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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12949–12958

Calculating the Fresnel diffraction of light from a shifted and tilted plane

Kenji Yamamoto, Yasuyuki Ichihashi, Takanori Senoh, Ryutaro Oi, and Taiichiro Kurita  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 12949-12958 (2012)
http://dx.doi.org/10.1364/OE.20.012949


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Abstract

We propose a technique for calculating the diffraction of light in the Fresnel region from a plane that is the light source (source plane) to a plane at which the diffracted light is to be calculated (destination plane). When the wavefield of the source plane is described by a group of points on a grid, this technique can be used to calculate the wavefield of the group of points on a grid on the destination plane. The positions of both planes may be shifted, and the plane normal vectors of both planes may have different directions. Since a scaled Fourier transform is used for the calculation, it can be calculated faster than calculating the diffraction by a Fresnel transform at each point. This technique can be used to calculate and generate planar holograms from computer graphics data.

© 2012 OSA

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(090.1760) Holography : Computer holography
(100.6890) Image processing : Three-dimensional image processing
(110.1758) Imaging systems : Computational imaging

ToC Category:
Physical Optics

History
Original Manuscript: February 24, 2012
Revised Manuscript: April 17, 2012
Manuscript Accepted: April 27, 2012
Published: May 23, 2012

Citation
Kenji Yamamoto, Yasuyuki Ichihashi, Takanori Senoh, Ryutaro Oi, and Taiichiro Kurita, "Calculating the Fresnel diffraction of light from a shifted and tilted plane," Opt. Express 20, 12949-12958 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12949


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References

  1. 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(10), 1567–1574 (2008). [CrossRef] [PubMed]
  2. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A10(2), 299–305 (1993). [CrossRef]
  3. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on titled planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A20(9), 1755–1762 (2003). [CrossRef]
  4. S. D. Nicola, A. Finizio, and G. Pierattini, “Angular spectrum method with correction of anamorphism for numerical reconstruction of digital holograms on tilted planes,” Opt. Express13(24), 9935–9940 (2005). [CrossRef] [PubMed]
  5. K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express18(17), 18453–18463 (2010). [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. A15(4), 857–867 (1998). [CrossRef]
  7. R. P. Muffoletto, “Numerical techniques for fresnel diffraction in computational holography,” PhD thesis (Louisiana State University, 2006).
  8. R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express15(9), 5631–5640 (2007). [CrossRef] [PubMed]
  9. L. Yu, U. An, and L. Cai, “Numerical reconstruction of digital holograms with variable viewing angles,” Opt. Express10(22), 1250–1257 (2002). [PubMed]
  10. J. Miura and T. Shimobaba, “Shifted-fresnel diffraction between two tilted planes (in Japanese),” Watake Seminar in TohokuYS–6–52 (2008).
  11. L. Onural, “Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface,” J. Opt. Soc. Am. A28(3), 290–295 (2011). [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Englewood, CO, 2005), Chap. 4.
  13. D. H. Bailey and P. N. Swarztrauber, “The fractional fourier transform and applications,” SIAM Rev. 33(3), 389–404 (1991). [CrossRef]

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