This PDF file contains the front matter associated with SPIE Proceedings Volume 6682, including the Title Page, Copyright information, Table of Contents, Introduction, and the Conference Committee listing.

This paper describes a new configuration of the channeled spectropolarimeter and its application for the spectroscopic measurement of Mueller matrix. The new configuration uses the channeled spectroscopic polarization state generator (CSPSG) consisting of a polarizer and two high-order retarders. The channeled spectropolarimeter using the CSPSG has features that up to four independent polarimetric parameters about a sample can be determined simultaneously from a single channeled spectrum and that it is almost immune to the wavefront perturbations induced by the sample. To apply the channeled spectropolarimetry for the full measurement of Mueller matrix, the CSPSG is combined with a rotating compensator spectropolarimeter. All elements of the spectroscopic Mueller matrix are determined from four channeled spectra. Its feature is that it requires only one rotating component for the full Mueller matrix measurement.

We describe measurements of atmospheric polarization made with an all-sky imaging spectro-polarimeter in five 10- nm-wide bands from 450 to 700 nm. The instrument uses two liquid crystal variable retarders and a fixed linear polarizer to measure the Stokes vector in each pixel of a 1 Mpixel image that covers the entire sky dome. Degree of polarization and angle of polarization images are shown for clear, partly cloudy, and smoke-filled conditions. Aerosols and clouds generally reduce the degree of polarization observed throughout the image, even in clear portions of partly cloudy skies. Comparisons of measurements and calculations show that the single-scattering algorithm in the early polarized Modtran (Mod-P) radiative transfer code provide adequate prediction of sky polarization at red and near-infrared wavelengths for low aerosol optical depths (~≤ 0.2), but significantly under-predict the degree of polarization for short wavelengths, especially with higher optical depths and in the vicinity of clouds.

The implementation of an imaging polarimeter able to capture dynamic scenes is presented. Our prototype is designed to work at visible wavelengths and to operate at high-speed, ie above 200 Hz, contrary to commercial or laboratory liquid crystal polarimeters previously reported in the literature. It has been used in the laboratory with controlled illumination conditions (wavelength, coherence or incoherence, incidence, ...) as well as in a natural environment with sunlight or any lamp or light source. The device consists of commercial components whose cost is moderate. The polarizing element is based on a ferroelectric liquid crystal modulator which acts as a half-wave plate at its design wavelength. The device has been fully characterized and verified to work up to 1 kHz. It produces a 90° polarization rotation. In this Orthogonal State Configuration Imagery (OSCI), images in degree of polarization (DOP) can be obtained with simple post-processing of two consecutive images. With a commercial CCD camera, operation up to 360 Hz is demonstrated, resulting in images whose quality is equivalent to that of classical low speed polarimeters.

A passive imaging polarimeter records the polarization state of light reflected by an object that is illuminated with an unpolarized and usually uncontrolled source. Passive polarimetric imagery has shown to be useful in many remote sensing applications including shape extraction, material classification and target detection/recognition. In this paper, we present an image segmentation algorithm that automatically extracts an object from multi-look passive polarimetric imagery. The term multi-look refers to multiple polarization measurements where the position of the source of illumination (typically the Sun in passive systems) changes between measurements. The proposed method relies on our previous work on estimating the complex index of refraction and reflection angle from multi-look passive polarimetric imagery. We experimentally showed that the estimates for the index of refraction were largely invariant to both the position of the source and the view angle. Consequently, we utilize the index of refraction as a feature vector to design an illumination invariant image segmentation algorithm. A clustering approach based on the classic c-means algorithm is used for segmenting objects based on their index of refraction. The proposed segmentation approach is validated by using data collected under laboratory conditions. Experimental results indicate that the proposed method is effective for segmenting various targets of interest.

We present a snapshot technique for performing spectrally-resolved Mueller matrix polarimetry, based on channeled spectropolarimetry. After discussing the measurement theory in detail, we present a simulated measurement of a polymer achromatic retarder. Finally, we review some methods for modifying the technique to achieve improved performance.

Imaging polarimetry is an emerging sensor technology that promises to improve the performance of sensor systems when used as an adjunct to conventional intensity-based imaging. Several prototype systems capable of being deployed from aircraft are under development. One system has successfully completed an airborne military utility assessment and is being transitioned to operational status. As this technology continues to gain interest, it will become necessary to both accurately predict the performance of proposed systems before they are fabricated as well as develop modeling and simulation tools that will allow their performance to be evaluated for various operational scenarios. In this paper we develop several performance prediction tools that can be used to address these needs; these models are based on the micro-polarizer array (MPA) implementation of imaging polarimeters as this architecture is at the forefront in the development of deployable systems. Focal plane array (FPA) well size, polarizer extinction ratio (ER), pixel crosstalk, and processing algorithms all play roles in the performance that can be attained by a proposed sensor. We discuss the polarimetric response of an MPA-based polarimetric detector and use this model to illustrate the effects of these parameters on the sensor's polarimetric performance, which we cast as noise equivalent degree of linear polarization (NeDoLP). Key conclusions from these analyses are that the detector well size sets the upper limit on performance and that pixel crosstalk will likely the biggest contributor to polarimetric loss in most systems.

Microgrid polarimeters, also known as division of focal plane (DoFP) polarimeters, are composed of an integrated array of micropolarizing elements that immediately precedes the FPA. The result of the DoFP device is that neighboring pixels sense different polarization states. The measurements made at each pixel can be combined to estimate the Stokes vector at every reconstruction point in a scene. DoFP devices have the advantage that they are mechanically rugged and inherently optically aligned. However, they suffer from the severe disadvantage that the neighboring pixels that make up the Stokes vector estimates have different instantaneous fields of view (IFOV). This IFOV error leads to spatial differencing that causes false polarization signatures, especially in regions of the image where the scene changes rapidly in space. Furthermore, when the polarimeter is operating in the LWIR, the FPA has inherent response problems such as nonuniformity and dead pixels that make the false polarization problem that much worse. In this paper, we present methods that use spatial information from the scene to mitigate two of the biggest problems that confront DoFP devices. The first is a polarimetric dead pixel replacement (DPR) scheme, and the second is a reconstruction method that chooses the most appropriate polarimetric interpolation scheme for each particular pixel in the image based on the scene properties. We have found that these two methods can greatly improve both the visual appearance of polarization products as well as the accuracy of the polarization estimates, and can be implemented with minimal computational cost.

In order to understand the phenomenology of optimum data acquisition and analysis and to develop an understanding of capabilities, field measurements of multiband, polarimetric data can substantially assist in developing a methodology to collect and to exploit feature signatures. In 1999, Duggin showed that images obtained with an 8-bit camera used as a polarimeter could yield additional information to that contained in a radiometric (S₀) image. It should be noted that Walraven and Curran had performed some very fine experiments almost two decades earlier, using photographic film, and North performed careful polarimetric measurements of the skydome using a four-lens polarimetric film camera and convex mirror in 1997. There have been a number of papers dealing with polarimetric field measurements since that time. Recently, commercial color cameras have become available that have 12-bit depth per channel. Here, we perform radiometric and chromatic calibrations and examine the possible use of a Nikon D200 10.2 mega pixel, 3 channel, 12-bit per channel camera fitted with a zoom lens as a potential field imaging polarimeter. We show that there are still difficulties in using off-the-shelf technology for field applications, but list some reasons why we need to address these challenges, in order to understand the phenomenology of data collection and analysis metrics for multiple data streams.

This paper presents the design of a visible band imaging polarimeter that can also function as a low light level intensity imager. The polarimeter is based on the division of aperture approach, acquiring four subimages simultaneously on a single CCD array. The system is currently designed to measure the first three normalized components of the Stokes vector through polarization filtering on three of the four available channels. The fourth channel remains unfiltered for radiometric sensing in low power situations. The opto-mechanical design allows for ease of assembly without requiring active alignment techniques, while maintaining a modular system. The modular nature provides a robust, flexible sensor that can be tailored to multiple applications.

