Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With Theoretical Prediction

We introduce a non-perturbative two scale Kirchhoff theory, in the context of light scattering by a rough surface. This is a two scale theory which considers the roughness both in the wavelength scale (small scale) and in the scales much larger than the wavelength of the incident light (large scale). The theory can precisely explain the small peaks which appear at certain scattering angles. These peaks can not be explained by one scale theories. The theory was assessed by calculating the light scattering profiles using the Atomic Force Microscope (AFM) images, as well as surface profilometer scans of a rough surface, and comparing the results with experiments. The theory is in good agreement with the experimental results.Comment: 6 pages, 8 figure

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

The composite scattering model for radar sea return

A composite scattering model, suitable for explaining the behavior of measured scattering cross sections of the ocean surface, is presented. Furthermore, utilizing this scattering model, the spectrums of the small gravity, gravity-capillary, waves will be predicted for MSA/MSC, 13.3 GHz Scatterometer data

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

Light scattering from cold rolled aluminum surfaces

We present experimental light scattering measurements from aluminum surfaces obtained by cold rolling. We show that our results are consistent with a scale invariant description of the roughness of these surfaces. The roughness parameters that we obtain from the light scattering experiment are consistent with those obtained from Atomic Force Microscopy measurements

The Effect Of Roughness On Bottom Loss From Elastic Ocean Bottoms

Acoustic interaction with the ocean bottom profoundly affects propagation in shallow waters. However, most forward ocean bottom interactions are modeled as if the bottom were a flat interface or use a simple model to quantify the additional loss. These assumptions either neglect or over-estimate the enhancement of ocean bottom loss due to scattering into the bottom. Scattering from and into elastic bottoms is particularly interesting since it can induce the production of an interface wave. In this study, finite element analysis is used to calculate acoustic scattering from elastic ocean bottoms with varying degrees of roughness. The forward scattering loss from these bottoms is calculated as a function of angle and then compared with the flat bottom reflection coefficient in order to gain insight on the conditions under which enhancement of bottom loss by rough interface scattering is significant.Applied Research Laboratorie

Radiative Transfer in a Discrete Random Medium Adjacent to a Half-Space with a Rough Interface

For a macroscopically plane-parallel discrete random medium, the boundary conditions for the specific coherency dyadic at a rough interface are derived. The derivation is based on a modification of the Twersky approximation for a scattering system consisting of a group of particles and the rough surface, and reduces to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave propagating in a discrete random medium with non-scattering boundaries. In a matrix-form setting, the boundary conditions for the specific coherency dyadic imply the boundary conditions for specific intensity column vectors which in turn, yield the expressions for the reflection and transmission matrices. The derived expressions are shown to be identical to those obtained by applying a phenomenological approach based on a facet model to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave

Modelling light scattering by absorbing smooth and slightly rough facetted particles

A method for approximating light scattering properties of strongly absorbing facetted particles which are large compared to the wavelength is presented. It consists in adding the approximated external diffraction and reflection far fields and is demonstrated for a smooth hexagonal prism. This computationally fast method is extended towards prisms with slightly rough surfaces by introducing a surface scaling factor in order to account for edge effects on subfacets forming the rough surface. These effects become more pronounced with decreasing subfacet dimension to wavelength ratio. Azimuthally resolved light scattering patterns, phase functions and degree of linear polarisation obtained by this method and by the Discrete Dipole Approximation are compared for hexagonal prisms with smooth and slightly rough surfaces, respectively.Peer reviewedSubmitted Versio