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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 1 — Jan. 3, 2011
  • pp: 32–39

Reference calculation of light propagation between parallel planes of different sizes and sampling rates

Petr Lobaz  »View Author Affiliations

Optics Express, Vol. 19, Issue 1, pp. 32-39 (2011)

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The article deals with a method of calculation of off-axis light propagation between parallel planes using discretization of the Rayleigh-Sommerfeld integral and its implementation by fast convolution. It analyses zero-padding in case of different plane sizes. In case of memory restrictions, it suggests splitting the calculation into tiles and shows that splitting leads to a faster calculation when plane sizes are a lot different. Next, it suggests how to calculate propagation in case of different sampling rates by splitting planes into interleaved tiles and shows this to be faster than zero-padding and direct calculation. Neither the speedup nor memory-saving method decreases accuracy; the aim of the proposed method is to provide reference data that can be compared to the results of faster and less precise methods.

© 2010 OSA

OCIS Codes
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: November 2, 2010
Revised Manuscript: December 10, 2010
Manuscript Accepted: December 12, 2010
Published: December 20, 2010

Petr Lobaz, "Reference calculation of light propagation between parallel planes of different sizes and sampling rates," Opt. Express 19, 32-39 (2011)

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  1. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004), 3rd ed.
  2. E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58(9), 1235–1237 (1968). [CrossRef]
  3. L. Onural, “Exact analysis of the effects of sampling of the scalar diffraction field,” J. Opt. Soc. Am. A 24(2), 359–367 (2007). [CrossRef]
  4. L. Onural, A. Gotchev, H. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic three-dimensional television,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1631–1646 (2007). [CrossRef]
  5. V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions,” Appl. Opt. 47(19), 3481–3493 (2008). [CrossRef] [PubMed]
  6. N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A 15(4), 857–867 (1998). [CrossRef]
  7. J.-L. Kaiser, E. Quertemont, and R. Chevallier, “Light propagation in the pseudo-paraxial fresnel approximation,” Opt. Commun. 233(4-6), 261–269 (2004). [CrossRef]
  8. E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974). [CrossRef]
  9. R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express 15(9), 5631–5640 (2007). [CrossRef] [PubMed]
  10. F. Zhang, G. Pedrini, and W. Osten, “Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution,” Opt. Lett. 31(11), 1633–1635 (2006). [CrossRef] [PubMed]
  11. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009). [CrossRef] [PubMed]
  12. M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005) (Special issue on “Program Generation, Optimization, and Platform Adaptation”). [CrossRef]

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