The intrinsic multiple-beam-splitting and polarization-altering properties of a diffraction grating are combined with linear photodetectors to achieve a simple and versatile photopolarimeter for the simultaneous and nearly instantaneous measurement of the four Stokes parameters of light in an arbitrary state of partial elliptical polarization. For spectroscopic applications the dispersive property of the grating is also employed with photodetector arrays to obtain Stokes parameter spectra.

We discuss scattering in the context of the Stokes vectors and Mueller matrices that completely characterize the polarization state of the scattered light. A polar nephelometer is used to measure the light scattering Mueller matrix elements of various ideal systems. These systems are fundamental and solvable theoretically. The scattering systems can be perturbed and the amount of perturbation can be quantified. The light-scattering signals can then be examined as a function of the amount of perturbation. Eventually, the perturbation dominates the system so that the addition of more of the perturbation does not significantly alter the appearance of the scattering system or of the polarized light scattering signals. These saturated systems may also be thought of as fundamental systems. In this paper we examine some fundamental systems and discuss models which predict the polarization state of some highly perturbed scattering systems.

A new Stokes polarimeter for high spatial resolution quantitative measurement of magnetic fields at multiple heights in the solar atmosphere has been constructed by the National Center for Atmospheric Research and the National Solar Observatory. The instrument uses the Vacuum Tower Telescope at Sunspot, New Mexico, and its existing horizontal spectrograph, universal birefringment filter, and image motion stabilization system. The polarimeter uses a rotating retarder polarization modulator with polarization calibration optics. Multiple paired CCDs are used for detection followed by video processing to produce spatial maps of the full state of polarization in restricted regions of the solar spectrum. Two spectral regions encompassing lines sensitive to the Zeeman effect, which form in the photosphere and low chromosphere, are recorded simultaneously. Significant developments include: construction of the new telescope post focus optical arrangement, creation of a polarization model for the telescope, construction of high-speed, low-noise solid state cameras, and construction of computer hardware for receiving and processing high-rate 12-bit digital data.

The assessment of the condition of the retinal nerve fiber layer plays an important role for the early detection of blinding eye diseases like glaucoma. We describe the application of a scanning laser polarimeter for quantitative measurements of the retinal nerve fiber layer thickness in vivo. The measuring beam of the scanning laser polarimeter is focused on the retina and penetrates the birefringent nerve fiber layer. The retardation of the light double- passing the nerve fiber layer is proportional to its thickness and is measured at 256 by 256 positions within a field of view of 15 by 15 degrees. The measurement time is less than 1 second. During the measurement, the polarization effects of the anterior segment of the human eye are canceled by a cornea polarization compensator. The retinal retardation values are displayed as a color coded map of the retinal nerve fiber layer thickness distribution.

A novel polarimeter for mapping the spatiotemporal state of polarization (SOP) of light is presented. A reference beam of light consisting of orthogonal linearly polarized two components interferes with an elliptically polarized signal beam whose SOP varies with space and time, and thereby a mesh-like interference pattern is formed over a wide-band MOS TV camera, followed by a computer. No use of any polarization component such as a rotating analyzer allows us to map a change in spatiotemporal SOP. The space- and time-dependent ellipse and azimuth for the elliptically polarized signal beam of light are mapped as an experimental demonstration.

Polarization elements are inadequately characterized for many applications. For retarders, usually only the retardance is specified. For polarizers, usually only the two principal transmittances or the extinction ratio are given. For polarization elements used in critical applications, this level of characterization is woefully inadequate. Defects of polarization elements are described, and the Mueller calculus suggested as the most appropriate measure of performance. Examples of the characterization of polarization elements as a function of angle of incidence, and as a function of wavelength are provided.

Polarization ray tracing, which consist of several extensions to geometrical ray tracing, calculates the evolution of polarization states along ray paths and determines the intrinsic polarization properties, such as diattenuation and retardance, associated with ray paths. This paper compares the suitability of the Jones, Mueller, and a three-dimensional polarization ray tracing calculi, examining the issues of local versus global coordinates, amplitude versus phase representations, inclusion of the wavefront aberration function, partially polarized light, measurements of images by polarimeters, and diffraction image formation by low and high numerical aperture beams.

