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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 900–913

Fourier spectrum of curvilinear gratings of the second order

Isaac Amidror  »View Author Affiliations


JOSA A, Vol. 15, Issue 4, pp. 900-913 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000900


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Abstract

The class of second-order curvilinear gratings consists of all the curvilinear gratings that are obtained by second-order spatial transformations of periodic gratings. It includes, for example, circular, elliptic, and hyperbolic gratings as well as circular, elliptic, and hyperbolic zone plates. Such structures occur quite frequently in optics, and their Fourier transforms may arise, for instance, in connection with the Fraunhofer diffraction patterns generated by these structures. I present the two-dimensional Fourier spectra of the most important second-order curvilinear gratings for gratings having any desired intensity profile (cosinusoidal, sawtooth wave, square wave, etc.). These analytic results are also illustrated by figures showing the various gratings and their spectra as they are obtained on a computer by two-dimensional fast Fourier transform.

© 1998 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(070.2580) Fourier optics and signal processing : Paraxial wave optics

History
Original Manuscript: July 24, 1997
Revised Manuscript: October 7, 1997
Manuscript Accepted: October 20, 1997
Published: April 1, 1998

Citation
Isaac Amidror, "Fourier spectrum of curvilinear gratings of the second order," J. Opt. Soc. Am. A 15, 900-913 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-4-900


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References

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  7. Note that the term “curvature” is defined in mathematics in a different way; see, for example, R. Courant, Differential and Integral Calculus (Wiley-Interscience, New York, 1988), Vol. II, p. 86.
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  16. The hyperbolic zone grating is also known as Girard grille; see, for example, S. Ananda Rao, “On the holographic simulation of a Girard grille,” reprinted in Selected Papers on Zone Plates, SPIE Milestone Series, Vol. MS 128 (SPIE; Bellingham, Wash., 1996), pp. 386–387.
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  22. A. Erdélyi, (ed.), Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. II, p. 39.
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