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An analytical approach is proposed to study the contribution of edge effects in the multiple high-frequency diffraction, according to guidelines of classical Kirchhoff theory in (scalar) wave propagation. We start from a suitable asymptotic analysis of the Kirchhoff diffraction integral, here set up in a generalized (iterated) form to describe the multiple reflections from an arbitrary sequence of curved reflecting (smooth) surfaces. The explicit formula obtained for a concrete example of double reflection is compared with the results from direct numerical simulation.

The multidimensional stationary-phase method for an asymptotic estimate of edge effects in the multiple Kirchhoff diffraction by curved surfaces