Two techniques are described for measuring polarization precisely: (1) Total internal reflection produces retardance that is an exact function of the incident angle, and can be the basis for an achromatic ellipsometer without wave plates useful within a limited angular field of view. (2) Rotation of a single linear polarizer always can be used to calibrate ellipsometers that are based upon insertable or rotating unknown Jones optical elements. Both techniques are based upon reversible processes in which the light-matter interaction does not change with the light path through the material. For all such processes there is a correspondence between transformations of the light state in physical space and transformations of the Stokes parameters on the Poincare sphere. This correspondence is important because it can be shown that the 3D transformation group for the Stokes parameters arises as a consequence of the definition of the Stokes parameters as quantum observables without referring to spatial characteristics for the light-state dual-element wave function. The correspondence is discussed.

A major limiting factor in polarization microscopy is the rotation of the plane of polarization at oblique interfaces in the optical train, which leads to severe degradation of image quality. Polarization aberration theory has provided an effective framework for studying two- dimensional image formation and optical restoration in these systems. Here we extend the polarization aberration model to three dimensions. A model system is chosen in which polarization aberrations are optically corrected and image quality restored. Closed-form expressions for the aberrated and restored 3-D space-variant point spread functions are derived, and the contributions of the various kinds of polarization aberrations are described.

Polarization analysis software that employs Jones matrix formalism to calculate the polarization sensitivity of an instrument design was developed at Hughes Danbury Optical Systems. The code is capable of analyzing the full ray bundle at its angles of incidence for each optical surface. Input is based on the system ray trace and the thin film coating design at each surface. The MODIS-N (Moderate Resolution Imaging Spectrometer) system is used to demonstrate that it is possible to meet stringent requirements on polarization insensitivity associated with planned remote sensing instruments. Analysis indicates that a polarization sensitivity less than or equal to 2 percent was achieved in all desired spectral bands at all pointing angles, per specification. Polarization sensitivities were as high as 10 percent in similar remote sensing instruments.

The 2-percent polarization sensitivity specification in many of NASA's Earth Observing System sensors has motivated Santa Barbara Research Center (SBRC) to develop computer programs that model the polarization characteristics of optical systems. In support of the Moderate Resolution Imaging Spectroradiometer program, SBRC has developed an analytical tool which unites the completed 3D lens design and coating designs to accurately predict an optical system's polarization characterization compensators, nonnormal incidence reflection and transmission from dichroic beam splitters and protected silver mirrors are analyzed without the need for proprietary coating prescriptions. The phenomenon of diattenuation and phase change are treated using the Jones matrix formalism.

Procedures for performing polarization ray tracing through birefringent media are presented in a form compatible with the standard methods of geometric ray tracing. The birefringent materials treated include the following: anisotropic optically active materials such as quartz, non-optically active uniaxial materials such as calcite, and isotropic optically active materials such as mercury sulfide or organic liquids. Refraction and reflection algorithms are presented which compute both ray directions and wave directions. Methods for computing polarization modes, refractive indices, optical path lengths, and Fresnel transmission and reflection coefficients are also specified.

Scattering pick-up from sample and environment is unavoidable in ellipsometric measurements, especially in the short wavelength region. Incoherent scattering has special properties that can simplify the analysis. The four-zone averaging in null ellipsometry can effectively cancel most of the scattering-induced errors. For rotating analyzer or rotating polarizer ellipsometry, the incoherent scattering from the sample causes the measured cos 2(Psi) and cos (Delta) to be smaller than the corresponding real cos 2(Psi) and cos (Delta) ; the incoherent scattering from the environment has similar effects for cos (Delta) as that from the sample. If the error by scattering dominates over the instrumental errors, the near-angle scattering can be estimated by comparing the results between null ellipsometry and rotating analyzer ellipsometry.

A theoretical analysis showing the evolution of the state of polarization of the light inside a bulk optic Faraday current sensor is presented. Factors affecting the performance of the device, such as the azimuth of the input state; angle of incidence on reflection and the presence of intrinsic birefringence in the material have been simulated with a computer. The results of the simulation are compared with those obtained experimentally with a triangular shaped sensor design.

