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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 6 — Jun. 1, 2014
  • pp: 1206–1214

Fast nonparaxial scalar focal field calculations

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

JOSA A, Vol. 31, Issue 6, pp. 1206-1214 (2014)

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An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh–Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.

© 2014 Optical Society of America

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

ToC Category:
Diffraction and Gratings

Original Manuscript: February 18, 2014
Revised Manuscript: April 1, 2014
Manuscript Accepted: April 7, 2014
Published: May 12, 2014

Matthias Hillenbrand, Armin Hoffmann, Damien P. Kelly, and Stefan Sinzinger, "Fast nonparaxial scalar focal field calculations," J. Opt. Soc. Am. A 31, 1206-1214 (2014)

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