In this paper we consider the relationship between surface roughness in scattering polarimetry and the eigenvalues of the 4 X 4 scattering coherency matrix. These eigenvalues have already been employed in Mueller matrix filtering and particle scattering studies, but here we show that they have a physical significance in terms of scattering amplitudes and that their ratios represent generalized measures of polarimetric coherence. One such ratio, the entropy H, has been introduced in earlier publications, but here we show that a new measure, the anisotropy A, can also be used for surface roughness studies. This parameter is closely linked to the circular polarization coherence but generalizes the concept to account for any residual correlations that may be present in the surface scattering. Increasing surface roughness causes depolarization and hence increasing scattering entropy. However, the distribution of depolarized energy amongst the smaller eigenvalues contains important information about the structure of the surface. Here we suggest how this information may be interpreted and demonstrate the theory by applying it to experimental data collected for laboratory manufactured rough surfaces with known statistical properties.

Depolarization is the reduction in degree of polarization which occurs when a light beam interacts with surfaces or optical elements. Depolarization is a scrambling of polarization states. The depolarization of Mueller matrices is studied here by mapping the resultant degree of depolarization for all possible polarized incident states. Example Mueller matrices are constructed with a variety of different depolarization properties to demonstrate the different depolarization degrees of freedom. These properties can then be applied to understand measurements of depolarization. A classification is presented where depolarization is considered as occurring before diattenuation, in series with diattenuation, or following diattenuation.

The performance of non-ideal polarizers is explored by modeling their behavior as the average of an ensemble of ideal polarizers of differing orientations. The appropriate forms of Jones and Mueller matrices are obtained and their transformation of completely and partially polarized light is described.

A simple algebraic procedure is applied to the problem of particle shape characterization in an ensemble of small randomly oriented spheroidal particles. It is shown that the eigenvalues of the system coherency matrix can be used to retrieve particle shape information. Optically active particles give rise to more general functional forms for the eigenvalues and system entropy, but still permit retrieval of information concerning particle morphology and microstructure.

Recently, the authors developed the deterministic aspects of a formalism for polarization optics. This formalism, called the unified polarization calculus, uses the Stokes-Mueller equation and the Lorentz group provide a conceptual framework and a systematic method to model and understand birefringence and dichroism in optical media. In this paper, we explore the stochastic aspects of the calculus.

To make accurate imagin polarimetry measurements, it is imperative that the individual polarization images comprising a data set are spatially well registered. Both the Stokes Imaging Polarimeter at the University of Alabama in Huntsville and the Multispectral IR Stokes Imagining Polarimeter at Night Vision Laboratories use a rotating quarter-wave linear retarder followed by a fixed linear polarizer to measure Stokes vector images. The rotating retarder cause small amounts of image wander at the detector array. In this paper, we quantify the effects of this image wander on the calculated polarization parameters, and present data indicating the maximum acceptable image wander for typical scenes.

Fluctuations in the polarization state of light scattered by ensembles of very small, randomly oriented spheroids and ellipsoids are calculated. For the regime of Gaussian single scattering, applicable to dilute particle suspensions and aerosols, it is shown how a goniometric measurement of the cross-correlation coefficient of light scattered into orthogonal polarization states by such particles could be used to estimate their mean aspect ratio, even in the presence of considerable shape polydispersity.

We give a derivation of the explicit form of the general Mueller matrix of polarization optics for the case of arbitrary and uniform birefringence and dichroism. We first point out that the general Mueller matrix is essentially a Lorentz transformation. Then a set of complex Lorentz generator and a complex polarization vector is introduced. The complex generators are related to the usual Lorentz generators of special relativity, while the complex vector is related to the Stokes representation of the birefringence and dichroism vectors. Next, the explicit form of the general Lorentz transformation, and subsequently the general Mueller matrix for arbitrary and uniform berefringence and dichroism is derived. The general form is used to derive new Mueller matrices for three special cases. The special cases are (1) the Mueller matrix for a material with finite dichroism and weak birefringence, (2) the Mueller material with both finite birefringence and dichroism that are equal in magnitude and perpendicular in direction. Then, we derive an algorithm to determine the material parameters from the general Mueller matrix elements. Finally, we apply the algorithm to theoretical and experimental Mueller matrices.