The coatings which are used on telescope mirrors and other optical interfaces can have a profound effect on the image quality formed by an optical system. This paper evaluates the defocus and astigmatism which are caused by the s- and p-phase shifts of coatings. These coating-induced wavefront aberrations are usually insignificant, but can, under certain circumstances, overshadow the geometric wavefront aberrations of the system. The wavefront aberrations induced by reflection-enhanced coatings on an f/1.5 Cassegrain telescope are numerically evaluated as an example.

The radiometric accuracy of space-borne instruments such as radiometers and spectroradiometers which make measurements of the earth and other celestial objects can be compromised by the linear polarization sensitivity (LPS) induced by the optical system. Most of these optical systems contain optical elements whose reflectance or transmission is polarization dependent, such as diffraction gratings, folding and scanning mirrors, dichroic filters, and optical fibers. Optical system incorporating such elements generally display linear polarization sensitivity; different linear polarization states incident with equal radiometric power will be measured as different power levels. If the incident polarization state is unknown, the linear polarization sensitivity cannot be compensated during the data reduction. The light reflected from the earth and other planets and moons is usually partially linearly polarized, but in a random distribution. Thus, to make accurate radiometric measurements of these bodies, a radiometer or spectrometer should have a low level of linear polarization sensitivity. This paper contains a mathematical description of LPS, contains references to systems which have imposed a LPS specification, describes some of the sources of LPS, describes how to model LPS by polarization ray tracing, and discusses methods to reduce the LPS of an optical system.

A reflective division-of-wavefront polarizing beam splitter is described that uses a dual- thickness transparent thin-film coating on a metal substrate. A previous design that used a partially clad substrate at the principal angle of the metal [Azzam, JOSA A 5, 1576 (1988)] is replaced by a more general one in which the substrate is coated throughout and the film thickness alternates between two non-zero levels. The incident linear polarization azimuth is chosen near, but not restricted to, 45 degree(s) (measured from the plane of incidence), and the angle of incidence may be selected over a range of values. The design procedure, which uses the two-dimensional Newton-Raphson method, is applied to the SiO₂-Au film- substrate system at 633 nm wavelength, as an example, and the characteristics of the various possible coatings are presented.

In this paper, the synthetical analyses on the derivation of alignment in the application of the polarization optical technique are presented upon the main error sources of this technique. Consequently, a novel alignment system is developed to improve the alignment technique, which is composed of a combination of two parallel polarizers, bidirectional-double path, two detectors, and electrical signa processor. Using this system, we have realized accurate alignments between PM fibers and their in-line devices.

In this paper, a unified formalism for treating polarization effects in single mode optical fibers is presented. Central to this approach is the utilization of operator and group theory techniques to exploit the analogy that exists between the dichroism and birefringence elements of the Mueller matrix of polarization optics, and the boost and rotation generators, respectively, of the Lorentz transformation of special relativity. This formalism incorporates the other popular polarization formalism (i.e., the Jones, the coherency (or density) matrix, and the Mueller formalisms) into a single unified formalism. Moreover, the formalism extends the range of exactly solvable models by providing a new and straightforward method of calculating both the deterministic and the stochastic Mueller operators for a number of useful cases.

The connection between the transformations of the Lorentz group and the Stokes parameter description of polarization phenomena is explored and elucidated. We begin by examining a monochromatic plane electromagnetic wave propagating through a dielectric medium. Using a representation of the Pauli spin matrices, expressions for the Stokes parameters (which are measurable quantities) are constructed from the electric field description of a completely polarized propagating wave. Next, the effect of a uniform birefringence on polarization phenomena is explored by casting the field description in the Stokes-Mueller matrix form. Also, the effect of a uniform dichroism on diattenuation phenomena is similarly explored. Finally, the connection between the Stokes parameter description and Lorentz transformations is elucidated by showing the Mueller matrices associated with birefringence and dichroism are, respectively, the rotations and boosts of the Lorentz group.

Two useful quantities, diattenuation and retardance, that characterize the polarization properties of a polarization element, are generalized for inhomogeneous polarization elements, i.e., the polarization elements with nonorthogonal eigenpolarizations. Moreover, an inhomogeneity parameter is introduced to characterize the inhomogeneity of a polarization element. The equations for calculating inhomogeneity, diattenuation, and retardance from the Jones matrix are presented. These equations are suitable for performing data reduction on Jones matrices or nondepolarizing Mueller matrices.

