OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 367–377

Complex-wave retrieval from a single off-axis hologram

Michael Liebling, Thierry Blu, and Michael Unser  »View Author Affiliations

JOSA A, Vol. 21, Issue 3, pp. 367-377 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (1681 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram’s samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.

© 2004 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(100.2000) Image processing : Digital image processing
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(180.3170) Microscopy : Interference microscopy

Original Manuscript: April 2, 2003
Revised Manuscript: November 11, 2003
Manuscript Accepted: November 14, 2003
Published: March 1, 2004

Michael Liebling, Thierry Blu, and Michael Unser, "Complex-wave retrieval from a single off-axis hologram," J. Opt. Soc. Am. A 21, 367-377 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948). [CrossRef]
  2. J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967). [CrossRef]
  3. M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).
  4. L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
  5. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994). [CrossRef] [PubMed]
  6. E. Cuche, F. Bevilacqua, Ch. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999). [CrossRef]
  7. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, Ch. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002). [CrossRef] [PubMed]
  8. E. Cuche, P. Marquet, Ch. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). [CrossRef]
  9. T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: A comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 224–233 (1997). [CrossRef]
  10. E. Cuche, P. Marquet, Ch. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000). [CrossRef]
  11. T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997). [CrossRef]
  12. C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng. 41, 2434–2437 (2002). [CrossRef]
  13. T. Kreis, “Computer-aided evaluation of holographic interferograms,” in Holographic Interferometry: Principles and Methods, P. K. Rastogi, ed. (Springer, Heidelberg, Germany, 1994), pp. 151–212.
  14. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986). [CrossRef]
  15. V. I. Vlad, D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, Vol. XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), pp. 261–317.
  16. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  17. W. W. Macy, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983). [CrossRef] [PubMed]
  18. K. A. Nugent, “Interferogram analysis using an accurate fully automatic algorithm,” Appl. Opt. 24, 3101–3105 (1985). [CrossRef] [PubMed]
  19. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986). [CrossRef] [PubMed]
  20. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987). [CrossRef] [PubMed]
  21. J. E. Greivenkamp, J. H. Bruning, “Phase-shifting interferometry,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  22. T. Kreis, Holographic Interferometry, Vol. 1 of Optical Metrology Series (Akademie Verlag, Berlin, 1996).
  23. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972). [CrossRef] [PubMed]
  24. L. Mertz, “Real-time fringe-pattern analysis,” Appl. Opt. 22, 1535–1539 (1983). [CrossRef] [PubMed]
  25. K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984). [CrossRef]
  26. P. L. Ransom, J. Kokal, “Interferogram analysis by a modified sinusoid fitting technique,” Appl. Opt. 25, 4199–4204 (1986). [CrossRef] [PubMed]
  27. M. Kujawińska, J. Wójciak, “Spatial phase-shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, Parts 1 and 2, F.-P. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).
  28. M. Kujawińska, “Spatial phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Bristol Institute of Physics, Bristol, UK, 1993), pp. 141–193.
  29. M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995). [CrossRef]
  30. P. H. Chan, P. J. Bryanston-Cross, S. C. Parker, “Fringe-pattern analysis using a spatial phase-stepping method with automatic phase unwrapping,” Meas. Sci. Technol. 6, 1250–1259 (1995). [CrossRef]
  31. K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996). [CrossRef]
  32. J. Schmit, K. Creath, “Window function influence on phase error in phase-shifting algorithms,” Appl. Opt. 35, 5642–5649 (1996). [CrossRef] [PubMed]
  33. T. Bothe, J. Burke, H. Helmers, “Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors,” Appl. Opt. 36, 5310–5316 (1997). [CrossRef] [PubMed]
  34. R. Windecker, H. J. Tiziani, “Semispatial, robust, and accurate phase evaluation algorithm,” Appl. Opt. 34, 7321–7326 (1995). [CrossRef] [PubMed]
  35. A. J. Moore, F. Mendoza-Santoyo, “Phase demodulation in the space domain without a fringe carrier,” Opt. Lasers Eng. 23, 319–330 (1995). [CrossRef]
  36. M. Servin, J. L. Marroquin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997). [CrossRef] [PubMed]
  37. J. L. Marroquin, M. Servin, R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997). [CrossRef]
  38. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998). [CrossRef]
  39. E. Yu, S. S. Cha, “Two-dimensional regression for interferometric phase extraction,” Appl. Opt. 37, 1370–1376 (1998). [CrossRef]
  40. K. G. Larkin, D. J. Bone, M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001). [CrossRef]
  41. S. Sotthivirat, J. A. Fessler, “Relaxed ordered subsets algorithm for image restoration of confocal microscopy,” in Proceedings of the 2002 IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI’02) (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 3, pp. 1051–1054.
  42. S. Sotthivirat, J. A. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A (to be published).
  43. M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003). [CrossRef]
  44. M. Unser, “Splines: a perfect fit for signal and image processing,” IEEE Signal Process. Mag. 16, 22–38 (1999). [CrossRef]
  45. M. Unser, A. Aldroubi, S. Schiff, “Fast implementation of the continuous wavelet transform with integer scales,” IEEE Trans. Signal Process. 42, 3519–3523 (1994). [CrossRef]
  46. G. Lai, T. Yatagai, “Generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 8, 822–827 (1991). [CrossRef]
  47. M. Pirga, M. Kujawińska, “Two directional, spatial-carrier, phase-shifting method for analysis of crossed closed fringe patterns,” Opt. Eng. 34, 2459–2466 (1995). [CrossRef]
  48. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A 12, 1997–2008 (1995). [CrossRef]
  49. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996). [CrossRef] [PubMed]
  50. K. Hibino, B. F. Oreb, D. I. Farrant, K. G. Larkin, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts,” J. Opt. Soc. Am. A 14, 918–930 (1997). [CrossRef]
  51. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000). [CrossRef]
  52. T. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771–778 (2002). [CrossRef]
  53. G. Paez, M. Strojnik, “Phase reconstruction from undersampled intensity patterns,” J. Opt. Soc. Am. A 17, 46–52 (2000). [CrossRef]
  54. Signal Processing Toolbox User’s Guide for Use with Matlab (The MathWorks, Inc., Natick, Mass., 2002).
  55. A. Marian, E. Cuche, Ch. Depeursinge, “Point spread function model for microscopic image deconvolution in digital holographic microscopy,” in Novel Optical Instrumentation for Biomedical Applications, A.-C. Boccara, ed., Proc. SPIE5143, 202–209 (2003). [CrossRef]
  56. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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