Resolution of the discrepancies between different physical optics solutions for rough surface scattering

Abstract

The analysis presented here resolves the discrepancies between the different high-frequency, physical optics expressions for the scattered field derived by several researchers in the field. On applying the divergence theorem (in two dimensions) the term associated with the edge effect is shown to vanish identically for all scatter directions. Thus it is also shown that the so-called edge effect which appears in earlier derivations of the physical optics solution for rough surface scattering is a result of premature truncation of the closed surface integral expression for the scattered fields. Therefore this term must be suppressed even when it is not very small compared to the scattered field in the off specular direction. Since the Kirchhoff approximations for the surface fields are used in the physical optics approach, it cannot account for wave diffraction by edges. The physical optics solution derived here for arbitrary source excitation is shown to satisfy reciprocity and realizability relationships in electromagnetic theory. The integrand in the integral expression for the scattered field is identified with the specific reflectance (per unit area) of the rough surface. Although the scalar acoustic problem is considered here in detail, the results are also applicable to electromagnetic scattering.