A generalized power law spectrum and its applications to the backscattering of soil surfaces based on the integral equation model

A generalized power law spectrum is proposed to describe the random rough surfaces in this paper. The parameters of the spectrum are related to the traditional physical parameters of root mean square (rms) height and correlation length. It can naturally reduce to the spectra of Gaussian and exponential correlation functions. The corresponding correlation functions are also derived. It can provide wider range of spectra to describe the random rough surfaces than other spectra. Based on the proposed spectrum, backscattering of soil surfaces is studied by using the integral equation model (IEM). The simulation results are compared with the experimental measurements of real soil surfaces at L, C, and X bands for the different roughness scales and moisture conditions. The reasonably good agreements between the measurements and the simulations are observed for all three-frequency bands and different incidence angles with the same sets of the physical roughness parameters.