Imaging polarimetry has emerged over the past three decades as a powerful tool to enhance the information available in a variety of remote sensing applications. We discuss the foundations of passive imaging polarimetry, the phenomenological reasons for designing a polarimetric sensor, and the primary architectures that have been exploited for developing imaging polarimeters. Considerations on imaging polarimeters such as calibration, optimization, and error performance are also discussed. We review many important sources and examples from the scientific literature.

/pdf/review-of-passive-imaging-polarimetry-for-remote-sensing-3kk5ut05ha.pdf

Review of passive imaging polarimetry for remote sensing applications

We describe the design, construction, alignment, and calibration of a photometric ellipsometer of the rotating-analyzer type Data are obtained by digital sampling of the transmitted flux with an analog-to-digital converter, followed by Fourier transforming of the accumulated data with a dedicated minicomputer With an operating mechanical rotation frequency of 74 Hz, a data acquisition cycle requires less than 7 msec The intrinsic precision attainable is high because precision is limited only by shot noise or intrinsic source instabilities, even when relatively weak continuum lamps are used as light sources Precision may be improved by accumulating the data for consecutive cycles at a fixed wavelength The system allows complex reflectance ratios to be determined as continuous functions of wavelength from the near infrared to the near ultraviolet spectral range Data reduction programs can be modified to calculate complex refractive index or dielectric function spectra, or film thicknesses and refractive indices, as well as the usual ellipsometric parameters tanpsi, cosDelta

High Precision Scanning Ellipsometer

The application of reciprocity principles in optics has a long history that goes back to Stokes, Lorentz, Helmholtz and others. Moreover, optical applications need to be seen in the context of applications of reciprocity in particle scattering, acoustics, seismology and the solution of inverse problems, generally. In some of these other fields vector wave propagation is, as it is in optics, of the essence. For this reason the simplified approach to light wave polarization developed by, and named for, Jones is explored initially to see how and to what extent it encompasses reciprocity. The characteristic matrix of a uniform dielectric layer, used in the analysis of interference filters and mirrors, is reciprocal except when the layer is magneto-optical. The way in which the reciprocal nature of a characteristic matrix can be recognized is discussed next. After this, work on the influence of more realistic attributes of a dielectric stack on reciprocity is reviewed. Some of the numerous technological applications of magneto-optic non-reciprocal media are identified and the potential of a new class of non-reciprocal components is briefly introduced. Finally, the extension of the classical reciprocity concept to systems containing components that have nonlinear optical response is briefly mentioned.

https://iopscience.iop.org/article/10.1088/0034-4885/67/5/R03/pdf

Reciprocity in optics

Polarimetry has a long and successful history in various forms of clear media. Driven by their biomedical potential, the use of the polarimetric approaches for biological tissue assessment has also recently received considerable attention. Specifically, polarization can be used as an effective tool to discriminate against multiply scattered light (acting as a gating mechanism) in order to enhance contrast and to improve tissue imaging resolution. Moreover, the intrinsic tissue polarimetry characteristics contain a wealth of morphological and functional information of potential biomedical importance. However, in a complex random medium-like tissue, numerous complexities due to multiple scattering and simultaneous occurrences of many scattering and polarization events present formidable challenges both in terms of accurate measurements and in terms of analysis of the tissue polarimetry signal. In order to realize the potential of the polarimetric approaches for tissue imaging and characterization/diagnosis, a number of researchers are thus pursuing innovative solutions to these challenges. In this review paper, we summarize these and other issues pertinent to the polarized light methodologies in tissues. Specifically, we discuss polarized light basics, Stokes-Muller formalism, methods of polarization measurements, polarized light modeling in turbid media, applications to tissue imaging, inverse analysis for polarimetric results quantification, applications to quantitative tissue assessment, etc.

