Intensity surge and negative polarization of light from compact irregular particles.

We study the dependence of the intensity and linear polarization of light scattered by isolated particles with the compact irregular shape on their size using the discontinuous Galerkin time domain numerical method. The size parameter of particles varies in the range of X=10 to 150, and the complex refractive index is m=1.5+0i. Our results show that the backscattering negative polarization branch weakens monotonously, but does not disappear at large sizes, up to the geometrical optics regime, and can be simulated without accounting for wave effects. The intensity backscattering surge becomes narrower with increasing particle size. For X=150, the surge width is several degrees.

Interpolating light-scattering properties of irregularly shaped, absorbing particles.

Success in developing remote-sensing methods is largely based on adequate modeling of target-particle shapes. In various terrestrial and cosmic applications, submicrometer- and micrometer-sized dust particles appear to have a highly irregular morphology. Light scattering by such irregularly shaped particles can be computed only with a numerical technique that, in practice, is a time-consuming approach, demanding significant computational resources. In this Letter, we discuss an efficient way to accelerate light-scattering computations through interpolation of the numerical results obtained at different levels of material absorption. We find a nonlinear dependence of reflectance, degree of linear polarization, and linear and circular polarization ratios on the imaginary part of refractive index Im(m). Over the range of ΔIm(m)=0.05, the dependence can be satisfactorily described with a cubic polynomial function, whose determination requires exact computations at four different values of Im(m). The light-scattering characteristics at other intermediate values of Im(m) can be inferred with great accuracy via interpolation.

Umov effect in single-scattering dust particles: effect of irregular shape.

The Umov effect manifests itself as an inverse correlation between the light-scattering maximum of positive polarization Pmax and the geometric albedo A of the target. In logarithmic scales, Pmax is linearly dependent on A. This effect has been long known in the optics of particulate surfaces and, recently, it was extended for the case of single-scattering dust particles whose size is comparable to the wavelength of the incident light. In this work, we investigate the effect of irregular shape on the Umov effect in single-scattering particles. Using the discrete dipole approximation (DDA), we model light scattering by two different types of irregularly shaped particles. Despite significant differences in their morphology, both types of particles reveal remarkably similar diagrams of log(Pmax) versus log(A). Moreover, in a power-law size distribution r-n with n=2.5-3.0, the Umov diagrams in both types of particles nearly coincide. This suggests little dependence on the shape of target particles in the retrieval of their reflectance using the Umov effect.

Phase-ratio imaging as applied to desert sands for tracking human presence.

The phase function is a measure of the light-scattered intensity, or radiance, as a function of scattering angle θ. A phase ratio is the ratio of two values of the phase function measured at different scattering angles and relates to the slope of the phase function. By taking the ratio of two images acquired at different illumination or observation conditions, a phase-ratio image can be constructed. Such images accentuate differences in the phase curves, rather than their intensities, and are more sensitive to microtopography than to material properties. We produce phase-ratio images from intensity images acquired at different observation times and locations in the desert environment of White Sands National Monument. Because of the lack of surface features, coregistration of the images is challenging, especially for images acquired from different observation locations. However, we do demonstrate that phase-ratio images can be used to identify disturbed sands. We also produce polarimetric and color-ratio images. These latter images do not suggest the possibility of identifying topographical differences due to human presence.

Light scattering by irregular particles much larger than the wavelength with wavelength-scale surface roughness.

We simulate light scattering by random irregular particles that have dimensions much larger than the wavelength of incident light at the size parameter of X=200 using the discontinuous Galerkin time domain method. A comparison of the DGTD solution for smoothly faceted particles with that obtained with a geometric optics model shows good agreement for the scattering angle curves of intensity and polarization. If a wavelength-scale surface roughness is introduced, diffuse scattering at rough interface results in smooth and featureless curves for all scattering matrix elements which is consistent with the laboratory measurements of real samples.

Light scattering by randomly irregular dielectric particles larger than the wavelength.

We present results of simulation of light scattering by randomly irregular particles that have dimensions larger than the wavelength of incident light. We apply the discontinuous Galerkin time domain method and compare the accurate solution with that obtained using an approximate geometric-optics model. A qualitative agreement is observed for scattering angle curves of intensity at the size parameter of X=60, whereas angular dependence of polarization appears to be more sensitive to the wave effects and requires larger sizes for application of geometrical optics.

Validity criteria of the discrete dipole approximation.

There are two widely accepted restrictions on the application of the discrete dipole approximation (DDA) in the study of light scattering by particles comparable to the wavelength: (1) when considering dielectric particles, the size of the cells must satisfy the condition kd|m|<0.5, where k is the wavenumber, d is the size of the cells, and m is the complex refractive index of the constituent material and (2) when considering conductive particles, the size of the cells must be small enough to reproduce sufficiently the evolution of the electromagnetic field in the skin layer. We examine both restrictions when the DDA is applied to irregularly shaped particles and show that its restrictions are not as strong as is widely accepted. For instance, when studying irregularly shaped particles averaged over orientations, even at kd|m|=1, the DDA provides highly accurate numerical results. Moreover, we show that the impact of using large constituent cells is similar to that produced by surface roughness; therefore, the replacement of the target particle by an array of large constituent cells has the same effect, qualitatively, as incorporating additional small-scale surface roughness on the particle. Such a modification of the target particle can be desirable in many practical applications of DDA when irregularly shaped particles are considered. When applying DDA to conductive, nonspherical particles, the insufficient description of the electromagnetic field in the skin layer does not lead to a violation of the Maxwell equations, although it has a visible but nonmajor influence on the light-scattering properties of the target.

Optimized matrix inversion technique for the T-matrix method.

We suggest a new approach to calculate the inverse matrix in scattering calculations using the T-matrix method. Instead of inversion of the full matrix, we suggest the inversion of two matrices, each of which contains half the number of rows. This approach allows significant time savings and a noticeable increase of the precision of scattering calculations due to fewer arithmetical operations. An iterative method can be applied to matrices whose dimension is also divisible by factors of 2, which can further increase the time savings and accuracy.

Electromagnetic phase differences in the coherent backscattering enhancement mechanism for random media consisting of large nontransparent spheres.

Phase curves of intensity are calculated for light scattering in media randomly packed with large nontransparent spheres (x=125), the surfaces of which reflect according to the Fresnel equations. We consider three values of refractive index: m = 0.73 + i5.93 (metal Al), 1.6 + i1.72 (metal Fe), and 1.5 + i0.1 (black glass). We use a Monte Carlo ray-tracing approach. Different kinds of electromagnetic phase differences of reciprocal trajectories are investigated for the second and third orders of scattering; the highest orders give comparatively small contributions due to the backward-scattering indicatrix of large nontransparent spheres. We find that the main electromagnetic phase difference between the direct and time-reversal (reciprocal) trajectories is the outer phase difference that depends only on the relative positions of the first and last points of the ray reflections and the phase angle. The inner phase difference is connected with the changing path length of the ray inside the medium. This depends on the particle size and the phase angle that is the angle between the source and receiver from the scatterer, i.e., 180 degrees minus the scattering angle. The inner phase difference can give oscillations in the phase curve consisting of second-order components if the medium consists of strictly monodisperse spheres. Usually the coherent backscattering enhancement is calculated ignoring the shadow-hiding effect. We show that accounting for the shadowing of the reciprocal trajectory is important for the formation of the backscattering effect. The third-order scattering surge is a superposition of wide and narrow opposition spikes that correspond to two different types of scattering trajectories, closed and opened ones. The first type is due to scattering by two particles; the second one corresponds to scattering by three particles.

Analytical light-scattering solution for Chebyshev particles.

