It is shown, contrary to the assertions of van den Berg,<sup>1</sup> that (1) the validity of the Rayleigh hypothesis has not been confirmed numerically, (2) the Rayleigh—Fourier (RF) method gives useful far-field results for sinusoidal gratings with height/period ratios far exceeding 0.3, (3) the Rayleigh—Yasuura method is not generally convergent in a numerical sense and is much less useful than the RF method, (4) the integrated-square error of the boundary condition is not a more reliable check of a numerical solution than the energy-balance error.
© 1982 Optical Society of America
A. Wirgin, "Reflection by a grating: Rayleigh methods: comments," J. Opt. Soc. Am. 72, 963-969 (1982)