OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: 4147–4157

Digital in-line holography in thick optical systems: application to visualization in pipes

Nicolas Verrier, Sébastien Coëtmellec, Marc Brunel, and Denis Lebrun  »View Author Affiliations


Applied Optics, Vol. 47, Issue 22, pp. 4147-4157 (2008)
http://dx.doi.org/10.1364/AO.47.004147


View Full Text Article

Enhanced HTML    Acrobat PDF (7705 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We apply digital in-line holography to image opaque objects through a thick plano–concave pipe. Opaque fibers and opaque particles are considered. Analytical expression of the intensity distribution in the CCD sensor plane is derived using a generalized Fresnel transform. The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models. Holograms obtained with a 12 mm thick plano–concave pipe are then reconstructed using a fractional Fourier transform. This method allows us to get rid of astigmatism. Numerical and experimental results are presented.

© 2008 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

ToC Category:
Holography

History
Original Manuscript: March 13, 2008
Revised Manuscript: July 1, 2008
Manuscript Accepted: July 1, 2008
Published: July 29, 2008

Citation
Nicolas Verrier, Sébastien Coëtmellec, Marc Brunel, and Denis Lebrun, "Digital in-line holography in thick optical systems: application to visualization in pipes," Appl. Opt. 47, 4147-4157 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-22-4147


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42, 827-833 (2003). [CrossRef]
  2. M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004). [CrossRef]
  3. E. Malkiel, J. Sheng, J. Katz, and J. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657-3666 (2003). [CrossRef]
  4. J. Garcia-Sucerquia, W. Xu, S. Jericho, P. Klages, M. Jericho, and H. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006). [CrossRef]
  5. C. S. Vikram, “Particle field holography,” in Cambridge Studies in Modern Optics (Cambridge U. Press, 1992).
  6. S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974-976(2001). [CrossRef]
  7. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294-302 (2001).
  8. S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331-340 (2002). [CrossRef]
  9. J. S. Crane, P. Dunn, B. J. Thompson, J. Z. Knapp, and J. Zeiss, “Far-field holography of ampule contaminants,” Appl. Opt. 21, 2548-2553 (1982).
  10. F. Nicolas, S. Coëtmellec, M. Brunel, D. Allano, D. Lebrun, and A. J. Janssen, “Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam,” J. Opt. Soc. Am. A 22, 2569-2577(2005). [CrossRef]
  11. L. Onural and P. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124-1132 (1987).
  12. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846-848 (1993).
  13. F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun. 268, 27-33 (2006). [CrossRef]
  14. C. Palma and V. Bagini, “Extension of the Fresnel transform to ABCD systems,” J. Opt. Soc. Am. A 14, 1774-1779 (1997). [CrossRef]
  15. A. J. Lambert and D. Fraser, “Linear systems approach to simulation of optical diffraction,” Appl. Opt. 37, 7933-7939(1998). [CrossRef]
  16. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931-1948 (1987).
  17. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).
  18. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005).
  19. A. E. Siegman, Lasers (University Science Books, 1986).
  20. J. J. Wen and M. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” Proc. IEEE Ultrason. Symp. 1137-1140 (1987).
  21. J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988). [CrossRef]
  22. C. Zheng, D. Zhao, and X. Du, “Analytical expression of elliptical Gaussian beams through nonsymmetric systems with an elliptical aperture,” Optik (Jena) 117, 296-298 (2006). [CrossRef]
  23. X. Du and D. Zhao, “Propagation of decentered elliptical Gaussian beams in apertured and nonsymmetrical optical systems,” J. Opt. Soc. Am. A 23, 625-631 (2006). [CrossRef]
  24. X. Du and D. Zhao, “Propagation of elliptical Gaussian beams in apertured and misaligned optical systems,” J. Opt. Soc. Am. A 23, 1946-1950 (2006). [CrossRef]
  25. X. Du and D. Zhao, “Propagation of elliptical Gaussian beams modulated by an elliptical annular aperture,” J. Opt. Soc. Am. A 24, 444-450 (2007).
  26. F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to microholography,” Appl. Opt. 23, 4140-4148 (1984).
  27. A. C. McBride and F. H. Kerr, “On Namias's fractional Fourier transforms,” IMA J. Appl. Math. 39, 159-175(1987). [CrossRef]
  28. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241-265 (1980). [CrossRef]
  29. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181-2186 (1993).
  30. D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245-258 (2003). [CrossRef]
  31. S.-C. Pei, M.-H. Yeh, and C.-C. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Process. 47, 1335-1348 (1999). [CrossRef]
  32. N. Verrier, S. Coëtmellec, M. Brunel, D. Lebrun, and A. J. E. M. Janssen, “Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction,” J. Opt. Soc. Am. A 25, 1459-1466 (2008). [CrossRef]
  33. D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454-487 (1949).

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