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.

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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

Coupling constants are introduced that determine the extent to which a component imperfection, window birefringence, or azimuth-angle error couple to cause an error of the specimen reflectance ratio. A unified scheme for treating these sources of error is presented. By expressing the coupling constants as functions of the nulling angles, any of the nulling methods can be considered. Results are presented for the compensator at ±π/4 and nulling by the polarizer and analyzer, which show the contributions of the different sources of error to ψ and Δ in the four ellipsometry zones. The limitations of one- and two-zone measurements are discussed. A procedure is described and demonstrated experimentally for determining the quantities characterizing the different sources of error in the ellipsometer. These results can be used in correcting data from one-, two-, or four-zone measurements.

Unified analysis of ellipsometry errors due to imperfect components, cell-window birefringence, and incorrect azimuth angles.

The absolute, average, and differential phase shifts that p- and s-polarized light experience in total internal reflection (TIR) at the planar interface between two transparent media are considered as functions of the angle of incidence phi. Special angles at which quarter-wave phase shifts are achieved are determined as functions of the relative refractive index N. When the average phase shift equals pi/2, the differential reflection phase shift delta is maximum, and the reflection Jones matrix assumes a simple form. For N > square root 3, the average and differential phase shifts are equal (hence deltap = 3 deltas) at a certain angle phi that is determined as a function of N. All phase shifts rise with infinite slope at the critical angle. The limiting slope of the delta-versus-phi curve at grazing incidence (partial partial differential delta/partial partial differential phi)phi=90 degrees = -(2/N)(N2 - 1)1/2 = -2 cos phic, where phic is the critical angle and (partial partial differential2 delta/partial partial differential phi 2)phi=90 degrees = 0. Therefore delta is proportional to the grazing incidence angle theta = 90 degrees - phi (for small theta) with a slope that depends on N. The largest separation between the angle of maximum delta and the critical angle is 9.88 degrees and occurs when N = 1.55377. Finally, several techniques are presented for determining the relative refractive index N by using TIR ellipsometry.

/pdf/phase-shifts-that-accompany-total-internal-reflection-at-a-5ghelyx63a.pdf

Phase shifts that accompany total internal reflection at a dielectric–dielectric interface

A division-of-amplitude photopolarimeter based on conical grating diffraction includes a diffraction grating and at least four photodetectors. An incident light beam is directed at the grating at an oblique incidence angle Φ and the grating grooves are inclined at an arbitrary angle α with respect to the plane of incidence. Each of the photodetectors is positioned to intercept one of the diffracted orders and may be an area array detector if spectropolarimetry use is desired. Polarizing means may be inserted in the paths of one or more of the diffracted orders. A division-of-amplitude photopolarimeter based on planar grating diffraction includes a diffraction grating and at least four photodetectors; the grating is placed in the conventional spectrometer orientation with its grating grooves perpendicular to the plane of incidence. Each of the photodetectors is positioned to intercept one of the diffracted orders, all of which lie in the plane of incidence and may be a linear array detector if spectropolarimetry use is desired. Polarizers are inserted in the paths of at least two of the diffracted orders between the grating and the detectors.

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Diffraction-grating photopolarimeters and spectrophotopolarimeters

The technique of generalized ellipsometry is briefly reviewed. An improved criterion for computing the normalized 2 × 2 complex reflection matrix of an anisotropic surface from multiple-null ellipsometer measurements (in excess of three) is given. Generalized ellipsometry, together with the recently developed 4 × 4-matrix methods for the study of the reflection and transmission of polarized light by stratified anisotropic media, provide the basic tools to carry out and to interpret ellipsometric measurements on anisotropic structures. As an example, the case of uniaxial (absorbing) crystals, with the optic axis parallel to the surface, is considered. From three or more null measurements at a single unknown orientation of the optic axis, the five parameters (the ordinary and extraordinary complex indices of refraction and the angle of inclination of the optic axis from the plane of incidence) that characterize a uniaxial crystal of calcite are all determined.

/pdf/application-of-generalized-ellipsometry-to-anisotropic-kqox0sewrs.pdf

Application of generalized ellipsometry to anisotropic crystals

Optimal optical parameters of the beam splitter that is used in the division-of-amplitude photopolarimeter are determined. These are (1) 50%–50% split ratio of the all-dielectric beam splitter, (2) differential phase shifts in reflection and transmission 
Δr and 
Δt that differ by ±π/2, and (3) ellipsometric parameters 
(ψr, ψt)= (27.368°, 62.632°) or (62.632°, 27.368°). It is also shown that for any nonabsorbing beam splitter that splits incident unpolarized light equally, the relationship 
ψr+ψt=π/2 is always satisfied.

/pdf/optimal-beam-splitters-for-the-division-of-amplitude-3u46ypobt4.pdf

Rasheed M. A. Azzam

Papers

Unified analysis of ellipsometry errors due to imperfect components, cell-window birefringence, and incorrect azimuth angles.

Phase shifts that accompany total internal reflection at a dielectric–dielectric interface

Diffraction-grating photopolarimeters and spectrophotopolarimeters

Application of generalized ellipsometry to anisotropic crystals

Optimal beam splitters for the division-of-amplitude photopolarimeter