A mathematical method of analysis of gratings having circularly concentric grooves is presented. The main emphasis is not on the ultimate calculation of the diffracted or scattered fields but rather on reducing the problem to a tractable form with clear physical interpretation, to which the point-matching method can be applied. This is done by starting with the Rayleigh–Fano equation for scattering from rough surfaces. For circular geometry, the problem initially appears intractable. However, by a series of Laplace and inverse Laplace transforms, the problem is reduced to a tractable form.
© 1983 Optical Society of America
J. M. Elson, "Mathematical analysis of gratings with circularly concentric grooves," J. Opt. Soc. Am. 73, 702-706 (1983)