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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

  • Editor: Franco Gori
  • Vol. 30, Iss. 3 — Mar. 1, 2013
  • pp: 527–536

Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

Erdem Şahin and Levent Onural  »View Author Affiliations


JOSA A, Vol. 30, Issue 3, pp. 527-536 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000527


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Abstract

We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a two-dimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.

© 2013 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(090.1995) Holography : Digital holography
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: December 19, 2012
Revised Manuscript: January 28, 2013
Manuscript Accepted: February 1, 2013
Published: February 28, 2013

Citation
Erdem Şahin and Levent Onural, "Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams," J. Opt. Soc. Am. A 30, 527-536 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-3-527

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