Scattering of light by a large, densely packed agglomerate of small silica spheres.

We model the measured phase function and degree of linear polarization of a macroscopic agglomerate made of micrometer-scale silica spheres using the methodology of multiple scattering. In the laboratory work, the agglomerate is produced ballistically, characterized by scanning electron microscopy, and measured with the $ {\text{PROGRA}^{2}} $PROGRA2 instrument to obtain the light scattering properties. The model phase function and degree of polarization are in satisfactory agreement with the experimental data. To our best knowledge, this is the first time the degree of linear polarization has been modeled well for a large, densely packed agglomerate composed of small particles with known sizes and shapes. The study emphasizes the relevance of the degree of linear polarization and gives insights into the effects of particle aggregation on the scattering characteristics.

Scattering and absorption in dense discrete random media of irregular particles.

We present an approximate numerical solution for the multiple scattering problem involving densely packed arbitrarily shaped small particles. We define incoherent volume elements that describe the statistics of the random medium and formulate an order-of-scattering solution for the entire random medium. We apply the T-matrix formalism to compute the incoherent interactions of irregular particles in the sequence of scattering events in the Monte Carlo radiative transfer algorithm. The T-matrices for the volume elements of arbitrarily shaped particles are computed by the volume-integral-equation (VIE)-based T-matrix method. We show that the approximate solution is in agreement with the numerically exact VIE solution for a small spherical random medium. Finally, we demonstrate the importance of applying irregular particle shape models in the analysis of multiple scattering by a large random medium of non-spherical particles.

Shapes and scattering properties of large irregular bodies from photometric data.

The macroscopic shapes, rotational states, and scattering parameters of atmosphereless bodies can be deduced from photometric measurements of total brightnesses in different viewing/illumination geometries. The problem is solved with nonlinear optimization techniques; the use of positive definite quantities effectively removes the apparent ill-posedness of the problem. Since the parameters of scattering laws such as the Hapke model cannot be unambiguously determined from photometric data only, we propose a simple empirical scattering model for the purpose. Our methods can obtain convex hull-like shapes even for strongly nonconvex objects; a conception of the major concavities can also be formed.

Light scattering by wood fibers.

We consider the scattering of light by single wood fibers both theoretically and experimentally. We describe the size and the shape distributions and the internal structure and chemical composition of the wood fibers. We have modeled the random shape of the hollow, cylindrical wood fiber by using multivariate lognormal statistics. We have computed wood-fiber absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray-optics approximation. Finally, we have provided experimental results from angular scattering measurements for wood fibers and present what we believe is the first comparison between these measurements and ray-optics computations for Gaussian random wood-fiber models. In spite of the complicated internal structure of the wood fiber, our model together with the ray-optics treatment explains the scattering measurements surprisingly well.

Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method.

We report, for the f irst time to our knowledge, comparisons of light-scattering computations for large, randomly oriented, moderately absorbing spheroids based on the geometric-optics approximation and the exact T-matrix method. We show that in most cases the geometric-optics approximation is (much) more accurate for spheroids than for surface-equivalent spheres and can be used in phase function computations (but not in polarization computations) for nonspherical particles with size parameters as small as 60. Differences in the single-scattering albedo between geometric-optics and T-matrix results are surprisingly small, even for small size parameters.

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.

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.

Scattering of light by crystals: a modified Kirchhoff approximation.

A modified Kirchhoff approximation (MKA) is developed for the scattering of light by randomly oriented crystals. The reflected and transmitted near fields are calculated from ray tracing; the corresponding far fields are then obtained via the vector Kirchhoff integral. On the shadow side of the particle, an additional near field exactly cancels the incident field and causes the forward diffraction. MKA contains a particle size dependence, which is not included in ray optics treatments, and satisfactory results can be obtained for size parameters larger than ten. The scattering phase functions and degrees of linear polarization are calculated for some hexagonal and cubic water ice crystals using MKA. The Kirchhoff approximation for particles other than crystals is discussed, and attention is paid to the backscattering enhancement due to the cyclic passage of internally or multiply externally reflected electromagnetic waves.

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.