Angular Patterns of Bistatic Scattering From Gamma-Distributed Rough Surfaces

We analyze the bistatic scattering of a gamma-distributed rough surface to explore the scattering properties in the context of polar angular patterns and specular angular beamwidth as a dependence on the degree of non-Gaussianity. We focus on the incoherent scattering because of its importance in remote sensing of rough surfaces, e.g., soil and sea ice. We use a 3 dB angular width, the width of the range of scattering angle, as a measure of angular broadening and dropping-off of the scattered power. Some insights into the physical significance are perceived. For the co-polarized scattering in the incident plane, as the skewness and kurtosis of Gamma height probability density (HPD) surface decreases, the scattering becomes narrower and concentrates more at the specular direction and has a faster decay than in the Gaussian surface at large angles. As the shape parameters increase, the incoherent scattering concentrates more at 0° of scattering angle for the cross-polarized scattering in the cross-plane. The narrow 3 dB angular width is located at the larger shape parameters (or low skewness and kurtosis) with a small to moderate root mean square (rms) height. The overall 3 dB angular width of the exponential power spectral density (PSD) surface is smaller than the Gaussian PSD surface. This study reveals that angular broadening is narrower, and the dropping-off of the scattered power is more significant for Gamma height distributed and exponential-correlated surfaces than the Gaussian surface.