Existing polarization-based image understanding techniques use information only from reflected light. Apart form incandescent bodies thermally emitted light radiation from elements of a scene in the visible spectrum is insignificant. However, at longer wavelengths such as in the IR thermal emission is typically quite prevalent form a number of scene elements of interest. FLIR imagery of both indoor and outdoor scenes reveals that many objects thermally emit a significant amount of radiation. Polarization from thermally emitting objects has been observed as long as 170 years ago from incandescent objects but since then there have only ben a limited number of empirical investigations into this phenomenon. This paper present a comprehensive model for explaining polarization of thermal emission from both rough and smooth surfaces, in agreement with empirical data, that can significantly enhance the image understanding of FLIR imagery. In particular it is possible to discern metal from dielectric materials under certain conditions, and from an accurate model for thermally emitted polarization it is possible to predictively model polarization signatures form CAD models of importance to automatic target recognition.

The pair of Fresnel amplitude reflection coefficients for internal and external reflection, that apply when p- polarized light is incident on an interface between two transparent media form opposite sides at the same angle of incidence, are considered jointly and plotted together. This creates an interesting family of curves, with the angle of incidence as a parameter. Besides the well known characteristics of total reflection at the critical angle and total refraction at the Brewster angle, some unusual properties become apparent that pertain to light reflection at the special angles of 45 degrees and 51.827 degrees. The Stokes relations apply strictly at normal incidence, and approximately at other angles for nearly vanishing interfaces. The corresponding result for the Fresnel reflection coefficient for the s polarization, and for the ratio of p and s reflection coefficients, are also obtained.

Most organic materials are quite opaque to IR radiation, making it nearly impossible to measure the polarization properties at these wavelengths. By placing the highly absorbing organic material on a high index of refraction prism and making use of the evanescent field present at the interface for angles exceeding the critical angle, it is possible to measure the organic material's polarization characteristics. Attenuated Total Reflection (ATR) devices have been constructed in-house for use in our IR polarimeter operating over the spectral range of 3-14 microns. Single bounce internal reflection ZnSe prisms are used in our devices to measure the polarization characteristics of highly absorbing materials. Using attenuated total reflection along with a dual rotating retarder polarimeter, it is possible to determine the full Mueller Matrix, and thus determine the linear and circular diattenuation and retardance. With this information we can determine the complex index of refraction, dichroic ratio, and isotropic ratio of materials which are opaque in the IR region. With this knowledge of the material polarization properties, it may be possible to determine the orientation of the molecules in films made of long helical organic molecules and determine the enantiomeric purity of stereo-isomers. The theoretical performance of these devices with a focus on the organic chemical applications has been determined and compared with experiments. In this paper we present a summary of the theoretical basis for the measurements and make comparisons with our measurements.

Recent work has shown that the use of a calibrated digital camera fitted with a rotating linear polarizer can facilitate the study of Stokes parameter images across a wide dynamic range of scene radiance values. Here, we show images of a MacBeth color chips, Spectralon gray scale targets and Kodak gray cards. We also consider a static aircraft mounted on a platform against a clear sky background. We show that the contrast in polarization is greater than for intensity, and that polarization contrast increases as intensity contrast decreases. We also show that there is a great variation in the polarization in and between each of the bandpasses: this variation is comparable to the magnitude of the variation in intensity.

In the largely unpolarized natural IR environment, water stands out as a notably polarized source. Water surfaces appear partially polarized in the IR through both reflection and emission. This polarization can be significant in environmental and military remote sensing applications where the water is either the intended source or possibly a false target. In this paper we show and interpret measurements in midwave and longwave IR bands. The midwave images show up to 7 percent s polarization in regions where warm objects reflect from the water. The longwave data also show s polarization in regions of sunglint, but elsewhere exhibit p polarization. Where the background is clear sky, the longwave signal is p polarized by up to 5 percent at large incidence angles.

