I show that the research reported by Arieli et al.
[Appl. Opt. 36, 9129 (1997)] has two serious
mistakes: One is that an important factor is lost in the formula
used in that study to determine the x-direction coordinate
transformation; the other is the conclusion that the
geometrical-transformation approach given by Arieli et al.
can provide a smooth phase distribution. A potential research
direction for obtaining a smooth phase distribution for a generic
two-dimensional beam-shaping problem is stated.
© 1998 Optical Society of America
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