This paper studies the scattering of a TE plane wave from a periodic random
surface generated by a stochastic binary sequence using a stochastic funct
ional method. The scattered wave is first expressed as a product of an expo
nential phase factor and a periodic stationary process. The periodic statio
nary process is then expressed by a harmonic series representation, that is
a 'Fourier series' with 'Fourier coefficients' given by mutually correlate
d stationary processes. These stationary processes are regarded as stochast
ic functionals of the binary sequence and they are represented by orthogona
l 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 nume
rically and illustrated in figures. It is found that, in the binary case, t
he second-order scattering cross section has a subtractive term and becomes
much smaller than the first-order one.