A polarimetric characterization of the reflective standard material Spectralon is presented. Samples of Spectralon with reflectances of 2 percent, 50 percent, 75 percent and 99 percent were examined. The characterization was accomplished using the Air Force Research Laboratory's spectropolarimeter in reflection mode. Data are presented for the spectral region .65 to 1.0 micrometers. Polarizance was measured for the four Spectralon samples at eight input beam incidence angles. All observations were made from normal to the Spectralon. It was found that as the incidence beam angle increases, the polarizance increases; and as the reflectance of the samples decreases, the polarizance increases.

We describe the design and development of an imaging polarimeter that will simultaneously measure Stokes vector images in the mid-wave IR and long-wave IR wavebands. We present an analysis of the expected errors that arise due to spectral variations in the polarization elements of the instrument across each waveband. FInally, instrument calibration and polarization images acquired in the MWIR waveband are presented.

The paper covers an issue of method and device for measurement of 2D retardance and principal plane azimuth distributions. The system based on the use of a laser return-path polarimeter which consists of a rotating polarizing beam splitter and a quarter wave plate. Two or four sets from four images are used for birefringence analysis. This allows to decrease the errors caused by imperfection of a polarizing beam splitter and a quarter wave plate. The basic expressions that describe the operation of the systems are presented. The main sources of error are discussed. The measured results of the 2D birefringence distribution of a plastic and standard phase plate of retardation are shown.

Applications of the polarization Michelson interferometer are reviewed. These include analog and binary polarization modulation, time shearing of a light pulse into a doublet of two separate pulses with orthogonal linear polarizations, creation of 'polarization-chirped' light pulses, generation of total and partial polarization states on and within the Poincare sphere, and measurement of the coherence and spectral properties of a quasimonochromatic light source.

A small rugged interferometer was required for measuring the depletion zones generated in a protein crystal growth experiment. The exploration for an optimum solution yielded an instrument that uses solid optical design techniques, where air is removed from the optical path and replaced with 'solid air' or glass. The interferometer is a Mach-Zehnder configuration with the reference and test arms separated as orthogonal polarization states with a polarization beam splitting cube (PBSC), then recombined by another PBSC, maintaining the orthogonality of the reference and test beam polarizations. An off-the-shelf liquid crystal variable phase plate was sufficient to produce the necessary 2(pi) phase shift. The device was built and tested and shoed excellent performance. The spatial resolution of the interferometer is limited only by the 0.011mm pixels at the 5 by 5 mm detector and the imager is operating at telecentric 1:1 conjugates. Phase resolution, using the Hariharan 5-step algorithm, is measured to be better than (lambda) /50. In this paper, calibration test results are presented and future upgrades are outlined.

SpecTIR Corporation has recently completed building the Research Scanning Polarimeter (RSP). This instrument was designed to provide highly accurate polarimetric measurement both from aircraft and from the ground. The spectral range of the measurement is form 410nm to 2250nm and the field of view of the instrument is scanned over a 120 degrees swath. Here we describe the results of the instrumental calibration and the quantitative interpretation of ground-based measurements. Recently we have acquired data using the RSP on an aircraft and a brief discussion of the information content of this data and some preliminary aerosol retrievals over the Pacific ocean are presented.

In this paper we introduce an instrument developed recently for measuring low level birefringence. Known as the Exicor system, this instrument has two detecting channels for measuring both the magnitude and orientation of linear birefringence in transparent optical materials. The Exicor system, employing a low birefringent photoelastic modulator (PEM), provides high level sensitivity of approximately 0.005 nm and good time resolution of < 2s per data point. We present applications of the Exicor system to a variety of otpical samples with industrial importance, including PEM optical elements, compact disc blanks, photomask blanks and other optical components.

