It has been shown that the model of a scattering medium composed of clusters located in the far zones of each other allows some properties of regolith-like surfaces to be quantitatively estimated from the phase dependences of intensity and polarization measured in the backscattering domain. From the polarization profiles, the sizes of particles, the structure and porosity of the medium, and a portion of the surface area covered with a disperse material can be determined. At the same time, the intensity profiles of the scattered light weakly depend on the sizes and structure of particles; they are mainly controlled by the concentration of scatterers in the medium and the shadow-hiding contribution at small phase angles. Since the latter effect is beyond the considered model, a good agreement between the model and the measured intensity cannot be achieved. Nevertheless, if a portion of the surface that participates in coherent backscattering has been found from the phase profile of polarization, the present model makes it possible to determine the relative contribution of the shadow-hiding effect to the brightness surge measured at zero phase angle. This, in turn, may allow the roughness of the scattering surface to be estimated. The model contains no free parameters, but there is currently no possibility to verify it comprehensively by the data obtained in laboratory measurements of the samples with thoroughly controlled characteristics, because such measurements are rare for a wide range of the properties of particles in a medium, their packing density, and phase angles.

Interpretation of photometric and polarimetric observations of atmosphereless celestial bodies faces the problems connected with both the insufficient accuracy and level of details in groundbased observations and the current state of the theory of the multiple scattering of light. In application to sparse media, where the electromagnetic waves, propagating between the scatterers, can be considered as spherical (the socalled far-field approximation), this theory is rather well developed for both the diffuse and coherent components of the scattered radiation. In this paper, we show that this theory can be also successfully applied to the measurements of polarization of light scattered by densely packed, though nonabsorbing or weakly absorbing, media. For this purpose, we calculated the models for a semi-infinite layer of the medium composed of randomly oriented clusters of spherical particles and compared them with the data of laboratory and astronomical measurements. The potential of the present approach is illustrated by an example of the interpretation of the polarization measurements of the ice satellites of Saturn—Rhea and Enceladus—which allowed some properties of the surface of these celestial bodies to be estimated. In particular, the ratio of the surface area that makes no contribution to the negative polarization of light reflected at small phase angles to the area producing the negative polarization branch was found. Under the assumption of the same albedo of these areas, this ratio turned out to be 3.31–3.66 and 1.7–3.8 for Rhea and Enceladus, respectively. For Enceladus, it is difficult to obtain a sufficiently narrow range of the estimated parameters, since the number of measurement points in the phase dependence of polarization of this satellite is small. For the surface of Rhea, the estimated packing density of particles, participating in the opposition effects, is approximately 15%, while their smallest size is of the order of the wavelength of visible light.

Over the last decade, considerable progress has been achieved in the theory of light scattering by morphologically complex objects, which extends the potential of correct interpretation of photometric and polarimetric observations. This especially concerns the backscattering domain, where the opposition effects in brightness and polarization are observed. Although the equations of radiative transfer and weak localization (coherent backscattering) are rigorously valid only for sparse media, the results of exact computer solutions of the Maxwell equations for a macroscopic volume filled with randomly positioned particles show that their application area can be wider. In particular, the observations can be correctly interpreted if the packing density of particles in the medium reaches 20–30%. The recently suggested approximate solution of the coherent backscattering problem allowed interesting effects in the spectra of Saturn’s satellites to be explained. In the densely packed media, the effects that are impossible in the sparse media and caused by the near-field contribution can be observed. To calculate the characteristics of radiation reflected by such a medium, it is not sufficient to solve the radiative transfer and weak localization equations, even if they are written in a form without the far-zone limitations. Nowadays, the influence of the interaction of particles in the near field can be analyzed only for the restricted ensembles of particles. It shows that the substantial increase of the packing density essentially changes the phase functions of intensity and polarization in the backscattering domain. This allows the packing density of particles in the medium and their absorbing properties to be estimated from the shape of the phase curves measured. However, the task of quantitative interpretation of the measurements of radiation reflected by a densely packed medium, in terms of sizes of particles, their refractive index, and packing density, still remains unsolved.

This book outlines the basic physical principles and practical methods of polarimetric remote sensing of Solar System objects and summarizes numerous advanced applications of polarimetry in geophysics and planetary astrophysics. In the first chapter we present a complete and rigorous theory of electromagnetic scattering by disperse media directly based on the Maxwell equations and describe advanced physically based modeling tools. This is followed, in Chapter 2, by a theoretical analysis of polarimetry as a remote-sensing tool and an outline of basic principles of polarimetric measurements and their practical implementations. In Chapters 3 and 4, we describe the results of extensive ground-based, aircraft, and spacecraft observations of numerous Solar System objects (the Earth and other planets, planetary satellites, Saturn's rings, asteroids, trans-Neptunian objects, and comets). Theoretical analyses of these data are used to retrieve optical and physical characteristics of planetary surfaces and atmospheres as well as to identify a number of new phenomena and effects. This monograph is intended for science professionals, educators, and graduate students specializing in remote sensing, astrophysics, atmospheric physics, optics of disperse and disordered media, and optical particle characterization.

We have found systematic variations in the depth of the absorption bands in the spectra of Saturn’s icy satellites and showed that these variations likely resulted from the coherentbackscattering effect (CBE). Our computer modeling of the CBE reproduces the observed spectral variations and also shows that they are strongly affected by the size and packing of particles. The variations in the absorption bands produced by the CBE not only allow us to improve interpretation of the spectra but also provide a promising approach to study size and packing of the regolith and dust particles.

We have found systematic variations in the spectra of Saturn's icy satellites Rhea and Iapetus obtained by the Cassini Visual and Infrared Mapping Spectrometer (VIMS). The main attribute of these variations is a significantly different depth of the absorption bands at different phase angles. We show that these variations likely result from the coherent backscattering effect (CBE). This effect has been mainly known as the probable reason for a steep opposition spike in brightness observed for some asteroids, moons, and Kuiper Belt Objects at phase angles smaller than 3°. The opposition spike has different steepness at different albedos due to the strong dependence of the CBE on the absorption of the material. As a result of this dependence, the impact of the CBE should be different within and outside of the absorption spectral bands. This produces a systematic change in the depth of the absorption bands at different phase angles, as we see in the VIMS spectra of Rhea and Iapetus. Neglecting this effect may result in misinterpretation of the spectra and misleading conclusions about compositional and particle size differences of icy bodies studied at different phase angles. Our computer modeling of the CBE reproduces the observed spectral variations and also shows that they are strongly affected by the size and packing of particles. Thus, the variations in the absorption bands produced by the CBE not only allow us to improve interpretation of the spectra, but also provide a promising approach to study size and packing of the regolith and dust particles.

The explanation of the opposition effects observed in brightness and polarization in different celestial bodies and laboratory samples is still far from being complete. The shadow hiding and coherent backscattering mechanisms are mentioned most frequently in this connection. In the present work, we consider one more scattering mechanism—the interaction of particles in the near field—and its influence on the brightness and polarization of light scattered by ensembles of particles at small phase angles. First, we analyze two manifestations of this mechanism: the field inhomogeneity in the vicinity of the scatterers and the shielding of particles by each other at distances compared with their sizes. Then, we use the model regolith described as an ensemble of clusters as constituents and compare the contributions of the coherent backscattering and the near-field effect to the intensity and polarization of light when the porosity of the ensemble is varied. The modeling confirms that the phase dependences of the intensity and polarization of light scattered by complex structures in the backscattering domain is mainly caused by these two mechanisms. The coherent backscattering works more effectively in sparse media, while the near-field effect manifests itself in more compact ensembles of wavelength-sized particles. However, it is difficult to distinguish quantitatively their contributions, even in models of simple structures. A number of observations, especially of moderate- and low-albedo objects, can be explained only by invoking the near-field effect.