Interest in polarimetric remote sensing is gaining momentum in the visible and remains strong in the microwave regions of the spectrum. However, passive polarimetric phenomenology in the 3-14 micron infrared (IR) region is complicated by the relative contributions and complementary polarization orientation of the thermally emitted and background reflected radiance. Although this modality has found success in specific missions (i.e. surface-laid landmine and tripwire detection), the dependence on time of day, scene conditions, scene geometry, collection geometry, etc. makes it difficult to easily perform empirical instrument design or tasking trade studies. This paper presents improvements to the modeling framework within the Digital Imaging and Remote Sensing Image Generation (DIRSIG) model to polarimetrically render scenes in the infrared. The DIRSIG model rigorously treats the polarimetric nature of both thermally emitted and background reflected scene radiance. The correct modeling of these two components is key to accurately predicting polarized signatures for various instrument designs and collection scenarios. The DIRSIG polarized BRDF and polarized directional emissivity models are described and compared to experimentally measured data. Results showing the sensitivity of polarimetric IR phenomenology to target and background material properties, collection geometry, and scene configuration are presented.

During the past decades a lot of research in the field of scatterometry and its applications has been done. Along with the goniometer devices such as the CASI several non-goniometrical approaches have been developed and investigated. Among these one main principle is the mapping of at least parts of the hemisphere onto planar sensors without the need of mechanical movements. This mapping can be realized using dioptrical, catoptrical and catadioptrical systems. In recent years we followed these three principles and built a series of devices based on the continuous optical mapping of the hemisphere to the plane, tested against a reference goniometer system (CASI). The functionality of these devices has been shown for coherent and non-coherent illumination, over VIS, NIR, SWIR and TIR. Monochromatic and hyperspectral measurements have been performed. The current paper gives a review on these systems and introduces some generalization of the optical properties of these devices, concluding in easy-to-handle design rules and concepts.

The sharp retroreflective peak that is commonly exhibited in the bidirectional reflectivity distribution function of diffuse surfaces was investigated for several materials relevant to ladar applications. The accurate prediction of target cross-sections requires target surface BRDF measurements in the vicinity of this peak. Measurements were made using the beamsplitter-based scatterometer at the U.S. Army's Advanced Measurements Optical Range (AMOR) at Redstone Arsenal, Alabama. Co-polarized and cross-polarized BRDF values at 532 nm and 1064 nm were obtained as the bistatic angle was varied for several degrees about, and including, the monostatic point with a resolution of better than 2 mrad. Measurements covered a wide range of incidence angles. Materials measured included polyurethane coated nylons (PCNs), Spectralon, a silica phenolic, and various paints. For the co-polarized case, a retroreflective peak was found to be nearly ubiquitous for high albedo materials, with relative heights as great as 1.7 times the region surrounding the peak and half-widths between 0.11° and 1.3°. The shape of the observed peaks very closely matched coherent backscattering theory, though the phenomena observed could not be positively attributed to coherent backscattering or shadow hiding alone. Several data features were noted that may be of relevance to modelers of these phenomena, including the fact that the widths of the peaks were approximately the same for 532 nm as for 1064 nm and an observation that at large incidence angles, the width of the peak usually broadened in the in-plane bistatic direction.

Variable coherence tomography (VCT) was recently developed by Baleine and Dogariu for the purposes of directly sensing the second-order statistical properties of a randomly scattering volume. In this paper we generalize the theory of VCT to include polarized inputs and scatterers. The measurement of the scattered coherency matrix or Stokes vector is not adequate in general to describe the surface, as these quantities depend on the coherence state of the incident beam. However, by controlling the polarized coherence properties of the beam with polarized VCT, we are able to design a method that can measure analogous information to the polarimetric BRDF, but do it from monostatic data. Such a method has potential impact on both polarimetric and scalar active remote sensing.

This paper presents calculations of a new formulation of the 3D Kirchhoff approximation which allows calculation of the scattering of vector waves from 2D rough surfaces containing infinite slopes. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. The equivalent 1D surface formulation is presented to introduce the method in a physically simpler form. Some preliminary calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method and are compared with the equivalent 1D calculations for the Kirchhoff and integral equation methods. Good agreement is found between the methods.

