In a recent paper by P. Wang et al. [J. Opt. Soc. Am. A 15, 684 (1998)] an analytic expression for calculating Fresnel diffraction is presented. Several mathematical problems with this analysis have been observed. In this comment, corrections to the analysis of Wang et al. are offered as well as an alternative view of this analysis. New formulas based on series of exponential polynomials that are everywhere convergent are derived. These new formulas eliminate the need to split the computational problem into two distinct regions. New series representations for two of the most important combinations of the Lommel functions of two variables are offered.
© 1999 Optical Society of America
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