I. Introduction
The problem of electromagnetic wave or optics scattering from a random rough surface has been investigated extensively for several decades, because of its broad applications in science and technology. The frequency characteristics of the conventional scattering cross section for rough surfaces cannot give the pulse characteristics, so it is necessary to study the fast algorithm on the calculation of the temporal scattered field. In the literature, Guo L.X. [1] derived analytic formulas of the two-frequency mutual coherence function (MCF) for the fractal rough surface, and studied the scattering pulse waveform in the time domain using the inverse Fourier transform of the two-frequency MCF. Ren Y.C. and Guo L.X. [2] focused on deriving an explicitly analytic expression of the two-frequency MCF in the case of two-dimensional Gaussian distributed rough surface, and studied the phenomenon of pulse broadening.