The Rayleigh–Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat’s principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order.
© 2000 Optical Society of America
(050.0050) Diffraction and gratings : Diffraction and gratings
(080.1010) Geometric optics : Aberrations (global)
(110.2990) Imaging systems : Image formation theory
(230.1950) Optical devices : Diffraction gratings
(260.1960) Physical optics : Diffraction theory
Virendra N. Mahajan, "Aberrations of diffracted wave fields. II. Diffraction gratings," J. Opt. Soc. Am. A 17, 2223-2228 (2000)