Elena V. Petrova

Backscattering Effects for Discrete Random Media: Theoretical Results

The effect of enhanced backscattering of light from discrete random media, often referred to as the coherent photometric opposition effect (or weak photon localization), is a remarkable optical phenomenon that is being studied actively. When the incident light is unpolarized, the opposition intensity peak may be accompanied by the so-called opposition polarization effect, which manifests itself as a sharp asymmetric negative-polarization feature at small phase angles. The optical phenomenon that causes these effects is the constructive interference of multiply scattered waves propagating along the same light-scattering paths in a medium but in opposite directions. The theoretical description of multiple scattering becomes more complicated for closely packed media because of potentially significant near-field effects that can depress the photometric opposition peak significantly and increase the depth of the negative-polarization feature. In this chapter, we discuss the opposition effects for semi-infinite sparse scattering media and study their dependence on concentration and microphysical properties of the constituent scatterers. Manifestations of the near-field interactions are illustrated by theoretical calculations for randomly oriented clusters of spherical particles.

Ice hazes and clouds in the Martian atmosphere as derived from the Phobos/KRFM data

Abstract During the 1989 Phobos mission, the KRFM instrument observed the equatorial region of Mars in eight spectral bands from 315 to 550 nm. Previous analysis of the data mostly concentrated on extracting the optical properties of the dust particles in the atmosphere of Mars and the properties of the surface (Moroz et al., Planet. Space Sci. 41, 569, 1993). Some features of the KRFM photometric profiles, which appear to be of atmospheric origin, have however, remained unexplained. The present work considers three cases that exhibit such features and infers the effects to be caused by various types of water ice in the atmosphere. (1) For two sessions of observations, the intensity in UV near the limb was much higher than the mean of the morning limb profiles, but decreased later to the mean level as the line of sight moved further from the limb. Explaining these variations with a model of a homogeneous constant silicate haze does not seem possible. A model including a time evolving, near surface layer of silicate partieles covered with water ice provides a better fit to the data. The inferred column density of water vapour that condensed overnight on the dust particles is about 0.5 × 10−5 gcm−2, and the sublimation rate of these ice mantles after sunrise is of the order of 10−15 g μm−2 s−3. The ice haze contribution to the total optical depth decreases from about 0.05 at dawn to zero within about an hour. (2) A brightness increase of another type, observed in the afternoon UV profiles of the Valles Marineris is shown to be consistent with the presence of water ice clouds. The dependence on the properties of the clouds is discussed. The size distribution of the cloud particles seems of secondary importance. Their assumed shape, however, is critical. For spherical particles, the optical depth of the cloud is deduced to be 0.05 and the water content within the cloud to be 0.54 × 10−5 g cm−2. For particles with slightly irregular shape and rough surface both of these estimates are three times higher. (3) The photometric profiles of the Tharsis Ridge where the KRFM traces passed over the Martian volcanoes exhibit an increase in brightness in all wavelengths, but stronger in shorter wavelengths. The spectral dependence of the measured brightening is analysed to extract the properties of the clouds around Arsia Mons and Pavonis Mons. The particles of these clouds are likely to be smaller than 1 μm, and the ice column density is estimated to be in the range of 2.5 × 10−6–4.1 × 10−6 g cm−2.

Light scattering by morphologically complex objects and opposition effects (a review)

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.

PROPERTIES OF DUST IN THE MARS ATMOSPHERE : A REVISED ANALYSIS OF PHOBOS/KRFM DATA

Abstract During the 1989 Phobos 2 mission, photometric observations of the equatorial region of Mars were made in eight spectral bands in the range from 315 to 550 nm by the KRFM spectrometer. The first analysis of these data which aimed at extracting the optical properties of the atmospheric dust (Moroz et al. , 1993) used an approximate approach for the radiative transfer, underestimating the effect of multiple scattering. The present analysis of the same data corrects for this limitation with the use of a doubling/adding method. The new analysis yields comparable values for the optical depth in the range 0.1–0.15. However, the imaginary part of the refraction index of the atmospheric particles almost doubles: m i = 0.030±0.005 for 315 nm and m i = 0.012±0.003 for 550 nm, compared with 0.015 and 0.005 before, while it continues to decrease as a function of wavelength.

Light scattering by densely packed systems of particles: near-field effects

The phenomenon of scattering and absorption of electromagnetic waves is actively used in many fields of science and engineering. Among them, there are the remotesensing techniques for studying different objects and testing the quality of materials. They are extensively used in such areas as radio physics and radiolocation (to study radio-wave propagation and the properties of different objects (Ishimaru, 1978; Bass and Fuks, 1979; Tsang and Kong, 2001; Tsang et al., 2000, 2001)), optics of the atmosphere and ocean, in climatology and ecology (McCartney, 1976; Quinby-Hunt et al., 2000; Mishchenko et al., 2006), and biophysics and optics of solutions and colloids (for sorting cells and suspensions and their non-contact investigation (Horan and Wheeles, 1977; Hoekstra and Sloot, 2000)).

Interaction of Particles in the Near Field and Opposition Effects in Regolith-Like Surfaces

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.

MARS AEROSOL OPTICAL THICKNESS RETRIEVED FROM MEASUREMENTS OF THE POLARIZATION INVERSION ANGLE AND THE SHAPE OF DUST PARTICLES

Abstract The estimates of the optical thickness of the “clear” atmosphere of Mars obtained from ground-based polarimetric observations are characterized by very low values. The sensitivity of polarization to the size and shape of scatterers raises the question of the effect of the irregular shape of solid aerosol particles on the optical thickness retrieved from the spectral dependence of the polarization inversion angle for Mars (the phase angle at which the polarization of the scattered radiation changes sign). The Stokes scattering matrix for irregular dust particles is calculated using the T-matrix method. The model of randomly oriented oblate polydisperse spheroids used in this study indicates a weak dependence of the polarization inversion angle on the optical thickness of aerosols τd: an increase in τd from 0.05 to 0.15 results in an inversion angle increase of less than 1°, whereas for spherical particles this change is about 5°. It is reasonable to expect that particles with more pronounced irregular shapes than spheroids may lead to more substantial depolarization and hence an even weaker sensitivity of the inversion angle to variations in the aerosol optical thickness. Thus, very low estimates of the optical thickness of the “clear” atmosphere of Mars retrieved from ground-based polarimetric observations using a spherical-shape approach for aerosol particles cannot be considered reliable. Ignoring the dust particle shape introduces similar uncertainties in the models of the Martian atmosphere as those caused by traditionally discussed errors in such parameters as refractive index or size distribution.

Irregular shape of particles and the Martian aerosols' properties

Abstract The influence of the irregular shape of aerosol particles on the scattering phase function is studied, with emphasis on the interpretation of Mars spectrophotometry data (the KRFM experiment of the Phobos mission). An early application of Mie theory to this problem has resulted in some estimations of the Fe2O3 content in Martian surface material (Moroz et al., Planet. Space Sci. 41, 569–585, 1993). The present work supposed the conclusion that such absorption is necessary, even if the particles are not spherical. However, the abundance of the absorber can be lower if irregularly shaped particles are considered, rather than spherical ones.

Reflectance model for densely packed media: Estimates of the surface properties of the high-albedo satellites of Saturn

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.