In this paper, we provide a review of the different approaches used for target decomposition theory in radar polarimetry. We classify three main types of theorem; those based on the Mueller matrix and Stokes vector, those using an eigenvector analysis of the covariance or coherency matrix, and those employing coherent decomposition of the scattering matrix. We unify the formulation of these different approaches using transformation theory and an eigenvector analysis. We show how special forms of these decompositions apply for the important case of backscatter from terrain with generic symmetries.

A review of target decomposition theorems in radar polarimetry

Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

There have been three basic approaches to optical tomography since the early 1980s: diffraction tomography, diffuse optical tomography and optical coherence tomography (OCT). Optical techniques are of particular importance in the medical field, because these techniques promise to be safe and cheap and, in addition, offer a therapeutic potential. Advances in OCT technology have made it possible to apply OCT in a wide variety of applications but medical applications are still dominating. Specific advantages of OCT are its high depth and transversal resolution, the fact, that its depth resolution is decoupled from transverse resolution, high probing depth in scattering media, contact-free and non-invasive operation, and the possibility to create various function dependent image contrasting methods. This report presents the principles of OCT and the state of important OCT applications. OCT synthesises cross-sectional images from a series of laterally adjacent depth-scans. At present OCT is used in three different fields of optical imaging, in macroscopic imaging of structures which can be seen by the naked eye or using weak magnifications, in microscopic imaging using magnifications up to the classical limit of microscopic resolution and in endoscopic imaging, using low and medium magnification. First, OCT techniques, like the reflectometry technique and the dual beam technique were based on time-domain low coherence interferometry depth-scans. Later, Fourier-domain techniques have been developed and led to new imaging schemes. Recently developed parallel OCT schemes eliminate the need for lateral scanning and, therefore, dramatically increase the imaging rate. These schemes use CCD cameras and CMOS detector arrays as photodetectors. Video-rate three-dimensional OCT pictures have been obtained. Modifying interference microscopy techniques has led to high-resolution optical coherence microscopy that achieved sub-micrometre resolution. This report is concluded with a short presentation of important OCT applications. Ophthalmology is, due to the transparent ocular structures, still the main field of OCT application. The first commercial instrument too has been introduced for ophthalmic diagnostics (Carl Zeiss Meditec AG). Advances in using near-infrared light, however, opened the path for OCT imaging in strongly scattering tissues. Today, optical in vivo biopsy is one of the most challenging fields of OCT application. High resolution, high penetration depth, and its potential for functional imaging attribute to OCT an optical biopsy quality, which can be used to assess tissue and cell function and morphology in situ. OCT can already clarify the relevant architectural tissue morphology. For many diseases, however, including cancer in its early stages, higher resolution is necessary. New broad-bandwidth light sources, like photonic crystal fibres and superfluorescent fibre sources, and new contrasting techniques, give access to new sample properties and unmatched sensitivity and resolution.

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Optical coherence tomography - principles and applications

Classification and Change Detection Using Landsat TM Data: When and How to Correct Atmospheric Effects?

This paper reviews the state of the art of optical coherence tomography (OCT), an interferometric imaging technique that provides cross-sectional views of the subsurface microstructure of biological tissue. Following a discussion of the basic theory of OCT, an overview of the issues involved in the design of the main components of OCT systems is presented. The review concludes by introducing new imaging modes being developed to extract additional diagnostic information.

Optical coherence tomography (OCT): a review

We present measured scattering matrices as functions of the scattering angle in the range 5°–173° and at wavelengths of 441.6 nm and 632.8 nm for seven distinct irregularly shaped mineral aerosol samples with properties representative of mineral aerosols present in the Earth's atmosphere. The aerosol samples, i.e., feldspar, red clay, quartz, loess, Pinatubo and Lokon volcanic ash, and Sahara sand, represent a wide variety of particle size (typical diameters between 0.1 and 100 μm) and composition (mainly silicates). We investigate the effects of differences in size and complex refractive index on the light-scattering properties of these irregular particles. In particular, we find that the measured scattering matrix elements when plotted as functions of the scattering angle are confined to rather limited domains. This similarity in scattering behavior justifies the construction of an average aerosol scattering matrix as a function of scattering angle to facilitate, for example, the use of our results for the interpretation of remote sensing data. We show that results of ray-optics calculations, using Gaussian random shapes, are able to describe the experimental data well when taking into account the high irregularity in shape of the aerosols, even when these aerosols are rather small. Using the results of ray-optics calculations, we interpret the differences found between the measured aerosol scattering matrices in terms of differences in complex refractive index and particle size relative to the wavelength. The importance of our results for studies of astronomical objects, such as planets, comets, asteroids, and circumstellar dust shells is discussed.

