Various aspects of polarization in remote sensing are presented including mathematical treatments and selected experimental observations. The observations are of the percent polarization from Haleakala volcanic ash, basalt powder, rhyolytic oumice. rose quartz, niccolite, ilmenite, black oak leaves. dried red pine needles, a New Haven red pine stand, moist soil, the sky above Mauna Loa Observatory, the sky above Long Island in summer and winter, and cirrus clouds. Also, space based shuttle photographic observations of polarization are described. Instrumental polarization from a Cassegrainian telescope is described as well as the design of an imaging soectropolarimeter for remote sensing. A list is presented of twelve polarimetric properties associated with remote sensing.

For the majority of optical systems it is typically assumed that the transmitted wave-front has uniform (or Gaussian) amplitude and constant polarization state. This is the default assumption of geometrical optics. This paper considers methods suitable for ana-lyzing systems where this assumption is not valid. Such methods of polarization analysis include polarization ray tracing and polarization aberration theory. Definitions of the basic classes of polarization phenomena and a review of the Jones calculus are included to form a basis for the discussion.

A highly motivated, systematic and fundamental approach to surface scattering requires that the initial surfaces be fundamental (perfect or ideal) and that the contamination to produce surface scattering be known and controlled. Rough surfaces are considered to be perturbed perfect surfaces that have reached their final condition through some continuum contamination process. This approach permits the classification of surfaces according to the light scattering response to the surface as it is perturbed away from its initial condition. All light scattering data are reported in the context of the Stokes vector and Mueller matrices. Some comparisons to ellipsometry and bi-directional reflection distribution functions (BRDF) are made.

Measurement of the state of polarization of light, emitted from different sources or scattered by various objects, is significant to astronomers, atmospheric scientists, biologists, chemists, physicists, and engineers, and has a wide range of important applications. Conventional optical polarimetry is based on discrete polarizing optical elements (POE), such as crystal polarizers and wave retarders. Integrated polarimeters (IPs) depart from this established practice in that they rely on photodectors only, and require no POE. An IP integrates the polarization analysis and photodetection functions in the detectors. Three IPs are discussed: (1) the rotating-detector ellipsometer (RODE), (2) the two-detector ellipsometer (TDE), and (3) the four-detector photopolarimeter (FDP), in ascending order of apparent complexity. RODE can measure the state of polarization of totally polarized light, except for handedness; TDE provides a fast measurement of the degree of linear polarization of light and can also be operated as a handedness-blind ellipsometer; and FDP measures all the four Stokes parameters of light which is generally partially elliptically polarized. The FDP has several important advantages: (1) It has no moving parts or modulators; (2) it has a rugged design of four solid-state detectors; (3) it uses efficiently all of the input light flux for polarization determination; and (4) it is readily interfaceable with an on-line microcomputer. Further extension of these concepts include the in-line light-saving IP, and IPs that use anisotropic photodetectors.

This paper treats the fundamentals of infrared spectropolarimetry as a step in understanding and designing better spatial light modulators. It describes the issues in converting a Fourier transform Epectrometer to perform spectropolarimetric measurements, and includes mathematics to interpret the resulting spectropolarimetric data. Two distinct differences exist between this proposed instrumentation and previous infrared crystal optics studies; 1.) this instrument acquires data at all wavelengths within its spectral range, and 2.) it measures Mueller polarization matrices. Conventional measurements with laser polarimeters take birefringence data with applied fields at a few laser wavelengths. With the spectropolarimeter, data is obtained on and near absorption bands where the most interesting phenomenae occur. By measuring Mueller matrices as a function of wavelength, data is acquired on polarization and scattering, effects which will ultimately limit the performance of a modulating crystal. Thus, more data is available on which to compare materials and optimize modulator designs. Better modulators must result from such investigations.

A possible method for measuring the polarization of high power laser fields (for example, industrial lasers, gas dynamic lasers, etc.) via a device with no moving parts is presented.

Some instrument considerations for detecting very low levels of light polarization -- below 1 ppm --are discussed. Recent linear and circular polarimetry of the whole disk of the Sun, at levels down to 3 x 10^-7, is reviewed as an outstanding example. Further developments and applications are indicated.

Measurements of the polarizing properties of the National Solar Observatory Vacuum Tower Telescope were taken from October 1986 to January 1987 using the NSO single channel Stokesmeter. A model of the telescope polarization using Mueller calculus and constrained by physical parameters of the instrument was derived. The inverse of this telescope matrix, applied to calibrated Stokes measurements yielded an RMS error of the inferred fit to the input relative to the actual input, of about 1% for 100% linearly polarized input light and better than 0.1% for unpolarized light. This is approximately the level of uncertainty in the calibration of the Stokesmeter. The main polarizing elements of the telescope were turret mirrors, retarders and diattenuators(partial polarizers), and the entrance window, which was a weak retarder.

Remote testing by measurement of the output polarization states given known input polarization states is used to determine the matrix of a serial system consisting of n spatially uniform, nonscattering, rotatable, polarization-modification devices of constant parameters. With a particular measurement procedure, 6n +3 polarization measurements are sufficient to determine uniquely the polarization modification matrix of the serial system in all of its rotational degrees of freedom. A numerical procedure is demonstrated for inverting measurements taken in a way which did not strictly conform to the nominal procedure. The numerical procedure is applied to the Sacramento Peak Vacuum Tower Telescope. The telescope contains three intermediate and rotationally distinguishable elements which represent oblique mirror reflections combined with vacuum stressed windows.

The creation of a 'polarization ray trace' code is described using traditional lens design and analysis computer codes which assume that a ray represents a scalar plane wave and thin-film codes which implicitly use the vector nature of an incident plane wave. Calculations which explicitly use the vector formalism, to provide a more realistic model of light, must have the capabilities of an optical ray trace code and a thin-films code. Both codes exist as separate entities. An expedient method of obtaining a polarization ray trace capability is to merge both types of codes. A description of a method to merge the codes is presented by summarizing the calculations performed as a ray proceeds through an optical system. Polarization formalism is reviewed, and the problems and pitfalls associated with the merger of the two codes is presented.

Performance degradations due to polarization mismatch are examined for a multiple subaperture optical array (Young System). A mathematical model for a linear array of N subapertures is presented. Extension to triangular and hexagonal arrays is accomplished via a wave propagation code.

A method which uses a single algorithm to trace rays in isotropic media and both ordinary and extraordinary rays in uniaxial media is presented. This method is designed to be compatible with conventional raytracing algorithms so that it is easily integrated into existing raytracing programs. A discussion of ray doubling in systems containing multiple uniaxial elements is also presented.

A computer program, the Polarization Aberration Diagrams Program, or PAD, has been written to explore the forms of polarization variation associated with ray paths through optical systems. PAD models quadratic variations of amplitude, phase, linear and circular retardance, and linear and circular diattenuation, such as are associated with lenses coated with retarding or diattenuating coatings, or lenses formed from retarding or diattenuating materials. Graphical results are presented for constant, linear, and quadratic variations of the eight forms of polarization in weakly polarizing optical systems.

An optical design and polarization analysis of the Air Force/NASA SAMEX solar vector magnetograph optical system is performed. Polarization aberration theory demonstrates that conventional telescope coating designs introduce unacceptably high levels of polarization aberrations into the optical sytem. Several ultra-low polarization mirror and lens coatings designs for this instrument are discussed. Balancing of polarization aberrations at different surfaces is demonstrated.

An analysis is made of the effect of birefringence in a sapphire dome on the performance of an imaging system located behind the dome. An incident ray is divided into ordinary and extraordinary ray components and a method is given to trace each component ray to the image plane. The method is applicable to any birefringent dome material with arbitrary crystal axis orientation. It is found that image blurring increases rapidly as the size of the system semi-aperture approaches the dome radius of curvature. There is considerable image blurring even for a small aperture when the crystal axis is not at 0 or 90 degrees from the system optical axis.

In order to understand the various phenomenon in fiber gyroscopes, we have developed a unified theory of polarization and vector coherence theory for fiber optics, using propagator techniques, which is valid for arbitrarily large relative polarization phase delays, arbitrary source polarization properties, in combination with birefringent phase modulation. The propagator representation makes clear the multi-path nature of the polarization effects, similar to the multiple scattering of waves, and an example illustrating this point is given. A "master" equation has been obtained for fiber gyroscopes which i s sufficiently general to permit modeling of the many parasitic effects and their interactions, as well as allow realistic assessment of methods for their reduction. As a result of the development of the propagator approach, several interesting results have been found. One important issue is the performance and characterization of the polarizer used in the fiber gyro. A theorem has been shown that "not all polarizers are created equal", even though they have equal extinction ratios. We have found that the fiber gyroscope probes properties of polarizers that cannot be probed without an interferometer that is equivalent to a ring interferometer. It has been found that there is a considerable difference in performance between two polarizers having the same extinction ratio, but one short, the other long, depending on the birefringence and mode coupling. This leads to an extended classification of polarizer properties beyond an ordinary Jones matrix. A new bound on polarizer performance using the propagator approach is given. Another important issue with fiber optic gyroscopes is drift as a function of temperature. Those familiar with testing of fiber gyroscopes are well aware of the often bizarre (highly non monotonic) drift behaviour as a function of temperature. It is shown how temperature drift can be related to the location of various types of birefringence in the gyro coil using a realistic coil model. The propagator for this coil model is also obtained.

A long-standing problem in polarized light microscopy has been the inability, due to polarization aberrations, to achieve simultaneously high spatial resolution and high contrast. The rotation of the plane of polarization at oblique interfaces between crossed polars causes the pupil function to resemble a dark cross rather than being uniformly dark. Likewise, the point spread function has the visual appearance of a four-leaf clover rather than the ideal Airy disk, and is also space-variant. Images formed with these systems are severely degraded. In this paper the theory of polarization aberrations is applied to the analysis of three solutions to this problem: Reducing the system aperture to block troublesome high-aperture rays; the AVEC-POL method, in which high bias compensation introduces counterbalancing aberrations; and the polarization rectifier, an optical element designed to introduce equal and opposite rotations of the electric vector.

A new method for polarization stabilization and prevention of polarization fade in fiber optic Michelson interferometers is presented. In contrast to previous techniques, the method is totally passive, does not utilize phase conjugation or other nonlinear optical effects, and requires no adjustments after initial setup. In addition, the method works independent of the amount and type of fiber and coupler birefringence, so that low-cost, ordinary optical fiber and couplers can be employed in this type of interferometer. This method also leads to a new kind of nonreciprocal effect sensor. The principles and theory of the effect are presented, as well as a particular stabilization scheme being implemented.

The double-polarization method is analyzed as optical means for determining the sign of the change in measurand in interferometric force sensing via fiber tension bending. It is shown that the additional phase shift between the orthogonally polarized and otherwise identical interference signals as introduced under tension bending is small as compared to the initial phase shift (quadrature condition). The method is tested by measuring the axial fiber strain via fringe counting under application of transverse force.

The operation of a Photo Elastic Modulator (PEM) type ellipsometer is described via Mueller matrix elements. The phase shift (6) and the relative amplitude attenuation ratio (tan ik) between orthogonal polarization components is contained in the Mueller matrix elements and can be obtained via combinations of measured matrix elements. A phase shift measurement accuracy of ±0.2° has been obtained without calibration. A computer controlled implementation is described along with simple algorithms to extract the ellipsometric constants. The Mueller matrix of a magneto optic film media system has been used along with one for a "leaky " beamsplitter to form the optical readout system matrix for an ideal system. One of the Stokes parameters is porportional to the differential detection signal often used in MO data detection schemes.

A technique is described for using polarization beamsplitters to mix the signal and local oscillator light beams in coherent differential detection systems. When the signal polarization and alignment states are uncertain, this scheme offers performance improvements over techniques using amplitude beamsplitters. In its most elaborate form, it offers the possibility of sensing the polarization state of the incoming signal, and therefore controlling it in the receiver.

Enhancement of the multiple-beam point spread function (PSF) is observed for the phase-conjugate return of a reference signal, when a scheme is implemented to counteract depolarizing effects. The effective performance of synthetic aperture systems requires the coherent interaction of incident electromagnetic fields. Once measures are taken to improve this interaction, far-field performance in the laboratory is enhanced as predicted by standard propagation code, i.e., Optical Analysis Software for Interactive Systems (OASIS).

Dielectric multilayer stacks consisting of repeated pairs of high and low index quarter-wave layers are often used for beamsplitters. At oblique angles of incidence, such coatings typically have a fairly high polarization ratio, i.e., different reflectance, transmittance and phase for the two orthogonal polarization planes s and p. We use a special refining computer program based on a damped least squares optimization technique to achieve very low polarization ratios with all-dielectric beamsplitter coatings. The average intensity varia-tion is less than 0.5 % in the wavelength interval from 500 nm - 600 nm for all given design examples, for angles of incidence from 40 to 60^o.

