The symmetry properties of point-spread functions of optical imaging systems with circular pupils aber-rated by a Zernike-circle polynomial aberration were discussed by Nijboer ["The diffraction theory of aber-rations," Ph.D. dissertation (University of Groningen, Groningen, The Netherlands, 1942)]. Although it wasnot pointed out by him, his analysis and some of his results are valid only for systems with large Fresnelnumbers. The symmetry properties for systems with small and large Fresnel numbers are discussed. Theanalysis is extended to systems with annular pupils aberrated by a Zernike-annular polynomial aberration.This analysis is further extended to pupils with nonuniform but radially symmetric illumination such as Gauss-ian. It is shown, in particular, that whereas, for uniform pupils, the axial irradiance of the imaging-forminglight cone for a primary spherical aberration is symmetric about the defocused point with respect to which theaberration variance is minimum, it is asymmetric for nonuniform pupils. The discussion is equally valid forfocused beams of light. Computer-generated pictures of point-spread functions of systems with circular andannular pupils aberrated by primary aberrations illustrating their symmetry properties are given.
© 1994 Optical Society of America
Virendra N. Mahajan, "Symmetry properties of aberrated point-spread functions," J. Opt. Soc. Am. A 11, 1993-2003 (1994)