Retroreflection is a property of a surface such that incident radiation is reflected directly back in the incident direction. Most bright diffusely reflecting surfaces have a retroreflectance strength up to twice that of off normal viewing; this is true for low coherence as well as laser illumination. The effect is known to occur for the lunar surface. However, for dark surfaces, the retroreflectance can be of an order of magnitude greater than off normal. The cause of retroreflectance is related to the scattering properties of a surface. For bright diffuse surfaces, and reduce the polarization of the surface. At large incident angles multiple scattering is less which results in a high polarization. The phenomenon is of great importance for laser target designator and missile guidance, particularly for low reflectance targets, thereby increasing their vulnerability. Thus it is a fallacy to paint or coat targets black to reduce their vulnerability to polarized laser radiation. Recent experiments on the retroreflectance of various surfaces show polarization, wavelength, and surface structure dependence. Also implicit in the causes of the phenomenon is the optical complex index of refraction of the surface material constituents. Data will be presented on the retroreflectance properties of surfaces, and the relation to the polarization of the incident radiation.

Birefringence in refractive components such as lenses has become an increasingly serious problem in semiconductor lithography as exposure wavelength decreases. Most measurements of birefringence are made with visible light but the light used for photolithography is in the UV and deep UV spectral regions. Measurements of the relative variation of stress-optic constants have been made for fused silica and calcium fluoride, the two primary transmissive optical materials used by this industry.

Researchers at the US Army Engineer Research and Development Center, in collaboration with researchers at the University of Arizona's Optical Sciences Center, have designed, constructed and developed a complete Stokes imaging spectropolarimeter. CTISP is a polarimetric extension to CTIS, developed by the authors associated with the Optical Science Center. Currently, CTISP characterizes an object's spectropolarimetric radiance over the 440 to 740 nm range using 20 nm spectral bins and subdividing the FOV with a 32 by 32 resolution for a total of 16 by 32 by 32 equals voxels. The output of CTISP is an estimate of the Stokes vector for each voxel.

In this paper we describe novel designs of IR versions of the parallel-slab division-of-amplitude photopolarimeter (IR-PS-DOAP) to measure the state of polarization of light as determined by the four Stokes parameters. The IR-PS-DOAP uses no movable parts or modulation and thus fast and simultaneous measurement is obtained. We present two different designs. The first employs a uniform, thin, transparent, film coating on the front surface of the parallel-slab. The second employs strips of thin, transparent, film coating on the front surface of the parallel-slab. A performance analysis comparison between the two will be presented. For wavelengths up to approximately 3.5 micrometers , SiO₂, is totally transparent and is selected to be the slab material for the IR-PS-DOAP. For wavelengths beyond 3.5 micrometers , SiO₂ becomes absorbent and will be replaced by another transparent material like Irtran2, for example. The instrument matrix of the system is non- singular; hence the state of polarization is completely determined. The IR-PS-DOAP is compact, light-weight, rugged and based on reflective optics, so that predictive theory of instrument performance is applicable.

We present a novel photopolarimeter capable of compete measurement of the state of polarization of light, as determined by the four Stokes parameters. This photopolarimeter uses a diffractive-optical-element as a beam splitter to divide the incident beam into four or more components. It uses no movable parts or modulation and thus fast and simultaneous measurements of the four Stokes parameters are obtained. The instrument matrix of this element photopolarimeter is compact, lightweight, and rugged, hence, it can be easily integrated for number of applications.

A comparison is made between the backscattering Mueller matrices of two bead-blasted aluminium samples at both 632.8nm HeNe and 10.6micrometers CO₂ lasers wavelengths. The samples are bead-blasted at two blasting pressures to vary the rms surface roughness and slope. These surfaces are characterized using a mechanical profilometer. Mueller matrices are determined with the detector fixed close to direct backscatter and the target angle varied between 0 degrees and 80 degrees. Results are presented of the angular variation of the major diagonal elements and off-diagonal elements m₁₂ and m₂₁ with increasing roughness to wavelength ratio. The copolarized scattering intensities and copolarized ratios derived from the Mueller matrices show similarities to microwave radar sea echo.

