The full-wave approach has been used to obtain the like- and cross-polarized single and double scattered electromagnetic fields from deterministic two dimensional rough surfaces. The single scattered fields are expressed in terms of two dimensional integrals. The double scattered fields are expressed in terms of four and six dimensional integrals. To evaluate the multiple scatter expressions, a supercomputer is needed. The corresponding geometrical optics expressions are derived for the doubly scattered fields in terms of one- and two-dimensional integrals. The results show that for normal incidence double scatter is significant in the backward direction when the mean square slope of the highly conducting surface is large. The magnitude of the total field in the near backscatter direction fluctuates due to interferences between the different multiple scatter waves and the single scattered wave.
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