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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 8 — Aug. 1, 2010
  • pp: 1856–1862

On the single point resolution of on-axis digital holography

Corinne Fournier, Loïc Denis, and Thierry Fournel  »View Author Affiliations


JOSA A, Vol. 27, Issue 8, pp. 1856-1862 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001856


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Abstract

On-axis digital holography (DH) is becoming widely used for its time-resolved three-dimensional (3D) imaging capabilities. A 3D volume can be reconstructed from a single hologram. DH is applied as a metrological tool in experimental mechanics, biology, and fluid dynamics, and therefore the estimation and the improvement of the resolution are current challenges. However, the resolution depends on experimental parameters such as the recording distance, the sensor definition, the pixel size, and also on the location of the object in the field of view. This paper derives resolution bounds in DH by using estimation theory. The single point resolution expresses the standard deviations on the estimation of the spatial coordinates of a point source from its hologram. Cramér–Rao lower bounds give a lower limit for the resolution. The closed-form expressions of the Cramér–Rao lower bounds are obtained for a point source located on and out of the optical axis. The influences of the 3D location of the source, the numerical aperture, and the signal-to-noise ratio are studied.

© 2010 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: March 15, 2010
Manuscript Accepted: May 14, 2010
Published: July 28, 2010

Virtual Issues
August 20, 2010 Spotlight on Optics

Citation
Corinne Fournier, Loïc Denis, and Thierry Fournel, "On the single point resolution of on-axis digital holography," J. Opt. Soc. Am. A 27, 1856-1862 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-8-1856


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References

  1. T. M. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).
  2. M. Jacquot, P. Sandoz, and G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001). [CrossRef]
  3. A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23, 1227–1235 (2006). [CrossRef]
  4. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006). [CrossRef] [PubMed]
  5. D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. (Bellingham) 48, 095801 (2009). [CrossRef]
  6. A. J. Den Dekker and A. Van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997). [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  8. A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. (Bellingham) 43, 239–250 (2004). [CrossRef]
  9. A. Stern and B. Javidi, “Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy,” J. Opt. Soc. Am. A 25, 736–741 (2008). [CrossRef]
  10. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 2005).
  11. P. Réfrégier, Noise Theory and Application to Physics: From Fluctuations to Information (Springer Verlag, 2004).
  12. C. W. Helstrom, “Detection and resolution of incoherent objects by a background-limited optical system,” J. Opt. Soc. Am. 59, 164–175 (1969). [CrossRef]
  13. S. Ram, E. Sally Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Signal Process. 17, 27–57 (2006). [CrossRef]
  14. S. Van Aert, D. Van Dirk, and A. J. den Dekker, “Resolution of coherent and incoherent imaging systems reconsidered—Classical criteria and a statistical alternative,” Opt. Express 14, 3830–3839 (2006). [CrossRef] [PubMed]
  15. M. Shahram and P. Milanfar, “Statistical and information-theoretic analysis of resolution in imaging,” IEEE Trans. Inf. Theory 52, 3411–3437 (2006). [CrossRef]
  16. P. Réfrégier, J. Fade, and M. Roche, “Estimation precision of the degree of polarization from a single speckle intensity image,” Opt. Lett. 32, 739–741 (2007). [CrossRef] [PubMed]
  17. A. Sentenac, C. A. Guérin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, “Influence of multiple scattering on the resolution of an imaging system: a Cramér–Rao analysis,” Opt. Express 15, 1340–1347 (2007). [CrossRef] [PubMed]
  18. C. R. Rao, “Information and the accuracy attainable in the estimation of statistical parameters,” Bull. Calcutta Math. Soc. 37, 81–89 (1945).
  19. H. Cramér, Mathematical Methods of Statistics (Princeton U. Press, 1946).
  20. F. Soulez, L. Denis, C. Fournier, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007). [CrossRef]
  21. S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef] [PubMed]
  22. F. Soulez, L. Denis, E. Thiebaut, C. Fournier, and C. Goepfert, “Inverse problem approach for particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (2007). [CrossRef]
  23. L. Denis, D. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: Error bounds and exact inversion,” Inverse Probl. 25, 115017 (2009). [CrossRef]
  24. S. Sotthivirat and J. A. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A 21, 737–750 (2004). [CrossRef]
  25. L. Denis, D. Lorenz, E. Thiebaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009). [CrossRef] [PubMed]
  26. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009). [CrossRef] [PubMed]

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