Surface scattering can be formulated in terms of coherence functions averaged over surface realizations. The resulting integrals for the average scattered intensity are superficially similar to those derived in conventional formulations like the Kirchhoff, Beckmann, and physical-optics models, but the coherence function is subject to some essential conditions, which are extensions of previously-derived conditions on the radiometric parame- ters of primary, partially-coherent sources and their propagated fields, that significantly influence the resulting scattered-intensity or BRDF solutions. The field approximation that leads to conventional radiance-like models is compared to a field approximation that leads to a particular coherence model of surface scattering, which is reviewed and verified against radiometric and atomic-force microscope (AFM) data due to a standard diffuse-gold reflector, representing apparently the first verified inverse reflectance solution for a non-contrived diffuse rough surface.

Most measured Mueller matrices tend to be slightly non physical due to noise and calibration issues. Based on a simple white noise model and higher dimensional geometrical considerations, only 1 out of 90 measured Mueller matrices for a non depolarizing sample should be physical, a number given by the relation [equation] which describes the ratio of the 9-dimensional solid angle inside a 9-dimensional 45° cone to the 9- dimensional solid angle in the entire 9-dimensional hypersphere. The remaining majority of measured matrices would be expected to be slightly non physical.

We present a brief discussion of the transmission ellipsometric function of an unsupported film/pellicle optical structure. We also briefly discuss different ellipsometric techniques that could be used to characterize an unsupported film/pellicle. The current state of data reduction either uses forward curve-fitting techniques or other numerical methods to obtain the refractive index of the optical slab and its thickness. Both methods are dependent on a good starting point and use an iterative approach to minimize a merit function that consumes much valuable time and memory resources. We present closed-form formulas to obtain both the refractive index and thickness. We spare the reader successive and involved transformations and algebraic manipulations to arrive at the closed forms. We provide the reader with an easy-to- follow step-by-step algorithm to obtain the system parameters. Also, we present a closed-form formula for the refractive index using two, and more, sets of measurements. In addition, we discuss the effect of film-thickness multiplicity and its separation. Other technique-specific closed-form formulas are given for different ellipsometric techniques. We also present numerical simulation results that prove the accuracy of the closed-form formulas, and that revealed an interesting and useful characteristic that we utilize. We close by introducing a closed-form formula to calculate the ratio of the unsupported film/pellicle to that of the ambient, which could be used to determine either experimentally. The advantages of closed-form inversion over forward curve fitting and numerical methods are numerous, including: 1) a much higher speed of obtaining the problem solution that allows for real-time applications, 2) it does not require human judgments or intervention, 3) absolute stability, 4) much higher accuracy, 5) no need for close-to-solution starting values of the unknown parameter(s), 6) no errors introduced by the formulas themselves, 7) smart, simple, and concise software programs, 8) use in new material characterization where starting-point-dependent numerical methods fail or require much trial and error.

Accurate calibration of polarimetric sensors is critical to reducing and analyzing phenomenology data, producing uniform polarimetric imagery for deployable sensors, and ensuring predictable performance of polarimetric algorithms. It is desirable to develop a standard calibration method, including verification reporting, in order to increase credibility with customers and foster communication and understanding within the polarimetric community. This paper seeks to facilitate discussions within the community on arriving at such standards. Both the calibration and verification methods presented here are performed easily with common polarimetric equipment, and are applicable to visible and infrared systems with either partial Stokes or full Stokes sensitivity. The calibration procedure has been used on infrared and visible polarimetric imagers over a six year period, and resulting imagery has been presented previously at conferences and workshops. The proposed calibration method involves the familiar calculation of the polarimetric data reduction matrix by measuring the polarimeter's response to a set of input Stokes vectors. With this method, however, linear combinations of Stokes vectors are used to generate highly accurate input states. This allows the direct measurement of all system effects, in contrast with fitting modeled calibration parameters to measured data. This direct measurement of the data reduction matrix allows higher order effects that are difficult to model to be discovered and corrected for in calibration. This paper begins with a detailed tutorial on the proposed calibration and verification reporting methods. Example results are then presented for a LWIR rotating half-wave retarder polarimeter.

We present a method for calibrating polarimeters that uses a set of well-characterized reference polarizations and makes no assumptions about the optics contained in the polarimeter other than their linearity. The method requires that a matrix be constructed that contains the data acquired for each of the reference polarization states and that this matrix be pseudo-inverted. Since this matrix is usually singular, we improve the method by performing the pseudo-inversion by singular value decomposition, keeping only the four largest singular values. We demonstrate the calibration technique using an imaging polarimeter based upon liquid crystal variable retarders and with light emitting diode (LED) illumination centered at 472 nm, 525 nm, and 630 nm. We generate the reference polarizations by an unpolarized source, a single polarizer, and a Fresnel rhomb. This method is particularly useful when calibrations are performed on field-grade instruments at a centrally maintained facility and when a traceability chain needs to be maintained.

Biaxial ellipsometry is a technique that measures the dielectric tensor and thickness of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (n_x+ ik_x, n_y+ ik_y and n_z + ik_z) and three Euler angles (Θ, Φ, Δ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging polarimeter equipped with a pair of microscope objectives with low polarization aberrations. The dielectric tensors for multilayer samples are determined from multi-spectral angle-of-incidence Mueller matrix images in either a transmission or reflection mode using an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones matrix image is first calculated by solving Maxwell's equations at each surface which is then transformed into a Mueller matrix image. An optimization algorithm then finds the best fit dielectric tensor based on matching the measured and calculated angle-of-incidence Mueller matrix images. One use for this application is to more accurately determine the dielectric tensors of biaxial films used in liquid crystal displays.

Passive polarimetric imagery conveys information that complements the information contained in intensity and spectral imagery. Passive polarimetric measurements have been exploited in many remote sensing applications such as shape extraction, surface inspection and object detection/recognition. In previous work Thilak et al. proposed an algorithm to estimate the index of refraction and view angle (object surface orientation) from multiple polarization images where the source position changes between measurements. That work relies on a specular polarimetric bidirectional reflectance distribution function (pBRDF) developed by Priest and Meier. The pBRDF incorporates a Mueller matrix that characterizes the polarized reflection properties of a target for any incident Stokes vector. The results in Thilak et al. assumed that scattering occurs in the plane of incidence, which means that the pBRDF matrix contains many zero elements. In this paper, we extend this work to an out-of-plane scattering geometry, which implies that the pBRDF matrix contains more non-zero elements. In the initial work presented here, a nonlinear optimization approach is utilized to estimate the incident and reflection angles from a single polarization measurement assuming knowledge of the surface index of refraction and azimuthal angle between source and receiver. The effectiveness of the proposed method is verified through computer simulation.

The aim of this study is to characterize the surface of thermobonded nonwovens which can be used as surgical gowns or caps in medical applications. These nonwovens consist of nets of polypropylene fibers which are more or less randomly tangled and the cohesion of this surface comes from its manufacturing process through the bonding points. The tactile feel of the consumer is known to depend on the structure of the surface, hence it will be deeply studied. We consider degree of polarization images of the samples. Firstly the bonding points of a calendered nonwoven are detected using the degree of polarization of the light reflected by the sample under polarized incidence and two sets of the same nonwoven are differentiated through the analysis of their bonding points and of their fibrous part. We show that the degree of polarization of the bonding points is linked to the intensity of the manufacturing process. The second part is about the fibrous part of the nonwovens, studied in order to determine the main orientation of the fibers.