The usefulness of Brown's polarization formalism as a paradigm for the dynamics of analogous linear systems is demonstrated. By connecting the rotations of the Lorentz group with birefringence and the Lorentz group boosts with dichroism, this formalism has offered closed-form solutions, expressed in the language of the Lorentz group, for the 4 X 4 Mueller matrices of polarization optics. First, we discuss the dynamics of a generic two-state system satisfying a Schrodinger-like differential equation. This equation is cast into a four dimensional form. Next, we show the solution of the latter to be a Lorentz transformation. Then, we analyze several specific examples. The examples include: (1) precession, (2) a magnetic dipole in a magnetic field, (3) a charged particle in an electric field, and (4) time- independent perturbation theory with phenomenological damping. We argue the approach of Brown's formalism provides a convenient conceptual framework to describe the physics and to interpret the measurement results of such systems. In addition, this approach broadens the role of the Lorentz group to areas other than special relativity and electromagnetic scattering.

We address the issue of physical realizability constraints on depolarizing scattering or imaging systems. In particular, the overpolarization problem, that is the problem of ensuring that the output degree of polarization is always smaller than (or equal to) unity, is discussed in detail. We derive a set of necessary conditions on the elements of a Mueller matrix. These conditions can be used to test the accuracy of polarimetric measurements and computations. Numerical examples are given.

A new ellipsometer concept is presented for which no polarizing optical components in the conventional sense and no moveable elements are necessary. With four beam splitters and four detectors, four intensities are measured. These data are needed to obtain all four Stokes parameters S₀, S₁, ₂, S₃ of the Stokes vector and so the general state of polarization of the radiation. It is shown that it is possible to determine the `optical instrument matrix' A and the `general instrument matrix' B, characterizing the whole measuring system theoretically and experimentally. The results of ex- and in-situ measurements verify the accuracy of this measuring principle. Applying suitable electronics the ellipsometer can be used as a high speed measuring device for (Psi) and (Delta) . Therefore, it is especially useful for real-time ellipsometry to analyze dynamic processes at surfaces and thin films.

A method for the correction of systematic errors generated by large orientational and retardance errors in the polarization optics in the dual rotating retarder polarimeter is presented. Small orientational and retardance errors (<1 degree(s)) can lead to large errors in the measured Mueller matrix (> 10% in some matrix elements). We incorporate correction terms for large orientation and retardance errors into the dual rotating retarder data reduction algorithm. Using these data reduction algorithms and a calibration step, the associated systematic errors are calculated and removed from the measured Mueller matrix. This procedure is especially useful for spectral and multi-wavelength systems in which the retardance and often the orientation of the retarders are wavelength dependent. The equations, the procedure to calculate the orientations of the polarization elements and the retardances of the retardation elements, and the method to correct for any errors are presented here. The effect of these errors on the calculated Mueller matrix elements and their correction is shown analytically and through experimental data taken on an infrared spectropolarimeter.

The difference in specular reflection of left and right circularly polarized light from a naturally optically active sample (an absorbing chiral liquid) was observed and measured as a function of wavenumber under conditions of double-pass total reflection. The imaginary part of the refractive index reached a maximum value on the order of 10^-4 (at 21,000 cm^-1); the real and imaginary parts of the complex gyrotropic parameter were on the order of 10^-8 and 5 X 10^-7, respectively. In accord with recent predictions, the observed differential circular reflection exceeded the intrinsic chiral parameters by some three orders of magnitude. This is the first observation of natural molecular optical activity by coherent light scattering.

A new technique is proposed for determining the refractive index and thickness of anisotropic films. Suppose the film is aligned in the X-Y plane, and that the plane of incidence includes the X-axis. From the reflectances of S- and P- polarized light, the principal refractive indices n_x, n_y, and n_z can be obtained along with the film thickness d. First, n_y and d can be derived from the S-polarized reflectance, since the S-polarization is parallel to the Y- axis. It is also possible to derive n_x in the same way. The P-polarization is in the X-Z plane and Fresnel equations for P-polarization are expressed by n_x, n_z, and d. Therefore, n_z can be determined using the P-polarized reflectance and the values already calculated for n_x and d. Trial measurements are made on a Sol-Gel derived LiNbO₃ film on an Al₂O₃ substrate, using a system with a reflectance measurement accuracy of the order of 0.01%. The values obtained for n_y (equals n_x), n_z and d are 1.980, 2.056, and 107.5 nm, respectively. According to the results of this simulation, the accuracy of the obtained values can be estimated as < 0.3%.