The fabrication and characterization of thin film optical retarders using liquid crystal polymer (LCP) material is presented. The advantages of LCP are high optical birefringence, high optical clarity, good surface quality, the possibility for large aperture applications, flexibility in orienting the crystal and low cost. An additional advantage over conventional liquid crystals is the processing on a single substrate as opposed to confinement between two hermetically sealed substrates, thus the prospect for compact multilayer stacks. Experimental result for single layer LCP thin films and numerical modeling of multilayer stacks are presented for on- and off-axis incident light.

A Fourier transform IR spectrometer-based broadband IR ellipsometer has been developed around a pair of high- quality Brewster angle polarizers. These polarizers consist of four Ge plates in a chevron geometry and have been measured to have extinction ratios of less than 10^-5 in the IR spectral region. The ellipsometer can be used in transmission or reflection mode for angles of incidence of 10⁰ to near grazing. We describe the design and construction of the ellipsometer and initial testing of the system using measurements on Si wafers from 2 micrometers to 12 micrometers wavelength. 5

Abstract not available.

Recent efforts in Earth remote sensing have focused on accurately measuring top-of-atmosphere and surface leaving radiances. Imaging radiometers such as GOES and MODIS have observed response vs. scan angle variations that are related to the polarization response of the instrument and must be accounted for in the calibration of the instrument. This paper presents the mathematical relationship between the polarization response of an instrument an its response vs. scan angle. It demonstrates the correlation between the two using MODIS pre-launch system level polarization and response vs. scan angle measurements. The ability to determine an instrument's polarization response post-launch from response vs. scan angle data is discussed.

Various in situ measurements of the light scattering diagram in cirrus clouds with a new airborne nephelometer, have been performed using several airborne campaigns. These measurements have been favorably compared with a theoretical scattering model. This model consists in computing the scattering of light by an ensemble of randomly oriented hexagonal ice crystals containing spherical impurities of soot and air bubbles. It is achieved by using a combination of ray-tracing, Mie theory,k and Monte-Carlo techniques. It allows to retrieve the six independent elements of these scattering matrix, and results are favorably compared with in situ nephelometer measurements. This good agreement provide an opportunity to use this model in order to analyze ADEOS-POLDER reflectance measurements over cirrus clouds. POLDER uses an original concept to observe cirrus clouds properties, especially because reflectances and polarized reflectances are measured, for a given scene, under several viewing directions. A first analysis of cirrus cloud spherical albedos over the terrestrial globe for November 10, 1996, shows a rather good agreement between measurement and modeling. Moreover, polarized reflectances are also calculated and show a satisfactory with measurements.

Galilean satellites have completely extraordinary radar properties in centimeter wave range. The ratio of intensities of left-handed and right-handed components of circular polarization of back-scattered radiation goes beyond 1.0 for them. Radar geometrical albedo of satellites is notably large too.

Several recent applications in polarimetry, ellipsometry, spectropolarimetry, and multiplexed galvanometric scanners require a single compact beam splitter capable of splitting an input beam of light into four or more components. Of special interest is to design a single beam splitter to produce multiple components of equal powers. We present a specific IR design of a parallel-slab beam splitter that uses a fused silica as a slab material, and it is strip- coated with Germanium thin film on the front and with a uniform silver coat on the back. Equal powers among the first four components can be achieved when the reflectance levels on the first, second, third, and fourth strip is equal to 20 percent, 68 percent, 54 and 18 percent respectively. Specific designs at wavelengths of 1.55, 2 and 5 micrometers are presented. At a wavelength of 5 micrometers , glass shows some absorption and is replaced by another transparent slab material. The choice of varying the otpical material of the slab and metric thickness of each strip provides a great flexibility in the design and operation of the beam splitter over a wide range of applications.

