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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 5 — May. 1, 2006
  • pp: 1227–1235

Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields

Adrian Stern and Bahram Javidi  »View Author Affiliations

JOSA A, Vol. 23, Issue 5, pp. 1227-1235 (2006)

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We describe the recording conditions that, together with the appropriate numerical reconstruction process, permit high-lateral-resolution reconstruction of in-line digital holograms. By high resolution, we mean a resolution that is beyond the Nyquist frequency, which is achieved by common methods. The proposed method is based on a previously reported generalized sampling theory that presents the conditions to precisely reconstruct fields that in certain cases may be sampled with a sampling rate lower than the Nyquist rate. We examine the hologram-recording process in the Wigner space. On the basis of this analysis, we demonstrate a simple high-resolution numerical reconstruction method.

© 2006 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(100.6890) Image processing : Three-dimensional image processing
(110.6880) Imaging systems : Three-dimensional image acquisition

ToC Category:

Original Manuscript: April 21, 2005
Revised Manuscript: September 22, 2005
Manuscript Accepted: September 23, 2005

Adrian Stern and Bahram Javidi, "Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields," J. Opt. Soc. Am. A 23, 1227-1235 (2006)

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  1. U. Schnars and W. Juptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
  2. B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 610-612 (2000). [CrossRef]
  3. L. Xu, K. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000). [CrossRef]
  4. Y. Frauel, E. Tajahuerce, M. A. Castro, and B. Javidi, "Distortion-tolerant three-dimensional object recognition with digital holography," Appl. Opt. 40, 3887-3893 (2001). [CrossRef]
  5. B. Javidi, E. Tajahuerce, and O. Matoba, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt. 40, 3877-3886 (2001). [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  7. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997). [CrossRef] [PubMed]
  8. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).
  9. E. A. Szilkas and A. E. Siegman, "Mode calculations in unstable resonators with flowing saturable gain. II. Fast Fourier transform method," Appl. Opt. 14, 1874-1879 (1975). [CrossRef]
  10. A. Riazi, O. P. Gandhi, and D. A. Christensen, "Efficient FFT computation of plano-plano interferometer modes for a wide range of Fresnel numbers," Opt. Acta 27, 529-535 (1980). [CrossRef]
  11. W. W. Smith and J. M. Smith, Handbook of Real-Time Fast Fourier Transforms (IEEE, 1995). [CrossRef]
  12. M. Sypek, "Light propagation in the Fresnel region. New numerical approach," Opt. Commun. 116, 43-48 (1995). [CrossRef]
  13. D. Mas, J. Perez, C. Hernandez, C. Vazquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003). [CrossRef]
  14. A. Stern and B. Javidi, "Analysis of practical sampling and reconstruction from Fresnel fields," Opt. Eng. 43, 239-250 (2004). [CrossRef]
  15. A. Stern and B. Javidi, "Sampling in the light of Wigner distribution," J. Opt. Soc. Am. A 21, 360-366 (2004); A. Stern and B. Javidi, "Sampling in the light of Wigner distribution," J. Opt. Soc. Am. A errata 21, 2038 (2004). [CrossRef]
  16. A. Stern and B. Javidi, "General sampling theorem and application in digital holography," in Proc. SPIE 5557, 110-123 (2004). [CrossRef]
  17. E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932). [CrossRef]
  18. M. J. Bastiaans, "Wigner distribution function and its application to first-order optics," J. Opt. Soc. Am. 69, 1710-1716 (1980). [CrossRef]
  19. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, "Space-bandwidth product of optical signals and systems," J. Opt. Soc. Am. A 13, 470-473 (1996). [CrossRef]
  20. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Understanding superresolution in Wigner space," J. Opt. Soc. Am. A 17, 2422-2430 (2000). [CrossRef]
  21. A. W. Lohmann, "Image rotation, Wigner distribution, and fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993). [CrossRef]
  22. V. Arrizon and J. Ojeda-Castaneda, "Irradiance at Fresnel planes of a phase grating," J. Opt. Soc. Am. A 9, 1801-1806 (1992). [CrossRef]
  23. J. Ojeda-Castañeda and A. Castro, "Simultaneous Cartesian coordinate display of defocused optical transfer functions," Opt. Lett. 23, 1049-1051 (1998). [CrossRef]
  24. P. B. Catrysse and B. A. Wandell, "Optical efficiency of image sensor pixels," J. Opt. Soc. Am. A 19, 1610-1620 (2002). [CrossRef]
  25. A. Gori, "Fresnel transform and sampling theorem," Opt. Commun. 39, 293-297 (1981). [CrossRef]
  26. L. Onural, "Sampling of the diffraction field," Appl. Opt. 39, 5929-5935 (2000). [CrossRef]
  27. J. M. Whittaker, "The Fourier theory of cardinal functions," Proc. Edinb. Math. Soc. 1, 169-176 (1929). [CrossRef]
  28. M. Unser, "Sampling—50 years after Shannon," Proc. IEEE 88, 569-587 (2000). [CrossRef]
  29. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty, I," Bell Syst. Tech. J. 40, 43-64 (1961).
  30. S. Mann and S. Haykin, "The chirplet transform: physical considerations," IEEE Trans. Signal Process. 43, 2745-2761 (1995). [CrossRef]
  31. K. Grochenig, Foundation of Time-frequency Analysis (Birkhäuser, 2001).
  32. W. Lukosz, "Optical systems with resolving powers exceeding the classical limit," J. Opt. Soc. Am. 56, 1463-1472 (1966). [CrossRef]
  33. D. Gabor, Theory of communication, J. Inst. Electr. Eng., Part 3 93, 429-457 (1946).
  34. D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application to super resolution: examples," J. Opt. Soc. Am. A 14, 563-567 (1997). [CrossRef]

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