On the use of the quasi specular model for surface parameter estimation

The specular point or quasi specular model has seen extensive use in inversion algorithms to estimate surface roughness, i.e. the variance of surface slopes, and the reflection coefficient of randomly rough surfaces from backscattered fields. In the quasi specular model, the mean scattering cross section per unit illuminated area of the rough surface is directly proportional the magnitude of the flat surface Fresnel reflection coefficient, R, and the probability density function (pdf) of the filtered surface slopes, i.e. for a one dimensional surface σ_{backscattered}⁰(Θ)=πsec³ (Θ)pdf∇s(tan^-1(Θ))|R(0^o )|2. In effect, the reflection coefficient influences the portion of the incident field scattered and the slope pdf determines the direction in which there is preferred scattering. The quasi specular model is developed from a high frequency approach in which the surface is assumed to be sufficiently rough in height that there is no coherent scattering but not so rough that multiple scattering is significant. Despite the model´s wide usage, no comprehensive quantitative study of the model´s range of validity as an inversion tool has been performed. In this presentation, quantitative results of a numerical study on the use of the quasi specular model for parameter estimation in two dimensions (i.e. a one-dimensional surface) are presented. The study shows how the accuracy of the quasi-specular model as an inversion tool varies over a wide range of parameters for Gaussian surfaces through the use of Monte Carlo simulation results where exact surface parameters are known. Of particular importance in the parameter estimation problem is the numerical noise present in any finite length Monte Carlo simulation and the angular region over which “data” is to be compared to the model. As with most problems of this nature, there are a number of tradeoffs and these will be explored