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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

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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 N×N pixels, in an area d×d, it is necessary to evaluate the Fresnel diffraction pattern at distances zd2/λN. 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

Original Manuscript: May 12, 1998
Revised Manuscript: October 16, 1998
Manuscript Accepted: October 22, 1998
Published: February 1, 1999

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)

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