Non-imaging monostatic laser polarimetry has been used in a number of scenarios to probe characteristics of both surfaces and intervening media. While the measurement technology required for laser polarimetry has matured, sophisticated data-processing algorithms have been relatively slow to develop; hence laser-polarimeter data has been typically under-utilized. This paper presents systematic applications of components analysis to laser-polarimeter data that distinguish among electromagnetic-wave scattering characteristics of materials and enable the development of adaptive discrimination and monitoring algorithms that are invariant to selected variables in a scene. Both principal-components analysis (PCA) and non-linear components analysis are used to derive orientation- or pose-invariant channels from Mueller matrices measured over all probe angles. Invariant channels trained by using data due to isotropic scatterers are then used to conduct blind monitoring, i. e., predicting the presence of the target in a scene of arbitrary orientation, with the resulting cluster diagrams presented with photos of the illuminated scene components. Training of a monitor invariant over dual variables is demonstrated using data due to anisotropic scatterers.

Hyper Rayleigh scattering is frequently used to determine the 6 rotational invariants of the first hyperpolarizability tensor. It requires numerous polarization-states of both incident- and scattered-light and thus justifies the use of a dual-rotating-retarder polarimeter. Optimization of our experimental setup by reducing the condition number of the polarization processing matrix allowed us to get optimal detector angle and retarder angular steps for two experimental configurations. Next, we calibrated our experimental setup by using a quartz plate sample in a two steps procedure: at first the first retarder then second one. The retardance and ellipticity angle of both retarders were estimated by minimizing a chi-square function. We estimated the standard deviation of each parameter from noise spreading and performed this calibration procedure for two experimental case-studies, i.e. two angular positions of the quartz sample.

Understanding the interaction of polarized light with materials is critical to applications such as remote sensing, laser radar, and quality control. The availability of angular and spatial information add additional dimensions to this understanding. A facility is constructed for Mueller Matrix Bidirectional Reflectance Distribution (MMBRDF) imaging. Polarized light at near infrared and visible wavelengths is scattered from samples ranging from bare metals to complex organic structures with various textures and orientations. The resulting scattered polarized light is measured with a Mueller matrix active imaging polarimeter. The in-plane MMBRDF is measured for a sanded aluminum sample as a demonstration of the facility. The aluminum is found to be a weak depolarizer, with a somewhat higher depolarization index at specular angles. Retardance is dominated by its linear component and is close to 180° for the majority of angles. Diattenuation is weak, especially in the specular region, and increases in the region further away from specular angles.

Polarization-sensitive optical systems include those requiring very accurate irradiance measurements and those where polarization is the intended measurement. Low-polarization optical system design is the process of minimizing system polarization introduced by surface geometry, thin film coatings and birefringent elements, and measuring system components to verify polarization performance. The complicated, multi-step, iterative low polarization optical system design process requires initial system design, witness sample fabrication and measurement, reverse engineering of fabricated coatings and coating redesign, end-to-end system polarization aberration analysis, and system measurement and calibration. Most of this process will be spent iterating between design and measurement phases until a final design is reached that can be fabricated and calibrated to perform within the desired system tolerances. This work discusses low polarization optical system design using a three-mirror off-axis camera as an example.

We present measurements of toroidal variable-line-space (TVLS) gratings for the Solar Ultraviolet Magnetograph Investigation (SUMI), currently being developed at the National Space Science and Technology Center (NSSTC). SUMI is a spectro-polarimeter designed to measure magnetic fields in the solar chromosphere by observing two UV emission lines sensitive to magnetic fields, the CIV line at 155nm and the MgII line at 280nm. The instrument uses a pair of TVLS gratings, to observe both linear polarizations simultaneously. Efficiency measurements were done on bare aluminum gratings and aluminum/MgF₂ coated gratings, at both linear polarizations.

Photoelastic modulator (PEM) based polarimeters have been used for plasma diagnostics of magnetically confined fusion devices for over 15 years. With the invention of a new laser operating at 47.7 and 57.2 microns, using this radiation for plasma diagnostics has become possible, providing that PEMs can be made for these wavelengths of radiation. Recently, a PEM has been made which meets these requirements. The device uses a silicon optical element with a single-layer polymer anti-reflective coating. Design decisions during the development and performance characteristics of the new PEM will be discussed. Topics include the choice of silicon as an optical element material, antireflective coating design and material choice, optical transmission, maximum retardation, useful aperture and modulation frequency.

