Landgrave and Berriel-Valdos presented axial and radial sampling expansions for three-dimensional light amplitude distribution around the Gaussian focal point. [J. Opt. Soc. Am. A 14, 2962 (1997)]. The expansions were obtained under the assumption that the pupil function was rotationally symmetric. We present a new derivation of the axial expansion that does not make use of arbitrary formal assumptions used by Landgrave and Berriel-Valdos and eliminates some faults of the derivation given by Arsenault and Boivin, who published this expansion in 1967 [J. Appl. Phys. 38, 3988 (1967)]. We also discuss generalizations of the axial expansion to the case of pupils that exhibit no symmetry with respect to the axis considered.
© 2003 Optical Society of America
Original Manuscript: July 29, 2002
Revised Manuscript: March 27, 2003
Manuscript Accepted: August 6, 2003
Published: December 1, 2003
Marek Kowalczyk, Tomasz Cichocki, Manuel Martı́nez-Corral, and Laura Muñoz-Escrivá, "Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment," J. Opt. Soc. Am. A 20, 2390-2392 (2003)