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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 7 — Mar. 1, 2011
  • pp: B58–B70

Quantization noise and its reduction in lensless Fourier digital holography

Nitesh Pandey and Bryan Hennelly  »View Author Affiliations

Applied Optics, Vol. 50, Issue 7, pp. B58-B70 (2011)

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Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.

© 2011 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(110.2970) Imaging systems : Image detection systems
(110.4280) Imaging systems : Noise in imaging systems
(090.1995) Holography : Digital holography

Original Manuscript: August 30, 2010
Manuscript Accepted: November 3, 2010
Published: January 10, 2011

Nitesh Pandey and Bryan Hennelly, "Quantization noise and its reduction in lensless Fourier digital holography," Appl. Opt. 50, B58-B70 (2011)

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  1. J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77 (1967). [CrossRef]
  2. M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with a computer,” in SPIE Milestone Series 144 (SPIE Press, 1998), pp. 645–646.
  3. L. Yaroslavskii and N. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).
  4. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994). [CrossRef] [PubMed]
  5. T. Colomb, J. Kühn, F. Charriere, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006). [CrossRef] [PubMed]
  6. P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]
  7. T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, “Remote metrology by comparative digital holography,” Appl. Opt. 45, 925–934 (2006). [CrossRef] [PubMed]
  8. T. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006). [CrossRef]
  9. N. Pandey and B. Hennelly, “Fixed-point numercial-reconstruction for digital holographic microscopy,” Opt. Lett. 35, 1076–1078 (2010). [CrossRef] [PubMed]
  10. T. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132(2002). [CrossRef] [PubMed]
  11. T. Naughton, J. McDonald, and B. Javidi, “Efficient compression of Fresnel fields for internet transmission of three-dimensional images,” Appl. Opt. 42, 4758–4764 (2003). [CrossRef] [PubMed]
  12. T. Naughton and B. Javidi, “Compression of encrypted three-dimensional objects using digital holography,” Opt. Eng. 43, 2233 (2004). [CrossRef]
  13. O. Matoba, T. Naughton, Y. Frauel, N. Bertaux, and B. Javidi, “Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram,” Appl. Opt. 41, 6187–6192(2002). [CrossRef] [PubMed]
  14. A. Shortt, T. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134(2006). [CrossRef] [PubMed]
  15. A. Shortt, T. Naughton, and B. Javidi, “Compression of optically encrypted digital holograms using artificial neural networks,” J. Display Technology 2, 401–410 (2006). [CrossRef]
  16. A. Shortt, T. J. Naughton, and B. Javidi, “Compression of digital holograms of three-dimensional objects using wavelets,” Opt. Express 14, 2625–2630 (2006). [CrossRef] [PubMed]
  17. G. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44, 1216–1225(2005). [CrossRef] [PubMed]
  18. E. Darakis and J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt. 46, 351–356 (2007). [CrossRef] [PubMed]
  19. E. Darakis, T. Naughton, and J. Soraghan, “Compression defects in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586 (2007). [CrossRef] [PubMed]
  20. A. Gotchev and L. Onural, “A survey on sampling and quantization in diffraction and holography,” in Workshop on Spectral Methods and Multirate Signal Processing, SMMSP (2006), pp. 179–190.
  21. D. Psaltis, E. Paek, and S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” in SPIE Milestone Series, 156 (SPIE Press, 1999), pp. 482–488.
  22. B. Javidi and J. Horner, “Single spatial light modulator joint transform correlator,” Appl. Opt. 28, 1027–1032(1989). [CrossRef] [PubMed]
