Comparison of radiative transfer Monte Carlo and volume integral equation methods of studying the clustering of small scatterers.

The effect of clustering of small scatterers on optical properties was studied by creation of a Poisson distributed plane-parallel geometry and slow cooling of the particle system in the sense of simulated annealing in an attempt to minimize the assumed total potential energy and sample the spatial distribution during the process. The optical properties were calculated by the volume integral equation method (VIEM). The scattering results for unclustered structures with different size parameters and packing densities were also compared with those given by Monte Carlo simulation for radiative transfer. In particular, measuring the intensity distribution of the VIEM is well suited to the classic radiative transfer approach.

Estimation of the wavelength-dependent effective refractive index of spherical plastic pigments in a liquid matrix.

Refractive-index data are important for the prediction of light scattering from spherical pigments. Reflectance from a slurry that contains plastic pigments was studied with the aid of a reflectometer. The effective refractive index of spherical plastic pigments in a slurry was determined by use of reflectance data and a phase-retrieval procedure based on the maximum-entropy method. This method provides a simple way to estimate the effective refractive index of pigments in a liquid matrix.

Stochastic modeling of paper structure and Monte Carlo simulation of light scattering.

A simplified stochastic model for the fiber structure of paper is introduced. The packing density and optical thickness of the fiber network are derived analytically, and their dependence on fiber characteristics can be seen. We undertake a Monte Carlo simulation of light scattering that is based on geometrical optics, using a realization of the model, which gives packing densities and optical thicknesses well in accordance with those given by the stochastic model and the scattering quantities as functions of three angles.

Laboratory measurements and T-matrix calculations of the scattering matrix of rutile particles in water.

We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm (in air). These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length/width ratio than measured.

Slope variations on the surface of Phobos.

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and micro-structures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from approximately 12 degrees on a 61m scale to approximately 7 degrees on a 216-272m scale. On the same scales, a value of the order of 2% has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.

Interpretation of the surface brightness of Phobos.

Analysis of disk resolved images of Phobos obtained by the Phobos 2 spacecraft allows us to study the surface scattering law and albedo variations. From low phase angle images we find variations in local geometric albedo approximately 10%, with a correlation length approximately 1km. The scattering law is reasonably well matched by the recent proposed LPI (Lumme et al. 1990a) model, which allows us to deduce a small scale (approximately 1 mm) surface roughness (approximately 0.5), defined here as the rms. tangent of the local surface normal relative to the mean surface normal in the Duxbury (1991) model of Phobos. This value is very close to what has been found for Mercury and the Moon.

Some photometric techniques for atmosphereless solar system bodies.

We discuss various photometric techniques and their absolute scales in relation to the information that can be derived from the relevant data. We also outline a new scattering model for atmosphereless bodies in the solar system and show how it fits Mariner 10 surface photometry of the planet Mercury. It is shown how important the correct scattering law is while deriving the topography by photoclinometry.

Diffuse reflection from a stochastically bounded, semi-infinite medium.

In order to determine the diffuse reflection from a medium bounded by a rough surface, we consider the problem of radiative transfer in a boundary layer characterized by a statistical distribution of heights. For the case that the surface is defined by a multivariate normal probability density, we derive the propagation probability for rays traversing the boundary layer and, from that probability, a corresponding radiative transfer equation. A solution of the Eddington (two stream) type is found explicitly, and examples are given. The results should be applicable to reflection from the regoliths of solar system bodies, as well as from a rough ocean surface.

Scattering of light by stochastically rough particles.

The single particle phase function and the linear polarization for large stochastically deformed spheres have been calculated by Monte Carlo simulation using the geometrical optics approximation. The radius vector of a particle is assumed to obey a bivariate lognormal distribution with three free parameters: mean radius, its standard deviation and the coherence length of the autocorrelation function. All reflections/refractions which include sufficient energy have been included. Real and imaginary parts of the refractive index can be varied without any restrictions. Results and comparisons with some earlier less general theories are presented. Applications of this theory to the photometric properties of atmosphereless bodies and interplanetary dust are discussed.

Light scattering by randomly oriented crystals.

The scattering phase function and the degree of linear polarization for small crystals oriented randomly in space have been computed using the geometric ray tracing theory and assuming that the crystals are homogeneous and isotropic. Calculations have been carried out for the main crystal geometries. Detection of halos from crystals other than hexagonal water ice is briefly discussed. The crystal size and shape parameters have also been averaged over some simple distributions in order to examine general light scattering properties of sharp-edged particles. A scalar physical optics correction has been developed for the geometric optics phase functions. Results can be applied to light scattering from regoliths and planetary rings, and possibly also to atmospheric halos. Retroreflecting crystals in the regolith would cause an opposition spike, a phenomenon observed for many bright satellites.