OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 935–948

Fast calculation of spherical computer generated hologram using spherical wave spectrum method

Boaz Jessie Jackin and Toyohiko Yatagai  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 935-948 (2013)
http://dx.doi.org/10.1364/OE.21.000935


View Full Text Article

Enhanced HTML    Acrobat PDF (3325 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A fast calculation method for computer generation of spherical holograms in proposed. This method is based on wave propagation defined in spectral domain and in spherical coordinates. The spherical wave spectrum and transfer function were derived from boundary value solutions to the scalar wave equation. It is a spectral propagation formula analogous to angular spectrum formula in cartesian coordinates. A numerical method to evaluate the derived formula is suggested, which uses only N(logN)2 operations for calculations on N sampling points. Simulation results are presented to verify the correctness of the proposed method. A spherical hologram for a spherical object was generated and reconstructed successfully using the proposed method.

© 2013 OSA

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display

ToC Category:
Holography

History
Original Manuscript: October 16, 2012
Revised Manuscript: November 19, 2012
Manuscript Accepted: November 22, 2012
Published: January 9, 2013

Citation
Boaz Jessie Jackin and Toyohiko Yatagai, "Fast calculation of spherical computer generated hologram using spherical wave spectrum method," Opt. Express 21, 935-948 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-935


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High power directional emission from microlasers with chaotic resonators,” Science280, 1544–1545 (1998). [CrossRef]
  2. N. M. Lawandy and R. M. Balachandran “Random laser?,” Nature373, 204, (1995). [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  4. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A10, 299–305 (1993), http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-10-2-299 . [CrossRef]
  5. Y. Sakamoto and M. Tobise, “Computer generated cylindrical hologram,” in Practical Holography XIX: Materials and ApplicationsTung H. Jeong and Hans I. Bjelkhagen, eds., Proc. SPIE5742, 267–274 (2005).
  6. A. Kashiwagi and Y. Sakamoto, “A fast calculation method of cylindrical computer-generated holograms which perform image-reconstruction of volume data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM OSA Technical Digest (CD) (Optical Society of America, 2007), paper DWB7, http://www.opticsinfobase.org/abstract.cfm?URI=DH-2007-DWB7 .
  7. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt.47, D63–D70 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-19-D63 . [CrossRef] [PubMed]
  8. Y. Sando, M. Itoh, and T. Yatagai, “Fast calculation method for cylindrical computer-generated holograms,” Opt.Express13, 1418–1423 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-5-1418 . [CrossRef] [PubMed]
  9. B. J. Jackin and T. Yatagai, “Fast calculation method for computer-generated cylindrical hologram based on wave propagation in spectral domain,” Opt.Express18, 25546–25555 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-25-25546 . [CrossRef] [PubMed]
  10. B. J. Jackin and T. Yatagai, “360° reconstruction of a 3D object using cylindrical computer generated holography,” Appl. Opt.50, H147–H152 (2011), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-34-H147 . [CrossRef] [PubMed]
  11. M. L. Tachiki, Y. Sando, M. Itoh, and T. Yatagai, “Fast calculation method for spherical computer-generated holograms,” Appl. Opt.45, 3527–3533 (2006), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-15-3527 . [CrossRef] [PubMed]
  12. R. J. Chien and B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys.136, 580–584 (1997). [CrossRef]
  13. J. R. Driscoll and D. M Healy, “Computing Fourier transfroms and convolutions on the sphere,” Adv. Appl. Math.15, 201–250 (1994). [CrossRef]
  14. N. N. Lebedev, Special Functions and their Applications (Prentice Hall, 1965).
  15. G. B. Arfken and H. J. Weber, Mathematical Method for Physicist (Academic Press, 2001).
  16. D. M. Healy, D. Rockmore, P. J. Kostelec, and S. Moore, “FFTs for the 2-sphere - improvements and variations,” J. Fourier. Anal. Appl.9, No.4, 341–385(1998). [CrossRef]
  17. P. N. Swarztrauber, “On computing the points and weights for Gauss-Legendre quadrature,” SIAM. J. Sci. Computing24. Issue. 3, 945–954(2002). [CrossRef]
  18. M. Wieczorek, SHTools, http://shtools.ipgp.fr/ .
  19. Z. G. Horvath, “Beyond the beam: A history of multidimensional lasers,” Opt. Photonics News23. No. 7/8, 36–41(2012). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited