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Optics Express

Optics Express

| THE INTERNATIONAL ELECTRONIC JOURNAL OF OPTICS

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 22 — Oct. 27, 2008
  • pp: 17215–17226

Reconstruction of sectional images in holography using inverse imaging

Xin Zhang, Edmund Y. Lam, and Ting-Chung Poon

Optics Express, Vol. 16, Issue 22, pp. 17215-17226        doi:10.1364/OE.16.017215

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  • OCIS Codes:
  • (090.1760) Holography : Computer holography
  • (100.3020) Image processing : Image reconstruction-restoration
  • (100.3190) Image processing : Inverse problems
  • (180.6900) Microscopy : Three-dimensional microscopy
  • (110.1758) Imaging systems : Computational imaging
ToC Category:
Holography

Citation
Xin Zhang, Edmund Y. Lam, and Ting-Chung Poon, "Reconstruction of sectional images in holography using inverse imaging," Opt. Express 16, 17215-17226 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17215

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Abstract

This paper discusses the reconstruction of sectional images from a hologram generated by optical scanning holography. We present a mathematical model for the holographic image capture, which facilitates the use of inverse imaging techniques to recover individual sections. This framework is much more flexible than existing work, in the sense that it can handle objects with multiple sections, and possibly corrupted with white Gaussian noise. Simulation results show that the algorithm is capable of recovering a prescribed section while suppressing the other ones as defocus noise. The proposed algorithm is applicable to on-axis holograms acquired by conventional holography as well as phase-shifting holography.

© 2008 Optical Society of America

» View Full Text: Acrobat PDF (492 KB)

History
Original Manuscript: June 19, 2008
Manuscript Accepted: October 6, 2008
Revised Manuscript: September 3, 2008
Published: October 13, 2008

References

  1. B. D. Duncan and T.-C. Poon, "Gaussian Beam Analysis of Optical Scanning Holography," J. Opt. Soc. Am. A 9, 229-236 (1992).
  2. B. W. Schilling and G. C. Templeton, "Three-dimensional Remote Sensing by Optical Scanning Holography," Appl. Opt. 40, 5474-5481 (2001). [CrossRef]
  3. T. Kim, T.-C. Poon, and G. Indebetouw, "Depth Detection and Image Recovery in Remote Sensing by Optical Scanning Holography," Opt. Eng. 41, 1331-1338 (2002). [CrossRef]
  4. P. P. Banerjee and R. M. Misra, "Dependence of Photorefractive Beam Fanning on Beam Parameters," Opt. Commun. 100, 166-172 (1993). [CrossRef]
  5. T.-C. Poon, "Recent Progress in Optical Scanning Holography," J. Holography Speckle 1, 6-25 (2004). [CrossRef]
  6. G. Indebetouw and W. Zhong, "Scanning Holographic Microscopy of Three-dimensional Fluorescent Specimens," J. Opt. Soc. Am. A 23, 1699-1707 (2006). [CrossRef]
  7. T.-C. Poon, "Scanning Holography and Two-dimensional Image Processing by Acousto-optic Two-pupil Synthesis," J. Opt. Soc. Am. A 2, 521-527 (1985).
  8. C. J. Kuo, "Electronic Holography," Opt. Eng. 35, 1528 (1996). [CrossRef]
  9. K. M. Johnson, M. Armstrong, L. Hesselink, and J. W. Goodman, "Multiple Multiple-exposure Hologram," Applied Optics 24, 4467-4472 (1985).
  10. G. Indebetouw, "Properties of a Scanning Holographic Microscopy: Improved Resolution, Extended Depth-offocus, and/or Optical Sectioning," J. Mod. Opt. 49, 1479-1500 (2002). [CrossRef]
  11. T. Kim, "Optical Sectioning by Optical Scanning Holography and a Wiener Filter," Appl. Opt. 45, 872-879 (2006). [CrossRef]
  12. H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, "Optical Sectioning for Optical Scanning Holography Using Phasespace Filtering with Wigner Distribution Functions," Appl. Opt. 47, 164-175 (2008). [CrossRef]
  13. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, Chichester, 2001).
  14. T.-C. Poon, Optical Scanning Holography with MATLAB, 1st ed. (Springer-Verlag, New York, 2007).
  15. J. Swoger, M. Martínez-Corral, J. Huisken, and E. Stelzer, "Optical Scanning Holography as a Technique for High-resolution Three-dimensional Biological Microscopy," J. Opt. Soc. Am. A 19, 1910-1918 (2002). [CrossRef]
  16. G. Indebetouw, W. Zhong, and D. Chamberlin-Long, "Point-spread Function Synthesis in Scanning Holographic Microscopy," J. Opt. Soc. Am. A 23, 1708-1717 (2006). [CrossRef]
  17. M. R. Banham and A. K. Katsaggelos, "Digital Image Restoration," IEEE Signal Processing Magazine 14, 24-41 (1997). [CrossRef]
  18. J.M. Blackledge, Digital Image Processing: Mathematical and Computational Methods, 1st ed. (Horwood,West Sussex, 2005).
  19. A. Tikhonov and V. Arsenin, Solutions of Ill-posed Problems, 1st ed. (V.H. Winston and Sons, Washington, 1977).
  20. F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction, 1st ed. (SIAM, Philadelphia, 2001).
  21. L. Vese, "A Study in the BV Space of a Denoising-deblurring Variational Problem," Appl. Math. Optimization 44, 131-161 (2001). [CrossRef]
  22. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and Calculus of Variations, 2nd ed. (Springer-Verlag, New York, 2006).
  23. C. R. Vogel, Computational Methods for Inverse Problems, 1st ed. (SIAM, Philadelphia, 2002).

Author Affiliations

Xin Zhang, Edmund Y. Lam

The University of Hong Kong

Ting-Chung Poon

Virginia Polytechnic Institute and State University

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