Abstract

In a recent paper by Wang et al. [J. Opt. Soc. A 15, 684 (1998)] a simple closed-form expression for the light amplitude behind a circular aperture illuminated by a spherical wave is derived. This result is shown to hold only in the special case where the observation point lies on the surface separating the shadow space from the space directly illuminated by rays from the source.

© 1998 Optical Society of America

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  1. P. Wang, Y. Xu, W. Wang, Z. Wang, “Analytic expression for Fresnel diffraction,” J. Opt. Soc. Am. A 15, 684–688 (1998).
    [CrossRef]
  2. To facilitate comparison with the formulas in Ref. 1, the variables c and x herein correspond to c=Ma/ρ and x=2πNρ/a.
  3. M. Born, E. Wolf, Principles of Optics, 3rd rev. ed. (Pergamon, New York, 1965) p. 442.

1998 (1)

J. Opt. Soc. Am. A (1)

Other (2)

To facilitate comparison with the formulas in Ref. 1, the variables c and x herein correspond to c=Ma/ρ and x=2πNρ/a.

M. Born, E. Wolf, Principles of Optics, 3rd rev. ed. (Pergamon, New York, 1965) p. 442.

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Equations (8)

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01 expicx2t2J0(xt)tdt
=D expicx2-icxexp-icx2(1+1/c2)-J0(x),
D=1/[1+P(c, x)],
P(c, x)=exp(1/c2)-1e-1.
P(c, x)n=1(-ic)nJn(x)=n=1-icnJn(x).
P(±1, x)=1
P(c, 0)=1/c2,allc0.
P(c, x)P(1/c, x)=1

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