OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 1 — Jan. 1, 2013
  • pp: A81–A91

Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise

M. Lesaffre, N. Verrier, and M. Gross  »View Author Affiliations

Applied Optics, Vol. 52, Issue 1, pp. A81-A91 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1522 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have performed off-axis heterodyne holography with very weak illumination by recording holograms of the object with and without object illumination in the same acquisition run. We have experimentally studied how the reconstructed image signal (with illumination) and noise background (without) scale with the holographic acquisition and reconstruction parameters that are the number of frames and the number of pixels of the reconstruction spatial filter. The first parameter is related to the frequency bandwidth of detection in time, the second one to the bandwidth in space. The signal to background ratio varies roughly like the inverse of the bandwidth in time and space. We have also compared the noise background with the theoretical shot-noise background calculated by Monte Carlo simulation. The experimental and Monte Carlo noise background agree very well with each other.

© 2013 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(120.2880) Instrumentation, measurement, and metrology : Holographic interferometry
(090.1995) Holography : Digital holography

Original Manuscript: August 10, 2012
Revised Manuscript: October 2, 2012
Manuscript Accepted: October 3, 2012
Published: October 29, 2012

M. Lesaffre, N. Verrier, and M. Gross, "Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise," Appl. Opt. 52, A81-A91 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London A 197, 454–487 (1949). [CrossRef]
  2. A. Macovski, “Considerations of television holography,” J. Mod. Opt. 18, 31–39 (1971). [CrossRef]
  3. J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967). [CrossRef]
  4. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994). [CrossRef]
  5. E. Leith, J. Upatnieks, and K. Haines, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. A 55, 981–986 (1965). [CrossRef]
  6. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994). [CrossRef]
  7. T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998). [CrossRef]
  8. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef]
  9. A.-F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000). [CrossRef]
  10. U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002). [CrossRef]
  11. Y. Pu and H. Meng, “Intrinsic speckle noise in off-axis particle holography,” J. Opt. Soc. Am. A 21, 1221–1230 (2004). [CrossRef]
  12. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002). [CrossRef]
  13. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999). [CrossRef]
  14. J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179–2181 (2002). [CrossRef]
  15. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. French, D. Nolte, and M. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26, 334–336 (2001). [CrossRef]
  16. P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44, 1806–1812 (2005). [CrossRef]
  17. P. Marquet, B. Rappaz, P. J. 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]
  18. M. Atlan, M. Gross, P. Desbiolles, É. Absil, G. Tessier, and M. Coppey-Moisan, “Heterodyne holographic microscopy of gold particles,” Opt. Lett. 33, 500–502 (2008). [CrossRef]
  19. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998). [CrossRef]
  20. T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481–483 (2007). [CrossRef]
  21. I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27, 1108–1110 (2002). [CrossRef]
  22. F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26, 1550–1552 (2001). [CrossRef]
  23. S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt. 45, 953–959 (2006). [CrossRef]
  24. I. Yamaguchi, T. Ida, M. Yokota, and K. Yamashita, “Surface shape measurement by phase-shifting digital holography with a wavelength shift,” Appl. Opt. 45, 7610–7616 (2006). [CrossRef]
  25. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998). [CrossRef]
  26. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001). [CrossRef]
  27. F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photo-detector arrays,” Opt. Lett. 25, 716–718 (2000). [CrossRef]
  28. M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909–911 (2007). [CrossRef]
  29. M. Gross, P. Goy, B. Forget, M. Atlan, F. Ramaz, A. Boccara, and A. Dunn, “Heterodyne detection of multiply scattered monochromatic light with a multipixel detector,” Opt. Lett. 30, 1357–1359 (2005). [CrossRef]
  30. N. Warnasooriya, F. Joud, P. Bun, G. Tessier, M. Coppey-Moisan, P. Desbiolles, M. Atlan, M. Abboud, and M. Gross, “Imaging gold nanoparticles in living cell environments using heterodyne digital holographic microscopy,” Opt. Express 18, 3264–3273 (2010). [CrossRef]
  31. F. Verpillat, F. Joud, P. Desbiolles, and M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Opt. Express 19, 26044–26055 (2011). [CrossRef]
  32. M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. 28, 2482–2484 (2003). [CrossRef]
  33. E. Absil, G. Tessier, M. Gross, M. Atlan, N. Warnasooriya, S. Suck, M. Coppey-Moisan, and D. Fournier, “Photothermal heterodyne holography of gold nanoparticles,” Opt. Express 18, 780–786 (2010). [CrossRef]
  34. P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.
  35. F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by sideband digital holography,” Opt. Express 17, 2774–2779 (2009). [CrossRef]
  36. W. Davenport and W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958).
  37. F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet, and C. Depeursinge, “Shot-noise influence on the reconstructed phase image signal-to-noise ratio in digital holographic microscopy,” Appl. Opt. 45, 7667–7673 (2006). [CrossRef]
  38. F. Charrière, 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]
  39. F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Display Technol. 6, 455–464(2010). [CrossRef]
  40. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000). [CrossRef]
  41. T. Kreis and W. Jueptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997). [CrossRef]
  42. P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008). [CrossRef]
  43. N. Verrier and M. Atlan, “Off-axis digital hologram reconstruction: some practical considerations,” Appl. Opt. 50, H136–H146 (2011). [CrossRef]
  44. L. Yu and M. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005). [CrossRef]
  45. H. A. Bachor, A Guide to Experiment in Quantum Optics(Wiley, 1998).
  46. M. Newberry, “Measuring the gain of a CCD camera,” Axiom Tech. Note 1, 1–8 (1998).

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