OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 13 — May. 1, 2010
  • pp: 2519–2528

Intensity based self-imaging

Habib Hamam  »View Author Affiliations


Applied Optics, Vol. 49, Issue 13, pp. 2519-2528 (2010)
http://dx.doi.org/10.1364/AO.49.002519


View Full Text Article

Enhanced HTML    Acrobat PDF (1181 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose an iterative method to optimize the phase profile of the initial field so that its intensity profile is observed periodically along the longitudinal (propagation) axis. The new method is inspired from the Gerchberg–Saxton technique, where the Fresnel transform is used, instead of the Fourier transform, for retrieving the phase profile of several light distributions (for example, 15 planes), instead of a Fourier pair of distributions. The additional challenge, with respect to the conventional Gerchberg–Saxton technique, is that the planes where constraints are applied number more than two. It turned out that when the number of periods increased, the spectrum of the obtained initial field converges toward including Montgomery’s rings (self-imaging condition).

© 2010 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: March 1, 2010
Revised Manuscript: March 25, 2010
Manuscript Accepted: March 26, 2010
Published: April 27, 2010

Citation
Habib Hamam, "Intensity based self-imaging," Appl. Opt. 49, 2519-2528 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-13-2519


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967). [CrossRef]
  2. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1989), Vol.  27, pp. 1–110. [CrossRef]
  3. O. Guyot and H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996). [CrossRef]
  4. A. P. Smirnov, “Fresnel images of periodic transparencies of finite dimensions,” Opt. Spectrosc. 44, 208–212 (1978).
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  6. M. Matczak and J. Mamczur, “Degenerate self-imaging Fourier filters,” Optoelectron. Rev. 9, 336–340 (2001).
  7. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).
  8. J. Fienup, “Phase retrieval algorithm: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  9. J. Miao, D. Sayre, and H. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
  10. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907(1986). [CrossRef]
  11. R. Bates and M. McDonnell, Image Restoration and Reconstruction (Oxford U. Press, 1986).
  12. S. Lindaas, M. Howells, C. Jacobsen, and A. Kalinovsky, “X-ray holographic microscopy by means of photoresist recording and atomic-force microscope readout,” J. Opt. Soc. Am. A 13, 1788–1800 (1996). [CrossRef]
  13. F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [CrossRef]
  14. T. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49–58 (2003). [CrossRef]
  15. J. Cowley, Diffraction Physics (North-Holland, 1975).
  16. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984). [CrossRef]
  17. T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999). [CrossRef]
  18. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990). [CrossRef] [PubMed]
  19. J. Leger, D. Chen, and Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19, 108–110 (1994). [CrossRef] [PubMed]
  20. R. Rolleston and N. George, “Image reconstruction from partial Fresnel zone information,” Appl. Opt. 25, 178–183 (1986). [CrossRef] [PubMed]
  21. N. Nakajima, “Phase retrieval from Fresnel zone intensity measurements by use of Gaussian filtering,” Appl. Opt. 37, 6219–6226 (1998). [CrossRef]
  22. T. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Report 179 (Cooperative Research Centre for Hardwood Fibre and Paper Science, 1999).
  23. T. Pitts and J. Greenleaf, “Fresnel transform phase retrieval from magnitude,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035–1045 (2003). [CrossRef] [PubMed]
  24. C. Henderson, G. Williams, A. Peele, H. Quiney, and K. Nugent, “Astigmatic phase retrieval: an experimental demonstration,” Opt. Express 17, 11905–11915 (2009). [CrossRef] [PubMed]
  25. T. Gureyeva, Y. Nesteretsa, D. Paganina, A. Poganya, and S. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006). [CrossRef]
  26. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953). [CrossRef]
  27. S. Kirkpatrick, C. Gelatt, and M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983). [CrossRef] [PubMed]
  28. M. Razzak, S. Guizani, H. Hamam, and Y. Bouslimani, “Optical post-egalization based on self-imaging,” J. Mod. Opt. 53, 1675–1684 (2006). [CrossRef]
  29. J. Goodman and A. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970). [CrossRef]
  30. H. Hamam, “A new measure for optical performance,” Optom. Vision Sci. 80, 175–184 (2003). [CrossRef]
  31. J. Honner and P. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984). [CrossRef]
  32. H. Hamam, “Intensity based self-imaging,” Java applet (January 2010), www.umoncton.ca/genie/electrique/cours/Hamam/Optics/Fresnel/IntensitySelfImaging/IntensitySelfImaging.htm.

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