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

For single-layer antireflection-coated (ARC) optical surfaces, the first five derivatives of reflectance with respect to angle of incidence φ for the p and s polarizations are zero at normal incidence, whereas the first three derivatives of differential transmission phase shift Δt =Δtp-Δts with respect to φ are also zero at φ=0. Consequently, ARC optical systems with numerical apertures of <0.7φ<45° exhibit fourth- and sixth-order polarization aberrations owing to retardance and diattenuation, respectively. Results for ARC Ge and ZnS surfaces are presented to illustrate these effects.

Fourth- and sixth-order polarization aberrations of antireflection-coated optical surfaces.

A tilted bilayer membrane, which consists of two thin films of transparent optically isotropic materials of different refractive indices, can function as a transmission quarter-wave retarder (QWR) at a high angle of incidence. A specific design using a cryolite-Si membrane in the infrared is presented, and its tolerances to small shifts of wavelength, incidence angle, and film thickness errors are discussed. Some designs provide a dual QWR in transmission and reflection. Such devices provide simple linear-to-circular (and circular-to-linear) polarization transformers. Bilayer eighth-wave retarders without diattenuation are also introduced.

/pdf/tilted-bilayer-membranes-as-simple-transmission-quarter-wave-4p5h4g1w8v.pdf

Tilted bilayer membranes as simple transmission quarter-wave retardation plates

The results of a preceding paper [ J. Opt. Soc. Am.65, 1464, ( 1975)] are viewed from a different angle as providing the basis for the design of film–substrate single-reflection linear partial polarizers (LPP), which also operate as reflection optical rotators. The important characteristics of a comprehensive set of discrete designs of SiO2-Si LPP’s at λ = 6328 A are shown graphically.

/pdf/design-of-film-substrate-single-reflection-linear-partial-2ix2ff35th.pdf

Design of film–substrate single-reflection linear partial polarizers*

IR reflection quarter-wave retarders (QWR5) are described that maintain the collinearity of the transmitted and incident beams. One QWR uses a symmetric prism of Ge (refractive index n = 4) with an apex angle of 119 deg. Light incident parallel to the base of the prism is totally refracted, without change of polarization, at the side faces of the prism that are coated with an appropriate transparent bilayer. Total internal reflection at the prism base produces the desired 90-deg retardance. The second QWR uses a right-angle Ge prism with its base coated with a PbTe layer ( n = 5.1) to introduce the required phase shift at a 55.18-deg angle of incidence. The entrance and exit faces are antireflection coated with a polarization-preserving bilayer. Both QWRs are reasonably insensitive to small (±8 deg) angle-of-incidence errors.

In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism

The complex Fresnel reflection coefficients rp and rs of p- and s-polarized light and their ratio ρ=rp/rs at the pseudo-Brewster angle (PBA) ϕpB of a dielectric–conductor interface are evaluated for all possible values of the complex relative dielectric function e=|e|exp(−jθ)=er−jei, ei>0 that share the same ϕpB. Complex-plane trajectories of rp, rs, and ρ at the PBA are presented at discrete values of ϕpB from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for ϕpB>70° (high-reflectance metals in the IR) rp at the PBA is essentially pure negative imaginary and the reflection phase shift δp=arg(rp)≈−90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0<ϕpB<45° and rp is pure real negative (δp=π) when θ=tan−1(cos(2ϕpB)), and the corresponding locus of e in the complex plane is obtained. In the limit of ei=0, er<0 (interface between a dielectric and plasmonic medium) the total reflection phase shifts δp, δs, Δ=δp−δs=arg(ρ) are also determined as functions of ϕpB.

/pdf/complex-reflection-coefficients-of-p-and-s-polarized-light-1igcvv6uyo.pdf

Rasheed M. A. Azzam

Papers

Fourth- and sixth-order polarization aberrations of antireflection-coated optical surfaces.

Tilted bilayer membranes as simple transmission quarter-wave retardation plates

Design of film–substrate single-reflection linear partial polarizers*

In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric-conductor interface.