In the study of lightwave systems, polarization related effects have become important considerations. This has led many researchers to focus on developing practical means of controlling the state of polarization of light. This paper demonstrates a polarization controller, consisting of a stack of three homogeneous nematic liquid crystal cells, that is capable of changing any state of polarization of light from one arbitrary state to another. by adjusting the voltages applied across each cell, the state of polarization can be controlled. The mathematical algorithm and the principles of this polarization controller are developed in the framework of the Stokes parameters, allowing an easy visualization and better understandings using Poincare sphere representation. In addition to providing the transformation functions for converting an arbitrary input polarization state to any output state, this paper describes the experiments that were carried out to illustrate and confirm the arbitrary polarization transformations.

Laser tracking and measuring system is made for real-time measurement of dynamic target in industry field and it can be made up into computer integral system with both measuring and controlling capacity. The system has no objective reference coordinate system, during the measurement, its coordinate frame is not fixed, so we call this coordinate system as Virtual Coordinate System. Laser tracking system involves interdisciplinary knowledge, such as laser dynamic aiming technique, laser interferometry, optical system and precision mechanism design, motor controller design and modern numerical computation. This paper mainly focuses on the otpical system analysis and design. The system, which can track and measure the dynamic target, uses the dual- frequency laser interferometer as the light source and length-measured sensor simultaneously. The interferometer produces linear-polarized orthogonal beam with two different frequencies. When the beam passes through the optical system, its polarization and amplitude will be both changed. This paper presents vector analysis method for the optical tracking systems and analyzes the polarization effect of the optical system on the light beam incident in any direction by Jones matrix analysis. On the basis of analytical and experimental results, the optical scheme is optimized in order to improve the tracking and measuring performance of the whole system.

THeoretical investigation of the distribution of light intensity close to the lens focus is discussed, the distribution itself being treated as a sum of unit vector plane waves. Each wave is characterized by a matrix coefficient, a wave vector, a vector of polarization, a matrix of polarization orientation and a Maxwell-Jones' vector. This approach offers to take easily into account polarization effects and aberrations of an optical system in image modeling. Calculations are based on fast Fourier transform.

It is known that the fact that symmetry of studied object permit reduction of the number of independent parameters of Mueller matrix of the object was firstly noted by F. Perrin. This work was carried out in scope of so-called direct problem of polarimetry. In the present paper the analysis of number of Mueller matrix independent parameters for nondepolarizing and input-independent classes of objects in scope of inverse problem of polarimetry is carried out.

PSR-1000 is a portable multispectral polarimeter which measures direct solar radiation and sky radiation at the same wavelength bands as a ADEOS/POLDER sensor. A calibration of our PSR-1000 was done based on Langley plot method involving gaseous absorption from October 27 to November 2 in 1997 at Mt. Mauna Kea in Hawaii Island. Then observations with the PSR-1000 were undertaken over the Seto Inland Sea of Japan in 1997, 1998 and 1999. This work describes a procedure to determine the calibration constants of PSR-1000 and an algorithm to retrieve aerosol characteristics from the polarization measurements of sky light.

This paper describes how to retrieve the optical properties of atmospheric aerosols over the ocean from ADEOS/POLDER measurements. POLDER provides the polarization and directional information of reflected light by the Earth's atmosphere and/or surface. The extracting algorithm for aerosols is based on the look-up table method. Our look-up table is compiled by multiple scattering simulations in an atmosphere-sea surface system. As result, global monthly mean aerosol properties, e.g. optical thickness of aerosols and Angstrom exponent, are obtained. It is found that the specific features of maritime aerosols are shown from our result. In addition, it seems that continental aerosols are blown over the ocean in April in the west Pacific Ocean and in the west coast of middle Africa. Our procedure is validated using the ship-based measurements.

A optical fiber device is described which can be used for wavelength division multiplexing, switching of optical signals and for optical fiber sensors. The device is formed by taking the central output port of 3 by 3 fused taper Bow- Tie optical fiber coupler back to the central input port to form optical fiber ring resonator with two inputs and two outputs.

