Abstract

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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References

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  1. Y. Arieli, N. Eisenberg, A. Lewis, I. Glaser, “Geometrical-transformation approach to optical two-dimensional beam shaping,” Appl. Opt. 36, 9129–9131 (1997).
    [CrossRef]
  2. H. Aagedal, M. Schmid, S. Egner, J. Müller-Quade, T. Beth, F. Wyrowski, “Analytical beam shaping with application to laser-diode arrays,” J. Opt. Soc. Am. A 14, 1549–1553 (1997).
    [CrossRef]
  3. T. Dresel, M. Beyerlein, J. Schwider, “Design and fabrication of computer-generated beam-shaping holograms,” Appl. Opt. 35, 4615–4621 (1996).
    [CrossRef] [PubMed]

1997

1996

Aagedal, H.

Arieli, Y.

Beth, T.

Beyerlein, M.

Dresel, T.

Egner, S.

Eisenberg, N.

Glaser, I.

Lewis, A.

Müller-Quade, J.

Schmid, M.

Schwider, J.

Wyrowski, F.

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Equations (11)

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y x = 0 .
F y dy = F y d y .
dy = y x d x + y y d y ,
F y = y 1 F y ,
- , y x , y   f x ,   y d x = y 1 - , y y x , y y   f x ,   y d x
y y = 2 a π   arcsin y R + 2 ay π R 2 R 2 - y 2 1 / 2 , for   | y | R ,
x x ,   y = ax R 2 - y 2 1 / 2 ,     for   | x | R 2 - y 2 1 / 2
ϕ x ,   y x = k   x x ,   y - x Z ,
ϕ x ,   y y = k   y x ,   y - y Z ,
2 ϕ x ,   y y x = 2 ϕ x ,   y x y .
x x ,   y y = y x ,   y x .

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