A new method of beam shaping by spatially inhomogeneous polarization is proposed and studied. Unlike the conventional techniques, the polarization state in the pupil plane of a far-field beam shaping system is modulated in a spatially variant pattern. It is shown that with carefully designed polarization manipulation, the smallest flat-top intensity focal pattern can be obtained. Theoretical analysis demonstrates the uniqueness of this new idea in terms of the size of the flat-top spot; experiments are described that successfully demonstrate the feasibility of this method to practical applications.

The properties of a 3 × 3 polarization ray tracing matrix formalism are presented and the role of this method in optical design. Properties of diattenuator matrices are derived and methods for analyzing diattenuation of arbitrary homogeneous and inhomogeneous matrices are presented. The 3 × 3 matrix formalism is used to analyze polarization properties of an example corner cube.

In this paper we report measurement results of optical lithography grade calcium fluoride samples using deep ultraviolet (DUV) birefringence and X-ray diffraction methods. Linear birefringence maps of a variety of calcium fluoride samples were generated from measurements at both optical lithography wavelengths (157 nm, 193 nm and 248 nm) and at 632.8 nm. Comparing the respective wavelength results for birefringence in certain samples showed significant differences in birefringence patterns observed at 157 nm and 633 nm for a light beam propagating along the [111] crystal axis. Such differences cannot be explained from the dispersion of stress birefringence at those wavelengths. Our interpretation is that the discrepancy in the birefringence patterns observed at 157 nm and 633 nm is due to crystal defects in those calcium fluoride samples. The crystal quality of those calcium fluoride samples was subsequently determined by X-ray diffraction techniques. The results obtained from both birefringence and X-ray data substantiate each other qualitatively for judging the crystal quality of calcium fluoride samples.

We introduce and experimentally demonstrate an achromatic polarization grating (PG), which manifests high diffraction efficiency (> 99.5%) over a broad range of spectrum. Unlike conventional phase gratings, this family of PGs has unique diffraction properties including three non-zero diffraction orders (m = 0,±1) with up to 100% efficiency and strongly polarization sensitive first-order diffraction. It has long been recognized that these diffractive optical elements are useful for beamsplitting, polarimetry, displays, and more. A conventional (Circular-type) PG implemented with a spiraling, in-plane, linear birefringence has a modest spectral range (Δλ/λ₀ congruent to 6.8%) over which it possesses > 99.5% efficiency. We have identified a two-layer twisted PG structure that achieves achromatic diffraction that achieves a five-fold improvement of the high efficiency bandwidth (Δλ/λ₀ congruent to 34.3%). We have successfully implemented this structure with reactive mesogens (polymerizable liquid crystals) with a small amount of left- and right-hand chiral agents, and here report on its operation over nearly the entire range of visible light. We also investigated the behavior of the achromatic PG with the finite-difference time-domain method using an Open Source software package WOLFSIM, developed at NC State University, in order to evaluate the angular selectivity and the paraxial limit.

The given paper considers experimental methods and means of laser polarimetry that can be used for control of polarization parameters of biotissues, in particular, in case of determination of the degree of pathological changes in human skin. The scheme and operation of universal automated imaging polarimeter are considered. The results of experimental research of Mueller matrices and corresponding polarization characteristics for thin cuts of human skin with visualization by means of vector analysis are presented.

There are many acceptable ways to construct an imaging polarimeter, each with its own benefits and drawbacks. The most common systems involve rotating elements, but use of these systems puts limitations on the dynamic nature of the scene. Division of Aperture (DoAP) and Division of Amplitude Polarimeters (DoAmP) solve the temporal synchronization issue by using multiple light paths, each of which has its own set of polarization optics. These systems can provide real-time imagery, but there are significant challenges surrounding optomechanical alignment and sensitivity to vibrations. Division of Focal Plane devices (DoFP) use an integrated array of micropolarizers to solve the temporal and mechanical alignment issues, but suffer from exactly 1 pixel of IFOV error that cannot be compensated for at the full resolution of the system. Recently we presented a concept that creates a highly parallel array of non-imaging DoAP devices. The design uses two microlens arrays to relay the image at an intermediate focal plane through a microgrid polarizer. The microlenses are configured such that each lens in the first array feeds four lenses in the second array, so as to create a non-imaging DoAP polarimeter. Our previous work was only a conceptual design. In this paper, we will present a design and ray-tracing analysis of a proposed system. We quantify the principal drawbacks of vignetting and crosstalk, and give expected performance parameters of a final device.