We develop a modification of the T-matrix method that allows for fast calculations of scattering properties of particles with irregular shapes. This modification uses the so-called Sh matrices, the elements of which depend on the shape of particles and do not depend on the particle size or optical constants; i.e., the introduction of Sh matrices makes possible the separation of these parameters within the T-matrix algorithm. For a given shape of a scattering object we calculate the Sh matrices only once and then can quickly calculate the T-matrix elements for a number of sizes and refractive indices. This, in particular, can provide rapid particle-size and refractive index averaging in a particle ensemble. This separation is useful for the derivation of an analytical light-scattering solution for Chebyshev particles.

Light backscatter by surfaces composed of small spherical particles.

We present measurements of phase angle curves of intensity and degree of linear polarization of powdery surfaces at two spectral bands centered near 0.44 and 0.63 microm. Three powder samples consisting of nonabsorbing spherical particles of sizes comparable with the wavelengths 0.5, 1.0, and 1.5 microm were examined. The particulate surfaces were measured in the phase angle range of 0.2 degrees-50 degrees by two different photometers and/or polarimeters. At small phase angles, powdery samples consisting of spherical particles (having very high albedo that resulted in significant multiple scattering) showed prominent features that corresponded to single-particle scattering. These features became more prominent after compressing the surfaces when we changed the packing density of the powders from 0.29 to 0.48. Noticeable differences were observed between polarimetric curves corresponding to different wavelengths. All the samples demonstrated prominent opposition intensity spikes at phase angles <2 degrees likely caused by the coherent backscatter enhancement due to multiple scattering within the particulate surface. The intensity phase curves at these two wavelengths were similar. The photopolarimetric measurements may have broad applications to the interpretation of photometry, spectroscopy, and polarimetry of the ice regoliths of high albedo satellites.

Discrete dipole approximation simulations of scattering by particles with hierarchical structure.

We use the discrete dipole approximation (DDA) method to calculate the intensity and the linear polarization degree of light scattered by agglomerated debris particles with hierarchical structure as functions of size parameter (varying from x = 2 to x = 14) and phase angle. Such structures are important, e.g., for cometary and interplanetary dust particles. Calculations for three combinations of refractive index were made, which correspond to regions of water ice, organic matter, and silicates. We examine the photometric and polarization properties of agglomerated particles with prefractal (Whitten-Sander model) and nonfractal porous structures of particle fragments formed by dipoles. We find that the aggregated particles can produce significant negative polarization at small phase angles. Increasing the packing density of dipoles and/or refractive index makes the negative polarization more prominent. The depth of the negative polarization branch depends on the type of internal structure: the negative polarization branch of particles having nonfractal structure is noticeably shallower in comparison with that of those having a prefractal structure. The negative polarization branch depth strongly depends on the imaginary part of the refractive index and increases with decreasing absorption. Polarization phase curves for agglomerated debris particles become smoother as the number of hierarchical levels increases.

Classical photometry of prefractal surfaces.

Using the scale invariance of classical photometry, we develop an approach to finding the photometric function of prefractal structures that form a random topography. The photometric function of the prefractal surfaces is found as the general solution of the resulting differential equation in partial derivatives. The function depends on two parameters: the number of hierarchical levels of the prefractal structures and the roughness parameter of the single-level generation. As a limiting case, the approach includes our previous theory that considered fractoids.

Backscattering and negative polarization of agglomerate particles.

We used the discrete dipole approximation to study the backscattering of agglomerate particles consisting of oblong monomers. We varied the aspect ratio of the monomers from approximately 1 (sphere) to 4, while we kept the total particle volume equivalent to that of an x = 10 sphere for m = 1.59 + i0 and 1.50 + i0 and considered two values of agglomerate packing density: rho = 0.25 and rho = 0.1. We found that these particles do not display a prominent brightness opposition effect but do produce significant negative polarization over a range of near-backscattering angles. Increasing the monomers' aspect ratio can make the negative polarization much more prominent. We have noted also that decreasing m and p can reduce the amplitude of the negative polarization for these particles.