A transition model for the reflection coefficient in surface scattering

In the development of wave scattering models for randomly dielectric rough surfaces, it is usually assumed that the Fresnel reflection coefficients could be approximately evaluated at either the incident angle or the specular angle. However, these two considerations are only applicable to their respective regions of validity. A common question to ask is what are the conditions under which we would choose one or the other of these two approximations? Since these approximations are basically roughness-dependent, how can we handle the in-between cases where neither is appropriate? In this paper, a physical-based transition function that naturally connects these two approximations is proposed. The like-polarized backscattering coefficients are evaluated with the model and are compared with those calculated with a moment method simulation for both Gaussian and non-Gaussian correlated surfaces. It is found that the proposed transition function provides an excellent prediction for the backscattering coefficient in the frequency and angle trends.