Thorsos and Winebrenner [1991] compare the formally averaged predictions of Bahar's full-wave theory, with and without Bahar's simplifying assumptions, with their numerical calculations from an exact integral equation, and with analytical results from small perturbation theory and the (first-order) Kirchhoff approximation. They show that for small heights and slopes and for moderate incidence angles the formally averaged full-wave theory without Bahar's simplifying assumptions agrees with their numerical evaluation of full-wave theory and with the Kirchhoff approximation but not with perturbation theory. On the other hand, numerical results from the exact integral equation agree with perturbation theory in the cases they examine. Thus for these cases they conclude that perturbation theory is valid, that the Kirchhoff approximation is not accurate, and that full-wave theory fails. By making Bahar's simplifying assumptions, namely, that correlations between surface heights and slopes may be neglected and that slopes at two different points are perfectly correlated, they find that full-wave theory agrees with small perturbation theory where it should. In his rebuttal Bahar [1991] reviews full-wave theory and it's relationship to Rice's [1951] original small-perturbation theory, points out what he says is a divergence of higher-order perturbation theory for small heights and slopes, and takes exception to the tapering function used by Thoros and Winebrenner in their numerical calculations. In this brief comment, I would like to try to clarify the central issue in this controversy, while hopefully bringing an alternate viewpoint to bear in some side issues.
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