Active remote sensing of atmospheric dust using relationships between their depolarization ratios and reflectivity.

The backscattered light from agglomerated debris particles shows that an approximate linear correlation exists between the logarithm of the geometric albedo $ \log(A )$ of polydispersions of agglomerated debris particles and their lidar linear or circular depolarization ratios, $ \unicode{x00B5}_L$ and $ \unicode{x00B5}_C$. The nature of the relationship depends on the complex refractive index of the particles in the distribution. This extension of the Umov law can be used for lidar and radar characterizations by placing constraints on the reflectivity of the particles. It suggests that an approximate inverse relationship exists between the lidar ratio and the lidar depolarization ratios whose scaling parameter depends on the refractive index of the aerosol population.

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.

Modeling light scattering by forsterite particles.

Laboratory optical measurements of forsterite particles reveal remarkably similar light-scattering responses in two samples that were thought to obey different size distributions. These measurements are modeled with irregularly shaped agglomerated debris particles having a refractive index of m=1.6+0.0005i that is representative of forsterite in the visible. Modeling closely reproduces the measurements of both samples, making retrieval of their size distributions possible.

Light scattering by random irregular particles of two classes of shape.

We calculate light scattering properties of random irregular particles of two different classes of shape, compact Gaussian random field particles and agglomerated debris particles, at size parameters X=50 and X=32. Surprisingly, very similar angular dependencies of all nonzero scattering matrix elements are obtained for both classes in the case of nonabsorbing material. For highly absorbing particles external scattering becomes dominant, which introduces a difference in the positive polarization due to different morphologies of their surfaces.

Effect of the orientation of the optic axis on simulated scattering matrix elements of small birefringent particles.

We study how the orientation of the optic axis affects single-scattering properties for small, birefringent calcite particles simulated using DDSCAT 7.1.1. We consider two irregular model particles, a flake and a rhomboid, in either a (i) fixed or (ii) random orientation. Simulations are performed for three volume-equivalent radii of 0.1, 0.45, and 1.0 µm. For each target, we repeat the computations for three sets of orientations of the optic axis. When a fixed spatial orientation of the target is considered, the simulations are significantly affected by the orientation of the optic axis. However, the effect is considerably weaker when assuming the same targets in random spatial orientation.

Interpretation of single-particle negative polarization at intermediate scattering angles.

We study the interrelation of the internal field of irregular particles to the far-field scattering characteristics by modifying the internal field of dipole groups. In this paper, we concentrate on the longitudinal component, i.e., the internal-field component parallel to the incident wave vector. We use the discrete-dipole approximation to determine the internal field and switch off the longitudinal component from the dipoles that have the highest energy density above a preset cutoff value. We conclude that only a relatively small number of core dipoles, about 5% of all dipoles, contribute to the negative linear polarization at intermediate scattering angles. These core dipole groups are located at the forward part of the particles. The number of core dipoles in the group becomes greater as particle asphericity increases. We find that the interference between the scattered waves from the core dipole groups, which was studied previously for spherical particles, is preserved to a large extent for nonspherical particles.

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.

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.

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.