The Comment by Kowalczyk et al. [J. Opt. Soc. Am. A 20, 2390 (2003)] on our paper on sampling expansions for three-dimensional light amplitude distributions in the vicinity of an axial image point [J. Opt. Soc. Am. A 14, 2962 (1997)] presents a “new” derivation of the axial sampling expansion (ASE), pointing out some “faults” in our derivation and that of Arsenault and Boivin [J. Appl. Phys. 38, 3988 (1967)], a derivation of which we were not aware. Finally, it also summarizes work done in generalizing the ASE to the case of nonrotationally symmetric pupil functions. The purpose of this reply is to clarify some relevant issues concerning the derivation of this kind of expansion, since, judging from some ideas expressed in their Comment, we believe these issues were left insufficiently clear in our paper. In doing this, we derive some additional sampling expansions.
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