Generally all existed measurement strategies in polarimetry are defined by characteristics of polarimeter' polarization state generator (PSG) and polarization state analyzer (PSA) and do not allow for the polarization properties of studied medium. Exceptions are perhaps the simple cases of media characterizing by single type of anisotropy (mainly linear birefringence or optical activity). As a rule the problem is reduced to measurement of all sixteen elements of Mueller matrix. At that, the case when one measure fifteen of less matrix elements results from the characteristics of PSG and PSA and is considered as intermediate steps of certain complete measurement cycle, during which all sixteen Mueller matrix elements are measured. In this paper we present the generalized polarimetric measurement equation which permits to allowing for the inequality in accuracy of polarimetric measurements and the polarization properties of studied medium. The method is based on modification of generalized polarimetric measurement equation for maximal compliance to the matrix model of studied medium allowing for the anisotropy of medium, symmetry and sizes of scatterers etc. This requires the utilization of versatile PSG and PSA in the polarimeter.

We present the initial results of an imaging polarimeter operating at 632.8 nm that simultaneously analyzes four polarization states on a single detector array. In a single snap shot, the polarimeter has the ability to characterize the polarization of a scene by determining the complete Stokes vector. Images are processed to show Degree of Polarization (DOP), Degree of Linear Polarization (DOLP), Degree of Circular Polarization (DOCP), ellipticity and the angle of linear polarization. Our approach utilizes a monolithic analyzer that allows us to avoid issues usually associated with division of amplitude polarimeters such as jitter and tight tolerance requirements. We discuss our optical design, calibration procedure, and test data.

Division of Focal Plane polarimeters (DoFP) operate by integrating an array of micropolarizer elements with a focal plane array. These devices have been investigated for over a decade, and example systems have been built in all regions of the optical spectrum. DoFP devices have the distinct advantage that they are mechanically rugged, inherently temporally synchronized, and optically aligned. They have the concomitant disadvantage that each pixel in the FPA has a different instantaneous field of view (IFOV), meaning that the polarization component measurements that go into estimating the Stokes vector across the image come from four different points in the field. In addition to IFOV errors, microgrid camera systems operating in the LWIR have the additional problem that FPA nonuniformity (NU) noise can be quite severe. The spatial differencing nature of a DoFP system exacerbates the residual NU noise that is remaining after calibration, and is often the largest source of false polarization signatures away from regions where IFOV error dominates. We have recently presented a scene based algorithm that uses frame-to-frame motion to compensate for NU noise in unpolarized IR imagers. In this paper, we have extended that algorithm so that it can be used to compensate for NU noise on a DoFP polarimeter. Furthermore, the additional information provided by the scene motion can be used to significantly reduce the IFOV error. We have found a reduction of IFOV error by a factor of 10 if the scene motion is known exactly. Performance is reduced when the motion must be estimated from the scene, but still shows a marked improvement over static DoFP images.

The in-plane Mueller matrix bidirectional reflectance distribution function (MMBRDF) is measured for a Spectralon calibration target with a reflectance of 99%. Measurements are acquired using a Mueller matrix active imaging, goniometric polarimeter operated in the near infrared at 1550nm. The Spectralon is measured for both incident and scattering angles from -80 degrees to 80 degrees to within 20 degrees of retro-reflection. A range of polarization states is generated and scattered polarization states are analyzed by means of a dual rotating retarder Mueller matrix polarimeter. Complete Mueller matrix data is measured with a high-resolution camera in image form. Polarization scatter data is presented in Mueller matrix angular arrays. As expected the Spectralon is a strong depolarizer and weak s-plane oriented diattenuator. It was also a weak retarder. Diattenuation and retardance are strongest at horizontal and vertical polarizations, and weakest for circular polarization states.