Given two transparent films of refractive index n₁ and n₂ on a given arbitrarily absorbing substrate of complex refractive index N₃ = n₃-jk₃, at a given oblique angle of incidence 0, solution sets for the film indices n₁ and n₂ are determined where the bilayer film-substrate external-reflection retarder system achieves a specified differential phase shift Δ and has equal p and s polarization reflectances where R_p = R_s. n₁, n₂ solution sets are presented in graphical form as solution zones in the n₁, n₂ plane for 0 = 45°, and Δ = ±90° and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. These n₁, n₂ solution sets are specifically found for two commonly utilized substrate materials in the visible and infrared wavelength regions, namely, fused silica and silver, respectively. Values of the normalized film thicknesses 1 and 2 , and the polarization-independent reflectance are separately inserted at various internal and boundary solution points, in the n1, n2 solution zones, on the n₁, n₂ graphs. For each n₁, n₂ solution set, there are two sets of film thicknesses r 1a' 2a and r 1b' 2b that allow equal p and s polarization reflectances and the specified differential phase shift A. For fused silica (where k3 = 0) and = ± 180°, the two sets of normalized film thicknesses satisfy the relationships 1, 2a c2b = 1 and gz(r 1 a, for each n₁,n₂ solution set.

The near-circular polarization state of a CO₂ laser beam (with λ = 10.6 μm) is investigated as the beam emerges from a two-reflection thin-film quarterwave phase retarding system, as a function of three typical alignment errors: the polarization azimuth angle φ, the incidence angle 0 of both reflectors simultaneously and a non-parallel mirror set. The ellipticity e, describing the polarization state of the laser beam, is first investigated as a function of the total phase shift and the p and s polarization reflectances through the two-reflection system, and the azimuth angle of linearly polarized incident beam. The ellipticity is then investigated for two actual systems: a quarter wave retarder (QWR)-zero phase shift reflector pair, and two eighth-wave retarders. The resultant ellipticity from each reflector pair is separately plotted as a function of the three above mentioned alignment errors and compared with actual measurements.

Coatings of optical surfaces for certain laser applications are designed to have very specific polarization characteristics. The polarization angle, psi, and the phase shift angle, delta, define the polarization characteristics of a surface at a given wavelength and at a given angle of incidence. Both psi and delta can vary greatly with wavelength and full characterization of the polarization of a coated surface requires the measurement of both psi and delta over a range of wavelengths and not just at single laser wavelengths. An ellipsometer has been built which is capable of expediently measuring both psi and delta at any selected wavelength from 400 to 2000 nanometers at any selected angle of incidence from 45 to 75 degrees. The ellipsometer uses an incanaescent lamp, a mono-chromator, and a silicon or a lead sulfide detector. The operation of the instrument is based on fixed angle settings and signal amplitude readings rather than on null settings and precision angle readings as in most common ellipsometers. Eight digitized signal level readings from a lock-in amplifier are needed for each measurement. A simple calculation gives the values for psi and delta. The ellipsometer is, in its present form, a manually operated prototype. Its construction would lend itself well to full automation and a true wavelength scanning ellipsometer could readily be built. The instrument is described and examples of ellipsometric scans of coatings designed for specific polarization characteristics are shown.

Ellipsometric measurement methods allow the characterization of interfaces or thin films between two media. The non-pertubing character combined with a remarkable sensitivity makes these optical techniques suitable for in-situ measurements. Therefore the study to thicknesses and refractive indices of thin films during a vacuum coating process is one of many applications. The present paper will introduce an automatic photometric ellipsometer, which can operate together with high vacuum and ultra high vacuum plants. This rotating-analyzer ellipsometer (RAE) is one that uses a motor driven rotating analyzer to detect the state of polarization of light after its reflection from a surface under measurement. The use of a 32-bit-microcomputer together with a floating point processor makes it possible to compute one thickness and one refractive index value every 1.8 second also for multi-layer systems consisting of dielectrics and metals. After a detailed discussion of the hardware components and of the software tools, the precision of the instrument will be demonstrated by means of different applications.