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Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm

We derive theoretically and validate numerically general relationships for the elements of the backscattering matrix and for the linear, delta(L), and circular, delta(C), backscattering depolarization ratios for nonspherical particles in random orientation. For the practically important case of randomly oriented particles with a plane of symmetry or particles and their mirror particles occurring in equal numbers and in random orientation, delta(C) = 2delta(L)/(1 - delta(L)). Extensive T-matrix computations for randomly oriented spheroids demonstrate that, although both delta(L) and delta(C) are indicators of particle nonsphericity, they cannot be considered a universal measure of the departure of particle shape from that of a sphere and have no simple dependence on particle size and refractive index.

Depolarization of light backscattered by randomly oriented nonspherical particles

In this paper we study the combined effects of size and shape of small solid state particles on the absorption, emission and scattering characteristics. We use the statistical approach to calculate these optical properties. In this approach the average optical properties of an ensemble of particles in random orientation are represented by the average optical properties of an ensemble of simple shapes. The validity of this approach is studied in detail for a uniform distribution of hollow spheres where the fractional volume of the central inclusion is varied. We apply the results to two different areas of interest, i) infrared spectroscopy; and ii) polarization of scattered light. The effects of particle size and shape on the optical characteristics are discussed. We compare the results using the distribution of hollow spheres with those obtained by using randomly oriented spheroids. Also we compare the results with observations and laboratory measurements. The distribution of hollow spheres is very successful in reproducing laboratory measurements of the scattering angle distribution of the degree of linear polarization for incident unpolarized light of randomly oriented irregular quartz particles. Furthermore, we show that we are able to derive the size distribution of dust grains by fitting the measured degree of linear polarization using computational result for hollow spheres. It is shown that the distribution of hollow spheres is a powerful tool for studying light scattering, absorption and emission by cosmic dust grains and in particular when large numbers of particle parameters need to be considered since the computational demand of the distribution of hollow spheres is small.

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Modeling optical properties of cosmic dust grains using a distribution of hollow spheres

Aims. In this paper we present two efficient implementations of the diffusion approximation to be employed in Monte Carlo computations of radiative transfer in dusty media of massive circumstellar disks. The aim is to improve the accuracy of the computed temperature structure and to decrease the computation time. The accuracy, efficiency, and applicability of the methods in various corners of parameter space are investigated. The effects of using these methods on the vertical structure of the circumstellar disk as obtained from hydrostatic equilibrium computations are also addressed. Methods. Two methods are presented. First, an energy diffusion approximation is used to improve the accuracy of the temperature structure in highly obscured regions of the disk, where photon counts are low. Second, a modified random walk approximation is employed to decrease the computation time. This modified random walk ensures that the photons that end up in the high-density regions can quickly escape to the lower density regions, while the energy deposited by these photons in the disk is still computed accurately. A new radiative transfer code, MCMax, is presented in which both these diffusion approximations are implemented. These can be used simultaneously to increase both computational speed and decrease statistical noise. Results. We conclude that the diffusion approximations allow for fast and accurate computations of the temperature structure, vertical disk structure and observables of very optically thick circumstellar disks.

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Radiative transfer in very optically thick circumstellar disks

From the contents: Preface.- 1. Description of Polarized Light.- 2. Single Scattering.- 3. Plane-parallel Media.- 4. Orders of Scattering and Multiple-Scattering Matrices.- 5. The Adding-doubling Method.- A. Mueller Calculus.- B. Generalized Spherical Functions.- C. Expanding the Elements of F (T).- D. Size Distributions.- E. Proofs of Relationships for Multiple-Scattering Matrices.- F. Supermatrices and Extended Supermatrices.- Bibliography.- Index.

Joop W. Hovenier

Papers

Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm

Depolarization of light backscattered by randomly oriented nonspherical particles

Modeling optical properties of cosmic dust grains using a distribution of hollow spheres

Radiative transfer in very optically thick circumstellar disks

Transfer of Polarized Light in Planetary Atmospheres: Basic Concepts And Practical Methods