The present paper deals with the factors influencing the accuracy of the DOAS and in particularly, with the changing of the depolarization ratio of the zenith scattered radiation and related variations of the retrieved NO₂ slant column. Ground based measurements carried out during 1997 and 1998 of the polarization state of the zenith- scattered radiation and the NO₂ slant columns have been obtained in 4075 angstrom - 4640 angstrom spectral interval. The depolarization ratio is calculated from the spectra registered with a sheet linear polarizer, inserted into the instrument. A linear regression analysis is applied to retrieve NO₂ slant columns. The obtained results are analyzed and discussed.

An interpretation is made of various algorithms that may be used to perform the polarization correction part of the calibration of the GOME-spectrometer on-board ERS-2. A description of the currently implemented algorithm, as deduced from the GOME extractor software is given. Errors are estimated by applying different correction algorithms to a sample of simulated observations. The currently implemented algorithm is shown to permit larger inaccuracies than necessary and small modifications are suggested that lead to substantial reduction in the errors, especially in the UV. Also, a new algorithm that deals more consistently with the variation of polarization with wavelength is presented. Our results are also relevant to SCIAMACHY, an instrument similar to but more versatile than GOME, to be launched on ENVISAT in 2000.

An attractive approach to realizing a real-time imaging polarimeter is to integrate an array of polarization- sensitive filers directly onto the focal plane array. This has the advantage of allowing all of the requisite polarization data to be acquired within each image frame. In this paper we discuss the design, fabrication, and performance of a diffractive optical element (DOE) that fulfills this requirement. The DOE consists of an array of broadband form birefringent quarter-wave plates and wire grid polarizers which are designed to allow the measurement of all four Stokes vector components for each image pixel.

We examine the performance limitations of a four-channel polarimeter in the presence of detection noise for arbitrary light levels. We treat the case where the light exiting the polarimeter is detected by a photon counting sensor at each of the four channels. Specifically, we theoretically describe the propagation of detection noise through the polarimeter calibration metric. The variances in the four estimated Stokes vector components, both orthogonal intensities and mutual phase delay are theoretically predicted for photon counting noise following Poison statistics, and additive Gaussian detection noise. The variances of these parameters depend on the average number of photons incident on the polarimeter, the root-mean-square read noise, and the polarimeter calibration matrix. This methodology allows for including fixed eros in the polarimeter calibration matrix. Various polarimeter designs, whose calibration matrices are known exactly, are examined for high, low and very low light levels. Theoretically performance curves are shown for various sensor parameters and light levels. The theoretically predicted values are compared to simulated results. Excellent agreement between theory and simulation is shown. The simulation also validates the use of the Gaussian probability density function for the parallel and normal components of the phase fluctuations, and results in an accurate theoretical prediction of phase delay fluctuations for arbitrary light levels. The phase delay noise cloud is illustrated for several cases.

A Two-Modulator Generalized Ellipsometer (2-MGE) has been extremely useful in characterizing optical properties of uniaxial bulk materials, thin films and diffraction gratings. The instrument consists of two polarizer- photoelastic modulator pairs, one operating as the polarization state generator and the other as the polarization state detector. Each photoelastic modulator operates at a different resonant frequency, making it possible to measure eight elements of the reduced sample; Mueller matrix simultaneously. In certain configurations, light reflection from non-depolarizing anisotropic samples can be completely characterized by a single measurement, and the entire reduced Jones matrix can be determined, including the cross polarization coefficients. The calibration of the instrument involves the measurement of the azimuthal angle of the polarizer with respect to the modulator, the modulation amplitude, and the modulator strain for each polarizer photoelastic modulator pair, where the lat two are functions of wavelengths. In addition, it is essential to calibrate the azimuthal modulator pair, where the lat two are functions of wavelengths. In addition, it is essential to calibrate the azimuthal angles of the polarization state generator and the polarization state detector with respect to the plane of incidence in the ellipsometry configuration that is used in the measurements. Because two modulators operating at different frequencies are used, these calibrations are actually easier and more accurate than for one modulator ellipsometers. In this paper, we will discuss these calibrations and the resultant accuracy limitations of the 2-MGE.