OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 7 — Jul. 1, 2011
  • pp: 1379–1386

Digital computation of the complex linear canonical transform

Changgeng Liu, Dayong Wang, John J. Healy, Bryan M. Hennelly, John T. Sheridan, and Myung K. Kim  »View Author Affiliations


JOSA A, Vol. 28, Issue 7, pp. 1379-1386 (2011)
http://dx.doi.org/10.1364/JOSAA.28.001379


View Full Text Article

Enhanced HTML    Acrobat PDF (670 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An efficient algorithm for the accurate computation of the linear canonical transform with complex transform parameters and with complex output variable is presented. Sampling issues are discussed and the requirements for different cases given. Simulations are provided to validate the results.

© 2011 Optical Society of America

OCIS Codes
(070.4560) Fourier optics and signal processing : Data processing by optical means
(080.2730) Geometric optics : Matrix methods in paraxial optics
(100.2000) Image processing : Digital image processing
(200.2610) Optics in computing : Free-space digital optics
(200.3050) Optics in computing : Information processing
(200.4560) Optics in computing : Optical data processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: January 4, 2011
Revised Manuscript: April 16, 2011
Manuscript Accepted: May 9, 2011
Published: June 10, 2011

Citation
Changgeng Liu, Dayong Wang, John J. Healy, Bryan M. Hennelly, John T. Sheridan, and Myung K. Kim, "Digital computation of the complex linear canonical transform," J. Opt. Soc. Am. A 28, 1379-1386 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-7-1379


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, 1979).
  2. S. Abe and J. T. Sheridan, “Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation,” Opt. Lett. 19, 1801–1803 (1994). [CrossRef] [PubMed]
  3. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970). [CrossRef]
  4. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979). [CrossRef]
  5. H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32–38 (1980). [CrossRef]
  6. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  7. H. T. Yura, S. G. Hanson, and T. P. Grum, “Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems,” J. Opt. Soc. Am. A 10, 316–323 (1993). [CrossRef]
  8. H. T. Yura, B. Rose, and S. G. Hanson, “Dynamic laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998). [CrossRef]
  9. P. A. Bélanger, A. Hardy, and A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980). [CrossRef] [PubMed]
  10. K. K. Sharma, “Fractional Laplace transform,” Signal, Image and Video Processing 4, 377–379 (2009). [CrossRef]
  11. B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Science in China Ser. F 49, 592–603 (2006). [CrossRef]
  12. B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983–990 (2007). [CrossRef]
  13. J.-J. Ding, “Research of fractional Fourier transform and linear canonical transform,” Ph.D. dissertation (National Taiwan University, 2001).
  14. J. Zhao, R. Tao, and Y. Wang, “Sampling rate conversion for linear canonical transform,” Signal Process. 88, 2825–2832 (2008). [CrossRef]
  15. F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981). [CrossRef]
  16. J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641–648(2009). [CrossRef]
  17. J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599–2601 (2008). [CrossRef] [PubMed]
  18. F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727–730 (2009). [CrossRef]
  19. A. Stern, “Sampling of linear canonical transformed signals,” Signal Process. 86, 1421–1425 (2006). [CrossRef]
  20. J. J. Healy and J. T. Sheridan, “Fast linear canonical transforms,” J. Opt. Soc. Am. A 27, 21–30 (2010). [CrossRef]
  21. B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928–937(2005). [CrossRef]
  22. A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383–2394 (2008). [CrossRef]
  23. H. M. Ozaktas, A. Koç, I. Sari, and M. A. Kutay, “Efficient computation of quadratic-phase integrals in optics,” Opt Lett. 31, 35–37 (2006). [CrossRef] [PubMed]
  24. J. J. Healy and J. T. Sheridan, “Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms,” Opt. Lett. 35, 947–949 (2010). [CrossRef] [PubMed]
  25. A. Koç, H. M. Ozaktas, and L. Hesselink, “Fast and accurate algorithm for the computation of complex linear canonical transforms,” J. Opt. Soc. Am. A 27, 1896–1908 (2010). [CrossRef]
  26. J. J. Healy and J. T. Sheridan, “Space–bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms,” J. Opt. Soc. Am. A 28, 786–790 (2011). [CrossRef]
  27. F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt. 45, 1102–1110 (2006). [CrossRef] [PubMed]
  28. F. Jia, “Study on the principle and applications of digital holography,” Master’s dissertation (Northwest University, 2008).
  29. C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 105802 (2009). [CrossRef]
  30. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996). [CrossRef]
  31. J. W. Brown and R. V. Churchill, Complex Variables and Applications (McGraw- Hill, 2004).

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