Birefringence can be obtained from the phase difference (Delta) between the ordinary and the extraordinary rays for normal transmission through a birefringent slab. Rotating analyzer ellipsometry (RAE) and null ellipsometry (NE) were used to measure (Delta) . NE gives accurate phase spectrum which shows linear dependence of phase on wave-number. The phase spectrum by RAE looks like a damped oscillatory curve. The calibration of RAE against NE shows that the extrema of RAE phase spectrum correspond to (Delta) equals m(pi) of NE spectrum, where m equals integer; the phases near m (pi) + (pi) /2 are about the same from both methods. Error caused by partially coherent interference of the multiple reflected waves within the slab consists basically of the sinusoidal functions of (Delta) and its harmonics, and is zero at (Delta) equals m(pi) . These errors can be suppressed by the least-square fit of m to a quadratic function of 1/(lambda) . The birefringence spectrum measured for a sapphire sample in the 0.4 to 0.9 micrometers wavelength region agrees with the handbook values.

The instrumental crosstalk associated with the Marshall Space Flight Center Vector Magnetograph and the solar crosstalk created by the magnetic field are described and their impact on the reconstruction of the solar vector magnetic field is analyzed. It is pointed out that identifying and correcting the crosstalk is important in the development of realistic models describing the solar atmosphere. Solar crosstalk is spatially dependent on the structure of the magnetic field while instrumental crosstalk is dependent on the position of the analyzer.

This paper reviews a scatterometer capable of measuring scatter throughout most of the sphere surrounding the sample. The instrument can be configured to operate at many different laser wavelengths, or with a broadband source, and at virtually any angle of incidence. Automated polarization control of both source and receiver has been accomplished, which allows calculation of incident and scattered Stokes vectors as well as the Mueller matrix associated with either reflective or transmissive samples. A unique 'no sample' method of instrument calibration and Mueller matrix calculation results in a normalized Mueller noise floor of only +/- 0.003.

An improved type of scanning and analyzer rotating magneto-optic spectroscopy has been designed and constructed. By adding an achromatic quart-wavelength retarder to the system and using Fourier transformation, the complete magneto-optic parameters, both polar Kerr rotation angle 6kand ellipticity k' have been measured in the 1.5-5-eV photon energy range and at a near normal incident angle of less than 2 degrees. A fine step motor with 1000 steps per revolution and a hollow shaft, on which the analyzer is directly mounted, is used to control precisely the analyzer azimuthal angle. The magnetic field, spectral scanning, and retarder position, as well as data processing are totally controlled by a microcomputer. The magneto-optic spectral results of the system is illustrated for FeTeCo film samples.

We draw attention here to a new optical instrument for studying transparent doped crystals and glasses. The device employs high sensitivity of laser polarimetry for detection of small magnetization alterations and offers a number of new research capabilities.

Polarimeter design often involves the use of the Mueller matrix formalism. For relatively simple, idealized optical systems this formalism provides elegant results. However, when polarimeters have several optical components and their imperfections are considered, the Mueller calculus can become complex. With the computing power readily available today it is possible to perform the Mueller calculus in software, both symbolically and numerically. This capability makes it feasible to design and operate polarimeters having complicated intensity functions due to non-ideal optical components. Using a generalized linear least squares method it is possible to recover source polarization from intensity measurements even if a polarimeter has imperfect components. What this requires is a determination of the polarimeter's modulation functions, either by computer modelling or by direct measurement using a known Stokes source. We discuss our work implementing computer-aided polarimetry using the Mueller calculus and application of this methodology for doing polarimetry with non-ideal optical components. In particular, we present results of a computer simulation of an imaging polarimeter which has a quarter-wave plate with nonuniform retardance. Our results indicate that by the polarimetry approach discussed here this retardance `imperfection' will not prevent the polarimeter from accurately measuring the source polarization.

A phase shifting technique of changing polarization state in a Twyman-Green interferometer is presented to measure the shape of the object surface. The wavefronts of the reference beam and object beam are orthogonally polarized. They are resolved by a quarter-wave plate and then detected by a polarizer as an analyzer. Four intensity measurements with phase difference associated with polarization variation are used to obtain interferometric phase corresponding to shape contour.

An experiment was performed on a front-side illuminated CCD to measure its linear diattenuation at 550 nm and 650 nm as a function of angle of incidence. The linear diattenuation of the CCD varies from 0 to 12 percent for 550 nm light from 0 to 40 deg and is less for the longer wavelength.

Polarization-sensitive Schottky photodiode (PSSP) construction and principle of its performance are described. PSSP is intended for light polarization determination in visible, infrared or near UV and for solving analogous applied optics problems. Experimental and calculated parameters are reported.

The properties of zero-order retardation plates fabricated from mechanically stretched phase- separated glass are presented and discussed. The dissolved stretched phase is silver halide. The values of the birefringence as a result of the elongated silver halide phase are studied as a function of the average particle aspect ratio and wavelength. The (lambda) /4 and (lambda) /2 thicknesses required for the wavelength interval 633 - 1520 nm were 0.5 - 3.0 mm. Advantages in the use of these glass waveplates in devices such as circular polarizers are discussed.

The field of view dependence of polarizing beam splitter cubes has been studied to characterize their behavior in imaging systems, such as optical computers, optical correlators, and other applications which involve non-collimated light. Significant polarization aberration is present in polarizing beam splitter cubes for two reasons, (1) the s and p orientations at the beamsplitting interface, which define the polarizing axes, vary with direction of propagation; and (2) the coating performance is a function of angle of incidence. Here we present measurements made on several polarizing beam splitter cubes from various vendors. The measurements show typical polarization behavior which is of concern when the cubes are used in imaging systems. A near infra-red imaging polarimeter is used to measure the cubes.

We have employed novel metal grid polarizers with improved polarization contrast to build a far-infrared rotating-analyzer ellipsometer. Using a step-tunable, optically pumped gas laser as the light source we can determine the complex dielectric function in the spectral range from 10 to 250 cm^-1. A cryostat allows reflection measurements under flat angles of incidence between temperatures from 10 to 300 K. We present measurements on high-T_CYBaCuO type ceramics.

A near-ideal, all-dielectric, reflection polarizer is described that employs selective totally destructive interference for the p polarization and constructive interference for the s polarization in a buried low-index (BLIND) film embedded in a high-index substrate near (within 10 degree(s) of) grazing incidence. A specific design is presented of an infrared polarizer that uses a film of refractive index 1.35 embedded in a Ge substrate of refractive index 4.1. Such a polarizer has a throughput for the s polarization of 92% and 99%, when operated at incidence angles of 80 degree(s) and 85 degree(s), respectively.

The design and analysis of a depolarizer for the NASA MODIS-T spectrometer is presented. The theory of spatial pseudodepolarizer operation and its effect on linear polarization sensitivity is described. Details of the HV depolarizer design and issues of depolarizer location and material are discussed. The image doubling and aberrations induced by the depolarizer and the trade-offs between increased polarization performance and decreased image quality are also addressed. The issues considered apply directly to depolarizer design for other remote sensing instruments.

A test program designed to study the DC modulation characteristics of longitudinal KD*P modulators and to determine what electrode structure might improve the performance of these devices is presented which was developed in the Marshall Space Flight Center. The physical constraints of these devices and the necessary electrical characteristics that the KD*P modulators must have to be used in the MSFC polarimeter are discussed.

Polarization dependent integrated optical devices are becoming increasingly important in order to control polarization for coherent optical detection schemes, gyros, bidirectional communications using optical circulators, electro-optical switching and electro-optical phase modulation. Typically, integrated optical components are made by titanium diffusion into LiNbO₃, ion-exchange or electric field assisted ion diffusion in glasses. The diffused ion concentrations determine the waveguide properties. Theloped to understand the physical limitations of these devices, and the necessary electrical characteristics that the KD^*P modulators must have for use in the MSFC polarimeter. imaging systems. A near infra-red imaging polarimeter is used to measure the cubes. measurement using a known Stokes source. We discuss our work implementing computer-aided polarimetry using the Mueller calculus and applius to design waveguide structures for polarization integrated optical devices.