarizing element; therefore the degree of polarization (DOP) is evaluated from two successive
acquisitions. Thus, when an object moves during the acquisition, issues occur in the polarization information
reconstructed from the two state pictures: edges of objects have neither the same DOP as the object itself nor the same
DOP as the background. In this paper, we present two methods to correct defects in DOP images of moving objects.
First, we present a post-processing temporal median filtering, correcting the DOP once computed. The second method
consists in performing a motion estimation to correct the object's displacement between the two polarization state
pictures. Comparison based on quantitative results with real data is provided.
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An imaging polarimeter records the polarization state of light reflected by an object that is illuminated with a
polarized source such as a laser. Active polarimetric imagery has been shown to be useful in many remote sensing
applications including shape extraction, material classification and target detection/recognition. In this paper, we
present a method that automatically extracts the angle of incidence, angle of reflection and the relative azimuthal
angle from Mueller matrix imagery. Mueller matrix imagery provides multiple measurements from which we can
construct a nonlinear system of equations. This system is solved using the Levenberg-Marquardt algorithm
which is a standard nonlinear equation solver. We experimentally demonstrate via computer simulations that
the parameter estimates can be estimated accurately using our approach.
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This paper will describe methods of measuring all of the components of the Stokes polarization vector for each pixel in a
scene using only one frame of passive optical sensor data, one radar pulse, or one radiometer integration interval. Both
active and passive sensors operating in any waveband from microwave to visible will be considered. For systems
operating in the millimeter wave and terahertz bands, the techniques developed by Dereniak and his students at the
University of Arizona will be discussed. For other wavebands, a technique developed by the author that requires the
coherent reception of two orthogonally-polarized signal components will be presented. This latter method works for both
for both broad-band and narrow-band active or passive signals, but requires focal planes and hardware in the visible and
infrared bands that may be too complicated for many applications. Results of calculations made for the millimeter and
terahertz bands will be presented.
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Detection and clearance of subsurface land mines has been one of the challenging humanitarian and
military tasks. Among the several surface land mines detection techniques available, passive polarimetric
in the visible range holds a high promise to lead a high probability of detection. In this paper we show
how a single sensor producing multiple polarized and unpolarized imagery can be used to improve the
probability of detection of subsurface land mines. This improvement is shown using the Receiver
Operation Characteristic (ROC) curve approach.
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Monostatic reflectance distribution function and Mueller matrix measurements were made of automobile panel samples
using a polarimetric laser reflectometer and a spectropolarimeter, and roughness measurements were made using a
surface profilometer. The spectropolarimeter measurements were made over the range 0.7 to 2.6 μm in the near and
short wave infrared, and the laser measurements were made at 1.06 μm. Depolarization indices for all polarimetric
measurements were calculated.
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We present radiometric and polarimetric calibrated imagery recorded in both the mid-wave IR
(MidIR) and long wave IR (LWIR) as a function diurnal variation over several multiday periods. We
compare differences in polarimetric and conventional thermal imagry for both IR atmospheric
transmission windows, i.e., 3-5μm and 8-12 μm regions. Meteorological parameters measured
during the study include temperature, relative-humidity, wind-speed/direction, precipitation, and
ambient atmospheric IR loading. The two camera systems used in the study differed significantly in
design. The LWIR polarimetric sensor utilizes a spinning achromatic retarder and is best suited for
static scenes, while the MidIR system is based on a division-of-aperture design and is capable of
recording polarimetric imagery of targets that are rapidly moving. Examples of both S0
(conventional thermal) and degree-of-linear polarization (DOLP) imagery are presented and
compared.
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Electro-optic (EO) imaging systems are commonly used to detect civilian and military targets during surveillance
operations and search and rescue missions. Adding the polarization of light as additional information to such active and
passive EO imaging systems may increase the target discrimination performance, as man made objects are known to
depolarized light in different manner than natural background. However, while the polarization of light has been used
and studied in the past for numerous applications, the understanding of the polarization phenomenology taking place
with targets used in cluttered backgrounds requires additional experimentations. Specifically, the target contrast
enhancement obtained by analyzing the polarization of the reflected light from either a direct polarized laser source as
encountered in active imagers, or from natural ambient illumination, needs further investigation. This paper describes an
investigation of the use of polarization-based imaging sensors to discriminate civilian and military targets against
different backgrounds. Measurements were carried out using two custom-designed active and passive imaging systems
operating in the near infrared (NIR) and the long-wave infrared (LWIR) spectral bands. Polarimetric signatures were
acquired during two distinct trials that occurred in 2007, using specific civilian and military targets such as cars and
military vehicles. Results demonstrate to what extent and under which illumination and environmental conditions the
exploitation of active and passive polarimetric images is suitable to enable target detection and recognition for some
events of interest, according to various specific scenarios.
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Polarization signature information is becoming more useful as an added discriminant in a variety of signature analysis
applications. However, there are few infrared scene projection systems that provide the capability to inject target
simulation images with polarization content into a seeker, or other imaging sensor. In this paper, we discuss a
polarization scene generator (PSG) concept that is applicable to testing sensor systems operating in cryogenic-vacuum
environments. This polarization scene generator concept demonstrator system was constructed from off-the-shelf
technology using commercially available mid-wave infrared (MWIR) scene projectors based on micromirror device
display technology, standard infrared polarizers, and standard IR cameras. The demonstrator system used two digital
micromirror device (DMD)-based displays, each projecting orthogonal polarization states, which were then combined to
generate images with pixels having independent S1 or S2 polarization content. This concept is robust because it is
relatively unconstrained by the IR scene generators used or by the seekers tested. This paper discusses the test results of
the concept demonstrator system with regard to sensitivity to misalignment, radiance mismatch, and display uniformity.
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It is known, that all four basic types of anisotropy, circular and linear birefringence and circular and linear dichroism, each taken separately, possess orthogonal eigenpolarizations. Generalized birefringence, i.e. the case of medium exhibiting linear and circular birefringencesimultaneously, is characterized by unitary matrix model and has orthogonal eigenpolarizations. At the same time, simultaneous presence of dichroism and birefringence in a medium may lead to nonorthogonal eigenpolarizations. However, to the best of our knowledge, so far there has been no systematic study of conditions under which such medium possesses orthogonal eigenpolarizations. Ascertainment of generalized conditions for orthogonality of medium's eigenpolarizations allows determining the structure and symmetry of matrix model
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Previously, we have investigated the use of Long-Wave Infra-Red (LWIR) polarimetric imaging for the detection of surface swimmers in a maritime environment. While better contrast and longer range are expected with Mid-Wave Infra-Red (MWIR) polarimetric imaging, the cost of such a system is higher than a polarimetric imager operating in the LWIR due to the advent of higher-performance micro-bolometer imaging arrays. The actual performance of a MWIR polarimetric imager to detect a person in the water is presented. A comparative analysis of system cost between MWIR and LWIR systems is also discussed.
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Light detection and ranging (LIDAR) has potential to be a successful technique for remote detection of airborne
biological warfare agents (BWA) that pose a health hazard. Potential techniques for detecting BWA often use
spectroscopy to probe molecular structure properties (e.g. UV-fluorescence, Raman and differential absorption
spectroscopy). An alternative approach is to differentiate BWA from background interferents by their differing
morphology; depolarisation offers one such method. Here, we investigate the feasibility of introducing depolarisation
into a short range (approximately 10 m) LIDAR designed to be a simple, inexpensive, low power consumption, portable
instrument.
T-matrix calculations are presented for a randomly oriented, polydisperse size distribution of Bacillus atrophaeus
spheroids. The relationship between backscatter depolarisation and particle aspect ratio is investigated at several incident
wavelengths corresponding to those produced by low cost, commercially available laser sources. Through a series of
simulations, we determine the best combination of wavelengths for a multi-wavelength instrument design that exploits
the concept of normalised depolarisation to determine particle aspect ratio, with the possibility of facilitating BWA
detection.
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The optical properties of a surface may change significantly in response to contaminants from the environment
and/or human activity. We utilize a first principles, physics-based radiometric ray tracing software package to
evaluate the spectral polarimetric bi-directional reflectance distribution function (p-BRDF) of the virgin and
contaminated surfaces. In the absence of contaminants and allowing only single bounces, we find the simulated
reflectance properties of randomly rough Gaussian surfaces to be well represented by micro-facet based p-BRDF
analytical models. However the addition of contaminants introduces phenomenology that falls outside the basic
assumptions of the micro-facet analytical p-BRDF models. We will present initial results of p-BRDF simulations
of random Gaussian surfaces with liquid contaminants.
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