OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 2 — Jan. 10, 2002
  • pp: 312–319

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform

Sébastien Coëtmellec, Denis Lebrun, and Cafer Özkul  »View Author Affiliations


Applied Optics, Vol. 41, Issue 2, pp. 312-319 (2002)
http://dx.doi.org/10.1364/AO.41.000312


View Full Text Article

Enhanced HTML    Acrobat PDF (837 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.

© 2002 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2650) Image processing : Fringe analysis
(100.3190) Image processing : Inverse problems

History
Original Manuscript: April 13, 2001
Revised Manuscript: September 10, 2001
Published: January 10, 2002

Citation
Sébastien Coëtmellec, Denis Lebrun, and Cafer Özkul, "Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform," Appl. Opt. 41, 312-319 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-2-312


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Upatnieks, A. VanderLugt, E. Leith, “Correction of lens aberrations by means of holograms,” Appl. Opt. 5, 589–593 (1966). [CrossRef] [PubMed]
  2. D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948). [CrossRef]
  3. G. Haussmann, W. Lauterborn, “Determination of size and position of fast moving glass bubbles in liquids by digital 3-D image processing of hologram reconstructions,” Appl. Opt. 19, 3529–3535 (1980). [CrossRef] [PubMed]
  4. H. J. Caulfield, “Automated analysis of particle holograms,” Opt. Eng. 24, 462–463 (1985). [CrossRef]
  5. L. Onural, M. T. Özgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992). [CrossRef]
  6. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993). [CrossRef] [PubMed]
  7. C. Buraga-Lefrebvre, S. Coëtmellec, D. Lebrun, C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000). [CrossRef]
  8. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994). [CrossRef]
  9. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Its Appl. 25, 241–265 (1980). [CrossRef]
  10. P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994). [CrossRef] [PubMed]
  11. G. Unnikrishnan, J. Joseph, K. Singh, “Fractional Fourier domain encrypted holographic memory by use of an anamorphic optical system,” Appl. Opt. 40, 299–306 (2001). [CrossRef]
  12. I. S. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000). [CrossRef]
  13. M. F. Erden, H. M. Ozaktas, “Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains,” J. Opt. Soc. Am. A 15, 1647–1657 (1998). [CrossRef]
  14. M. A. Kutay, H. Ozaktas, “Optimal image restoration with the fractional Fourier transform,” J. Opt. Soc. Am. A 15, 825–833 (1998). [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
  16. C. Özkul, D. Lebrun, D. Allano, M. A. Abdelgani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991). [CrossRef]
  17. D. Mendlovic, M. Ozaktas, A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt. 33, 6188–6193 (1994). [CrossRef] [PubMed]
  18. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  19. A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms,” IMA J. Appl. Math. 39, 159–175 (1987). [CrossRef]
  20. D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Wigner-related phase spaces for signal processing and their optical implementation,” J. Opt. Soc. Am. A 17, 2339–2354 (2000). [CrossRef]
  21. W. Mecklenbräuker, F. Hlawatsch, The Wigner Distribution. Theory and Applications in Signal Processing (Elsevier, Amsterdam, 1997), pp. 59–83.
  22. L. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994). [CrossRef]
  23. A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transforms,” J. Opt. Soc. Am. A 11, 1798–1801 (1994). [CrossRef]
  24. J. W. Goodman, Introduction to Fourier Optics, 2th ed. (McGraw-Hill, New York, 1996).
  25. F. J. Marinho, L. M. Bernardo, “Numerical calculation of fractional Fourier transforms with a single fast-Fourier-transform algorithm,” J. Opt. Soc. Am. A 15, 2111–2116 (1998). [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