The theory of light scattering by systems of spherical particles is applied to study the light scattering by discrete random media. A microphysical approach of statistical electromagnetics is used to derive the vector radiative transfer equation for semi-infinite densely packed media composed of identical spherical particles. The equation obtained corresponds to the sum of the ladder diagrams in the diagrammatic representation of the Bethe–Salpeter equation. The new vector radiative transfer equation is compared with that for sparse media. The effective refractive index as it enters in our equation is calculated from the known generalization of the Lorentz–Lorenz equation. Some numerical results of calculations of the reflection matrix are presented and compared with those for sparse media. The differences between the theoretical description of light scattering by closely packed and sparse media are discussed in detail.

A new simple algorithm for calculation of 3D geometric chirality degree is constructed. The problem is considered in context of the electromagnetic waves diffraction on a periodic complex-shape elements structure. Dependences of the chirality degree for cylindrical spirals and tetrahedrons on their geometrical characteristics are demonstrated. The results are compared with calculations of the degree of circular polarization of wave scattered by randomly oriented structures.

In the present paper some numerical results, based on the theory developed in double and third scattering approximation are presented. The influences of microphysical and morphological properties of discrete random medium on photometric and polarimetric characteristics of backscattered radiation are discussed. If the effective refractive index of the medium is kept the same, the differences in the features of the opposition effects are caused by differences in the microscopic characteristics of the scatterers. From theoretical observations, it is concluded that the results demonstrate that the state of polarization of the back scattered radiation is controlled by the state of polarization of singly scattered radiation. It is well known that the positive polarization of light scattered by isolated particle leads to a negative polarization feature in the backscattering direction. The angular dependence of the polarization state for wavelength sized spherical particles is much more complex and oscillatory. The interference may lead to a more complex dependence of polarization on the scattering angle, with positive and negative polarization regions appearing simultaneously. The resulting interference of doubly scattered waves can result in positive polarization as well as negative polarization.

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 μm. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.

The angular dependence of brightness and linear polarization of randomly oriented aggregates has been investigated in order to find rules connecting their scattering properties with their structure, packing density, complex refractive index, and number and size of the spheres forming the aggregate. Our study is based on an interpretation in terms of successive orders of scattering, in particular on the analysis of the contribution of the interference and near-field effects. Such an approach allowed us to explain and interrelate the main peculiarities of the angular dependence of the intensity and polarization displayed by aggregates. Of special interest are the aggregates showing a so-called negative branch of linear polarization of light scattered into angles close to the backscattering direction. It has been shown that the enhancement of intensity and the negative polarization in this angular range are mainly caused by the interference of multiply scattered waves as well as by near-field effects. If the number of particles in the aggregate is large enough and its size is comparable to the wavelength, the backscattering enhancement is caused by the particles in the surface layers of the aggregate, where the radiation field is mostly homogeneous, while the negative branch is mainly generated by the deeper layers of particles, where the radiation field is inhomogeneous with chaotic changes of amplitudes and phases. This results in a rather weak dependence of the negative polarization on particle location in the deeper layers of the aggregate and on particle number but not on packing density.

We examine the coherent opposition effect from a medium containing arbitrary scatterers. A rigorous analysis of all interactions is numerically unwieldy, so we examine first and second-order effects. We proceed to a ray-tracing analysis. While not as elegant, the results are more easily accessible, and the effect of multiple interactions can be examined with relative ease. While scattering from small particles leads to a negative polarization opposition effect, scattering from larger spheres, comparable to the wavelength can lead to a positive or negative polarization opposition effect.

Coherent backscattering of light by discrete random media, otherwise known as weak photon localization, is a remarkable optical phenomenon caused by constructive interference of waves propagating along the same light-scattering paths but in opposite directions. A well-known manifestation of coherent backscattering is an intensity peak centered at exactly the backscattering direction. It also has been established that when the incident beam is unpolarized then the coherent backscattering intensity peak can be accompanied by a sharp asymmetric peak of negative polarization with a minimum centered at a very small phase angle. It has been suggested that coherent backscattering could be a contributor to some effects observed for solar system bodies in visible light and at radiowave frequencies [1-4]. However, accurate theoretical computations of weak photon localization based on first physical principles are difficult and have been used in analyses of planetary observations in only a handful of publications: This chapter briefly discusses manifestations of coherent backscattering and reviews the exact theory of this phenomenon and its applications to analyses of laboratory data and remote-sensing observations.