Practical Multiple Scattering for Rough Surfaces

Microfacet theory concisely models light transport over rough surfaces. Specular reflection is the result of single mirror reflections on each facet, while exact computation of multiple scattering is either neglected, or modeled using costly importance sampling techniques. Practical but accurate simulation of multiple scattering in microfacet theory thus remains an open challenge. In this work, we revisit the traditional V-groove cavity model and derive an analytical, cost-effective solution for multiple scattering in rough surfaces. Our kaleidoscopic model is made up of both real and virtual V-grooves, and allows us to calculate higher-order scattering in the microfacets in an analytical fashion. We then extend our model to include nonsymmetric grooves, allowing for additional degrees of freedom on the surface geometry, improving multiple reflections at grazing angles with backward compatibility to traditional normal distribution functions. We validate the accuracy of our model against ground-truth Monte Carlo simulations, and demonstrate its flexibility on anisotropic and textured materials. Our model is analytical, does not introduce significant cost and variance, can be seamless integrated in any rendering engine, preserves reciprocity and energy conservation, and is suitable for bidirectional methods

Quasi-specular reflection from particulate media

Specular reflection is known to play an important role in many fields of scattering applications, e.g., in remote sensing, computer graphics, optimization of visual appearance of industrial products. Usually it can be assumed that the object has a solid surface and that the properties of the surface will dictate the behavior of the specular component. In this study I will show that media consisting of wavelength-sized particles can also have a quasi-specular reflection in cases where there is ordered structure in the media. I will also show that the quasi-specular reflection in particulate media is more than just a surface effect, and planar particle arrangement below the very surface can give arise to quasi-specular reflection. This study shows that the quasi-specular reflection may contribute in some cases in the backscattering direction, together with coherent backscattering and shadow-hiding effects

Analytic height correlation function of rough surfaces derived from light scattering

We derive an analytic expression for the height correlation function of a rough surface based on the inverse wave scattering method of Kirchhoff theory. The expression directly relates the height correlation function to diffuse scattered intensity along a linear path at fixed polar angle. We test the solution by measuring the angular distribution of light scattered from rough silicon surfaces, and comparing extracted height correlation functions to those derived from atomic force microscopy (AFM). The results agree closely with AFM over a wider range of roughness parameters than previous formulations of the inverse scattering problem, while relying less on large-angle scatter data. Our expression thus provides an accurate analytical equation for the height correlation function of a wide range of surfaces based on measurements using a simple, fast experimental procedure.Comment: 6 pages, 5 figures, 1 tabl

Light scattering from self-affine fractal silver surfaces with nanoscale cutoff: Far-field and near-field calculations

We study the light scattered from randomly rough, one-dimensional self-affine fractal silver surfaces with nanoscale lower cutoff, illuminated by s- or p-polarized Gaussian beams a few microns wide. By means of rigorous numerical calculations based on the Green theorem integral equation formulation, we obtain both the far- and near-field scattered intensities. The influence of diminishing the fractal lower scale cutoff (from below a hundred, down to a few nanometers) is analyzed in the case of both single realizations and ensemble average magnitudes. For s polarization, variations are small in the far field, being only significant in the higher spatial frequency components of evanescent character in the near field. In the case of p polarization, however, the nanoscale cutoff has remarkable effects stemming from the roughness-induced excitation of surface-plasmon polaritons. In the far field, the effect is noticed both in the speckle pattern variation and in the decrease of the total reflected energy upon ensemble averaging, due to increased absorption. In the near field, more efficient excitation of localized optical modes is achieved with smaller cutoff, which in turn leads to huge surface electric field enhancements.Comment: REVTeX 4, 10 page

Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates

Electromagnetic wave scattering from planar dielectric films deposited on one-dimensional, randomly rough, perfectly conducting substrates is studied by numerical simulations for both p- and s-polarization. The reduced Rayleigh equation, which is the integral equation satisfied by the scattering amplitude after eliminating the fields inside the film, is the starting point for the simulation. This equation is solved numerically by considering a random surface of finite length, and by introducing wave number cut-offs in the evanescent part of the spectrum. Upon discretization, a system of linear equations is obtained, and by solving this matrix system for an ensemble of surface realizations, the contribution to the mean differential reflection coefficient from the incoherently scattered field, $<\partial R_\nu/\partial \theta>_{incoh}$ (\nu=p,s), is obtained nonperturbatively. It is demonstrated that when the scattering geometry supports at least two guided waves, $_{incoh}$, has, in addition to the well known enhanced backscattering peak, well-defined satellite peaks in agreement with theory, for most of the parameters considered.Comment: 11 pages and 11 figure

Evaluation of the present theoretical basis for determination of planetary surface properties by earth-based radar

Spaceflight programs such as the planned Viking landing on Mars require the determination of planetary surface slopes and surface dielectric constants by earth-based methods. Heavy reliance is often placed on radar backscattering data for estimation of these surface properties. An assessment is presented of the basic theory by which the raw radar data are interpreted, and it is shown that serious difficulties and internal inconsistencies are present in the available theoretical formulas. The discussion brings into question the reliability of the presently available results for these surface properties as obtained by earth-based radar methods

Boundary scattering of phonons: specularity of a randomly rough surface in the small perturbation limit

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length $L$ compared with the acoustic wavelength, the specularity reduction is given by $4\eta^2k^2$, where $\eta$ is the RMS roughness and $k$ is the acoustic wavevector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to $\eta^2k^4L^2$, with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of $L$. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering