Wave scattering from a periodic random surface generated by a stationary binary sequence

This paper studies the scattering of a TE plane wave from a periodic random surface generated by a stochastic binary sequence using a stochastic functional method. The scattered wave is first expressed as a product of an exponential phase factor and a periodic stationary process. The periodic stationary process is then expressed by a harmonic series representation, that is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence and they are represented by orthogonal binary functional expansions with band-limited binary kernels. The binary kernels are determined up to the second order from the boundary condition. Then, several statistical properties of the scattering are calculated numerically and illustrated in figures. It is found that, in the binary case, the second-order scattering cross section has a subtractive term and becomes much smaller than the first-order one.