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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. 16, Iss. 2 — Feb. 1, 1999
  • pp: 316–322

Matrix description of near-field diffraction and the fractional Fourier transform

Sara Bradburn Tucker, Jorge Ojeda-Castañeda, and W. Thomas Cathey  »View Author Affiliations


JOSA A, Vol. 16, Issue 2, pp. 316-322 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000316


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Abstract

We describe a matrix multiplication procedure for evaluating the pixelated version of the near-field pattern of a discrete, one- or two-dimensional input. We show that for an input with <i>N</i>×<i>N</i> pixels, in an area <i>d</i>×<i>d</i>, it is necessary to evaluate the Fresnel diffraction pattern at distances <i>z</i>≥<i>d</i><sup>2</sup>/λ<i>N</i>. Our numerical algorithm is also useful for evaluating the fractional Fourier transform by multiplying by a special phase matrix with fractional parameter ε. If the phase matrix is evaluated at ε=1, we find the discrete Fourier transform matrix.

© 1999 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(350.6980) Other areas of optics : Transforms

Citation
Sara Bradburn Tucker, Jorge Ojeda-Castañeda, and W. Thomas Cathey, "Matrix description of near-field diffraction and the fractional Fourier transform," J. Opt. Soc. Am. A 16, 316-322 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-2-316

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