OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 9335–9340

Arbitrary shape surface Fresnel diffraction

Tomoyoshi Shimobaba, Nobuyuki Masuda, and Tomoyoshi Ito  »View Author Affiliations

Optics Express, Vol. 20, Issue 8, pp. 9335-9340 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (876 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to O(N2) in one dimensional or O(N4) in two dimensional cases, where N is the number of sampling points. However, the calculation cost of the proposed method is O(N log N) in one dimensional or O(N2 log N) in two dimensional cases using non-uniform fast Fourier transform.

© 2012 OSA

OCIS Codes
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display
(090.1995) Holography : Digital holography
(090.5694) Holography : Real-time holography

ToC Category:

Original Manuscript: February 27, 2012
Revised Manuscript: April 1, 2012
Manuscript Accepted: April 2, 2012
Published: April 6, 2012

Tomoyoshi Shimobaba, Nobuyuki Masuda, and Tomoyoshi Ito, "Arbitrary shape surface Fresnel diffraction," Opt. Express 20, 9335-9340 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. W. Goodman, Introduction to Fourier Optics (3rd ed.) (Robert & Company, 2005).
  2. Okan K. Ersoy, Diffraction, Fourier Optics And Imaging (Wiley-Interscience, 2006).
  3. E. G. Williams, Fourier Acoustics – Sound Radiation and Nearfield Acoustical Holography (Academic Press, 1999). [PubMed]
  4. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006). [CrossRef]
  5. T. C. Poon (ed.), Digital Holography and Three-Dimensional Display (Springer, 2006). [CrossRef]
  6. D. Leseberg and C. Frére, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt.27, 3020 (1988). [CrossRef] [PubMed]
  7. C. Frere and D. Leseberg, “Large objects reconstructed from computer-generated holograms,” Appl. Opt.28, 2422–2425 (1989). [CrossRef] [PubMed]
  8. L. Yu, Y. An, and L. Cai, “Numerical reconstruction of digital holograms with variable viewing angles,” Opt. Express10, 1250–1257 (2002). [PubMed]
  9. H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt.48, H212–H221 (2009). [CrossRef] [PubMed]
  10. T. Tommasi and B. Bianco, “Frequency analysis of light diffraction between rotated planes,” Opt. Lett.17, 556–558 (1992). [CrossRef] [PubMed]
  11. 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. A15, 857–867 (1998). [CrossRef]
  12. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A20, 1755–1762 (2003). [CrossRef]
  13. G. B. Esmer and L. Onural, “Computation of holographic patterns between tilted planes,” Proc. SPIE6252, 62521K (2006). [CrossRef]
  14. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt.47, 1567–1574 (2008). [CrossRef] [PubMed]
  15. A. Dutt and V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA)14, 1368–1393 (1993). [CrossRef]
  16. Q. H. Liu and N. Nguyen, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microw. Guid. Wave Lett.8, 18–20 (1998). [CrossRef]
  17. Q. H. Liu, N. Nguyen, and X. Y. Tang, “Accurate algorithms for nonuniform fast forward and inverse Fourier transforms and their applications,” IEEE Trans. Geosci. Remote Sens.1, 288–290 (1998).
  18. L. Greengard and J. Y. Lee, “Accelerating the Nonuniform Fast Fourier Transform,” SIAM Rev.46, 443–454 (2004). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

Supplementary Material

» Media 1: AVI (740 KB)     
» Media 2: AVI (795 KB)     

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited