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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. 31, Iss. 8 — Aug. 1, 2014
  • pp: 1832–1841

Numerical solution of nonparaxial scalar diffraction integrals for focused fields

Matthias Hillenbrand, Damien P. Kelly, and Stefan Sinzinger  »View Author Affiliations


JOSA A, Vol. 31, Issue 8, pp. 1832-1841 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001832


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Abstract

In this paper, we present sampling conditions for fast-Fourier-transform-based field propagations. The input field and the propagation kernel are analyzed in a combined manner to derive sampling criteria that guarantee accurate calculation results in the output plane. These sampling criteria are also applicable to the propagation of general fields. For focal field calculations, geometrical optics is used to obtain a priori knowledge about the input and output fields. This a priori knowledge is used to determine an optimum balance between computational load and calculation accuracy. In a numerical example, correct results are obtained even though both the input field and the propagation kernel are sampled below the Nyquist rate. Finally, we show how chirp z-transform-based zoom-algorithms may be analyzed using the same techniques.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(110.2990) Imaging systems : Image formation theory
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.2560) Optical design and fabrication : Propagating methods

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: May 7, 2014
Revised Manuscript: June 27, 2014
Manuscript Accepted: June 27, 2014
Published: July 28, 2014

Citation
Matthias Hillenbrand, Damien P. Kelly, and Stefan Sinzinger, "Numerical solution of nonparaxial scalar diffraction integrals for focused fields," J. Opt. Soc. Am. A 31, 1832-1841 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-8-1832

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