  23. A. Bourquard, F. Aguet, and M. Unser, “Optical imaging using binary sensors,” Opt. Express 18, 4876–4888 (2010). [CrossRef] [PubMed]
  24. W. Dallas and A. Lohmann, “Phase quantization in holograms-depth effects,” Appl. Opt. 11, 192–194 (1972). [CrossRef] [PubMed]
  25. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748(1967). [CrossRef] [PubMed]
  26. F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 28, 3864–3870 (1989). [CrossRef] [PubMed]
  27. R. Powers and J. Goodman, “Error rates in computer-generated holographic memories,” Appl. Opt. 14, 1690–1701(1975). [CrossRef] [PubMed]
  28. P. Naidu, “Quantization noise in binary holograms,” Opt. Commun. 15, 361–365 (1975). [CrossRef]
  29. M. Seldowitz, J. Allebach, and D. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987). [CrossRef] [PubMed]
  30. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Communication Technology 12, 162–165 (1964). [CrossRef]
  31. J. Goodman, Introduction to Fourier Optics (Roberts & Co., 2005).
  32. D. Kelly, B. Hennelly, N. Pandey, T. Naughton, W. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009). [CrossRef]
  33. H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000(2008). [CrossRef]
  34. A. Oppenheim and R. Schafer, Discrete-Time Signal Processing (Prentice-Hall, 1999).
  35. A. Sripad and D. Snyder, “A necessary and sufficient condition for quantization errors to be uniform and white,” IEEE Trans. Acoust. Speech Signal Process. 25, 442–448 (1977). [CrossRef]
  36. J. Schoukens and J. Renneboog, “Modeling the noise influence on the Fourier coefficients after a discrete Fourier transform,” IEEE Trans. Instrum. Meas. 35, 278–286 (1986).
  37. R. Shiavi, Introduction to Applied Statistical Signal Analysis: Guide to Biomedical and Electrical Engineering Applications (Academic, 2007). [PubMed]
  38. J. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2007).
  39. O. A. Skydan, F. Lilley, M. J. Lalor, and D. R. Burton, “Quantization error of ccd cameras and their influence on phase calculation in fringe pattern analysis,” Appl. Opt. 42, 5302–5307 (2003). [CrossRef] [PubMed]
  40. H. Gudbjartsson and S. Patz, “The Rician distribution of noisy MRI data,” Magnetic Resonance Medicine 34, 910–914 (1995). [CrossRef]
  41. D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hill, 1960).
  42. J. Maycock, C. Elhinney, B. Hennelly, T. Naughton, J. McDonald, and B. Javidi, “Three-dimensional scene reconstruction of partially occluded objects using digital holograms,” Appl. Opt. 45, 2975–2985 (2006). [CrossRef] [PubMed]
  43. E. Buckley, “Holographic laser projection technology,” Information Display 24, 12 (2008).
  44. P. Hariharan and Z. Hegedus, “Reduction of speckle in coherent imaging by spatial frequency sampling,” J. Mod. Opt. 21, 345–356 (1974). [CrossRef]
  45. J. Dainty, “Laser speckle and related phenomena,” in Topics in Applied Physics (Springer-Verlag, 1975), Vol.  9, p. 298.
  46. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976). [CrossRef]
  47. J. Maycock, B. Hennelly, J. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. 24, 1617–1622 (2007). [CrossRef]
  48. J. Lim and H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 20, 472–480 (1981).
  49. T. Crimmins, “Geometric filter for speckle reduction,” Appl. Opt. 24, 1438–1443 (1985). [CrossRef] [PubMed]
  50. D. Monaghan, D. Kelly, N. Pandey, and B. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009). [CrossRef] [PubMed]
  51. F. Charriére, B. Rappaz, J. Kühn, T. Colomb, P. Marquet, and C. Depeursinge, “Influence of shot noise on phase measurement accuracy in digital holographic microscopy,” Opt. Express 15, 8818–8831 (2007). [CrossRef] [PubMed]
  52. M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909–911 (2007). [CrossRef] [PubMed]
  53. J. Lukas, J. Fridrich, and M. Goljan, “Digital camera identification from sensor pattern noise,” IEEE Trans. Info. Foren. Sec. 1, 205–214 (2006). [CrossRef]

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