/pdf/tissue-polarimetry-concepts-challenges-applications-and-4fp6pfuwhm.pdf

Tissue polarimetry: concepts, challenges, applications, and outlook

• We describe a new technique for the measurement of retinal nerve fiber layer thickness and compare its results with histopathologic measurements in the same eyes. For these studies, two fixed monkey eyes were incised and placed on a pedestal in a plastic viewing dish. The eyes were perfused to maintain a pressure between 10 and 20 mm Hg. An ellipsometer, an optical device used to measure the change in polarization of light (retardation), was implemented in a laser tomographic scanner to obtain polarization data from the two monkey retinas. For the 15 measured locations, retardation ranged between a mean (± SD) of 0.9° ± 1.8° and 23.7° ± 0.3°. Subsequently, retinal nerve fiber layer thickness was measured at the imaged points in epoxy resin-embedded sections by an observer masked to the ellipsometry data. These values ranged between 20.4 μm and 213.9 μm. There was an excellent correlation (R =.83) between retardation and the histopathologic measurement of retinal nerve fiber layer thickness. Quantitating retinal nerve fiber layer thickness may enhance discrimination between glaucomatous and normal eyes earlier than is currently available by anatomic and functional approaches.

Histopathologic Validation of Fourier-Ellipsometry Measurements of Retinal Nerve Fiber Layer Thickness

All 16 elements of the Mueller matrix of an optical system (sample) can be encoded onto, hence can be retrieved from, a single detected signal using a class of photopolarimeters with modulated polarizing and analyzing optics. The general theory of operation of such polarimeters is presented. We also propose a specific new photopolarimeter whose polarizing and analyzing optics are modulated by synchronously rotating two quarter-wave retarders at angular speeds ω and 5ω. When the light flux leaving such polarimeter is linearly detected, a periodic signal J=a0+∑n=112(an cos nωft+bn sin nωft) is generated, with fundamental frequency ωf = 2ω. From the Fourier amplitudes a0, an, bn, to be measured by performing a discrete Fourier transform (DFT) of the signal ℐ, the 16 elements of the Mueller matrix are simply determined.

Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal.

We extend the scope of the Mueller calculus to parallel that established by Jones for his calculus. We find that the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the Stokes vector. We determine the differential matrix m for eight basic types of optical behavior, find its form for the most general anisotropic nondepolarizing medium, and determine its relationship to the complex 2 × 2 differential Jones matrix. We solve the Stokes-vector differential equation for light propagation in homogeneous nondepolarizating media with arbitrary absorptive and refractive anisotropy. In the process, we solve the differential-matrix and Mueller-matrix eigenvalue equations. To illustrate the case of inhomogeneous anisotropic media, we consider the propagation of partially polarized light along the helical axis of a cholesteric or twisted-nematic liquid crystal. As an example of depolarizing media, we consider light propagation through a medium that tends to equalize the preference of the state of polarization to the right and left circular states.

/pdf/propagation-of-partially-polarized-light-through-anisotropic-3x1kechmlb.pdf

Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus

The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, ψi, Δi,) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A ≠ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on the detectors are required, and a thin dielectric (e.g., thermal oxide) layer would suffice. The differential reflection phase shift Δ is unrestricted for the first and third detectors and has optimum values of ±90° for the second. The optimum rotation angles of the POI are ±45° and ±135°. The optimum values of the surface parameter ψ are 27.37°, 22.5° or 67.5°, and 0 or 90° for the first, second, and third reflections, respectively. The following topics are also considered: (1) the partition of energy among detectors, (2) the effect of tilting the last detector, (3) operation of the FDP over a broadband spectral range, (4) choice of the light-beam path, and (5) calibration.

/pdf/general-analysis-and-optimization-of-the-four-detector-4kl90kfer4.pdf

General analysis and optimization of the four- detector photopolarimeter

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Rasheed M. A. Azzam

Papers

Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal.

Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus

General analysis and optimization of the four- detector photopolarimeter

Stokes-vector and Mueller-matrix polarimetry [Invited].

Fiber-optic four-detector polarimeter