This paper describes a new theory of random surface scattering based on the group theoretic consideration of the stochastic homogeneity of the infinite random surface. To show the basic idea of the theory, we only discuss scalar wave scattering for one-dimensional random surface that is described by a reactance boundary condition having a random reactance of a stationary random function. A form of the stochastic wave solution associated with the random boundary condition is determined by the group theoretic consideration. The wave solution is then written in terms of a stationary random function that is approximately solved as a stochastic functional of the random surface. The optical theorem, the angle dependence of the incoherent scattering, and the energy flow of the surface wave are calculated and are shown in the figures.
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