OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 3 — Mar. 1, 2011
  • pp: 290–295

Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface

Levent Onural  »View Author Affiliations

JOSA A, Vol. 28, Issue 3, pp. 290-295 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (441 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented.

© 2011 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(070.7345) Fourier optics and signal processing : Wave propagation

Original Manuscript: July 30, 2010
Revised Manuscript: October 26, 2010
Manuscript Accepted: December 2, 2010
Published: February 4, 2011

Levent Onural, "Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface," J. Opt. Soc. Am. A 28, 290-295 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed.(Mc-Graw-Hill, 1996).
  2. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergammon, 1965).
  3. G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am. 57, 546–547(1967). [CrossRef] [PubMed]
  4. É. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58, 1235–1237 (1968). [CrossRef]
  5. L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Image Comm. 22, 169–177(2007). [CrossRef]
  6. 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]
  7. L. Onural, “Impulse functions over curves and surfaces and their applications to diffraction,” J. Math. Anal. Appl. 322, 18–27 (2006). [CrossRef]
  8. D. Leseberg and C. Frère, “Computer generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3024 (1988). [CrossRef] [PubMed]
  9. C. Frère and D. Leseberg, “Large objects reconstructed from computer generated holograms,” Appl. Opt. 28, 2422–2425 (1989). [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. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10, 299–305 (1993). [CrossRef]
  12. 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, 857–867 (1998). [CrossRef]
  13. G. B. Esmer, “Computation of holographic patterns between tilted planes,” Master’s thesis (Bilkent University, 2004).
  14. G. B. Esmer and L. Onural, “Simulation of scalar optical diffraction between arbitrarily oriented planes,” in Proceedings of 2004 First International Symposium on Control, Communications and Signal Processing, ISCCSP 2004 (IEEE, 2004), pp. 225–228. [CrossRef]
  15. 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. A 20, 1755–1762 (2003). [CrossRef]
  16. K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to holography,” Appl. Opt. 47, D110 –D116 (2008). [CrossRef] [PubMed]
  17. H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212 (2009). [CrossRef] [PubMed]
  18. K. Matsushima and A. Kondoh, “Wave optical algorithm for creating digitally synthetic holograms of three-dimensional surface objects,” Proc. SPIE 5005, 190–197 (2003). [CrossRef]
  19. K. Matsushima, “Performance of the polygon-source method for creating computer-generated holograms of surface objects,” in Proceedings of ICO Topical Meeting on Optoinformatics /Information Photonics (International Commission for Optics, 2006), pp. 99–100.
  20. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the poligon-based method,” Appl. Opt. 48, H54 (2009). [CrossRef] [PubMed]
  21. G. B. Esmer, “Calculation of scalar optical diffraction field from its distributed samples over the space,” Ph.D. thesis (Bilkent University, 2010).
  22. A. W. Lohmann. “Three-dimensional properties of wave-fields,” Optik (Jena) 51, 105–117 (1978).

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

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited