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

  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1537–1546

Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography

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


JOSA A, Vol. 19, Issue 8, pp. 1537-1546 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001537


View Full Text Article

Enhanced HTML    Acrobat PDF (560 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate that the fractional-order Fourier transformation is a suitable method to analyze the diffraction patterns of particle field holograms. This method permits reconstruction of in-line digital holograms beyond the Fraunhofer condition ( d 2 / λ z 10 ) . We show that the diameter of spherical particles is measured with good accuracy. Simulation and experimental results are presented.

© 2002 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(090.0090) Holography : Holography
(100.0100) Image processing : Image processing

History
Original Manuscript: January 3, 2002
Revised Manuscript: March 7, 2002
Manuscript Accepted: March 15, 2002
Published: August 1, 2002

Citation
Sébastien Coëtmellec, Denis Lebrun, and Cafer Özkul, "Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography," J. Opt. Soc. Am. A 19, 1537-1546 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-8-1537


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Onural, “Diffraction from a wavelet point a view,” Opt. Lett. 18, 846–848 (1993). [CrossRef]
  2. S. Belaı̈d, D. Lebrun, C. Özkul, “Application of two-dimensional wavelet transform to hologram analysis: visualization of glass fibers in turbulent flame,” Opt. Eng. 36, 1947–1951 (1997). [CrossRef]
  3. D. Lebrun, S. Belaı̈d, C. Özkul, “Hologram reconstruction by use of optical wavelet transform,” Appl. Opt. 38, 3730–3734 (1999). [CrossRef]
  4. C. Buraga, 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]
  5. L. Onural, M. T. Özgen, “Extraction of the three-dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992). [CrossRef]
  6. S. Coëtmellec, D. Lebrun, C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform,” Appl. Opt. 41, 312–319 (2002). [CrossRef] [PubMed]
  7. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980). [CrossRef]
  8. A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms,” IMA J. Appl. Math. 39, 159–175 (1987). [CrossRef]
  9. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation. I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993). [CrossRef]
  10. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993). [CrossRef]
  11. P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994). [CrossRef] [PubMed]
  12. P. Pellat-Finet, G. Bonnet, “Fractional order Fourier transform and Fourier optics,” Opt. Commun. 111, 141–154 (1994). [CrossRef]
  13. P. Pellat-Finet, “Transfert du champ électromagnétique par diffraction et transformation de Fourier fractionnaire,” C. R. Acad. Paris, t.320, Série IIb, 91–97 (1995).
  14. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  16. H. M. Nuzzensveig, “High frequency scattering by an inpenetrable sphere,” Ann. Phys. (Leipzig) 33 (1965).
  17. G. A. Tayler, B. J. Thompson, “Fraunhofer holography applied to particle size analysis: a reassessment,” Opt. Acta 23, 261–304 (1976).
  18. A. Sahin, H. M. Ozaktas, D. Mendlovic, “Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions,” Opt. Commun. 120, 134–138 (1995). [CrossRef]
  19. A. Sahin, H. M. Ozaktas, D. Mendlovic, “Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters,” Appl. Opt. 37, 2130–2141 (1998). [CrossRef]
  20. 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]
  21. A. W. Lohmann, Bernard H. Soffer, “Relationships between the Radon–Wigner and the fractional Fourier transform,” J. Opt. Soc. Am. A 11, 1798–1801 (1994). [CrossRef]
  22. T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997). [CrossRef]
  23. D. Mendlovic, Z. Zalevsky, R. Dorsch, Y. Bitran, A. Lohmann, H. Ozaktas, “New signal representation based on the fractional Fourier transform: definitions,” J. Opt. Soc. Am. A 12, 2424–2431 (1995). [CrossRef]
  24. W. Mecklenbräuker, F. Hlawatsch, The Wigner Distribution. Theory and Applications in Signal Processing (Elsevier, Amsterdam, 1997), pp. 59–83.
  25. R. Bexon, G. D. Bishop, J. Gibbs, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976). [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