OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 19462–19478

Microscopy image resolution improvement by deconvolution of complex fields

Yann Cotte, M. Fatih Toy, Nicolas Pavillon, and Christian Depeursinge  »View Author Affiliations

Optics Express, Vol. 18, Issue 19, pp. 19462-19478 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (2297 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Based on truncated inverse filtering, a theory for deconvolution of complex fields is studied. The validity of the theory is verified by comparing with experimental data from digital holographic microscopy (DHM) using a high-NA system (NA=0.95). Comparison with standard intensity deconvolution reveals that only complex deconvolution deals correctly with coherent cross-talk. With improved image resolution, complex deconvolution is demonstrated to exceed the Rayleigh limit. Gain in resolution arises by accessing the objects complex field - containing the information encoded in the phase - and deconvolving it with the reconstructed complex transfer function (CTF). Synthetic (based on Debye theory modeled with experimental parameters of MO) and experimental amplitude point spread functions (APSF) are used for the CTF reconstruction and compared. Thus, the optical system used for microscopy is characterized quantitatively by its APSF. The role of noise is discussed in the context of complex field deconvolution. As further results, we demonstrate that complex deconvolution does not require any additional optics in the DHM setup while extending the limit of resolution with coherent illumination by a factor of at least 1.64.

© 2010 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(100.1830) Image processing : Deconvolution
(100.5070) Image processing : Phase retrieval
(100.6640) Image processing : Superresolution
(110.0180) Imaging systems : Microscopy
(090.1995) Holography : Digital holography

ToC Category:
Image Processing

Original Manuscript: June 11, 2010
Revised Manuscript: July 26, 2010
Manuscript Accepted: August 25, 2010
Published: August 30, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Yann Cotte, M. Fatih Toy, Nicolas Pavillon, and Christian Depeursinge, "Microscopy image resolution improvement by deconvolution of complex fields," Opt. Express 18, 19462-19478 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. V. Aert, D. V. Dyck, 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]
  2. J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, "Three-dimensional imaging by deconvolution microscopy," Methods 19, 373-385 (1999). [CrossRef] [PubMed]
  3. C. Vonesch, "Fast and automated wavelet-regularized image restoration in fluorescence microscopy," Ph.D. thesis, EPFL, LIB Laboratoire d’imagerie biomédicale (2009).
  4. W. Wallace, L. H. Schaefer, and J. R. Swedlow, "A workingperson’s guide to deconvolution in light microscopy," Biotechniques 31, 1076 (2001). [PubMed]
  5. B. Colicchio, O. Haeberl, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the lls and map deconvolution algorithms by automatic determination of optimal regularization parameters and pre-filtering of original data," Opt. Commun. 244, 37-49 (2005). [CrossRef]
  6. F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, "Super-resolution orientation estimation and localization of fluorescent dipoles using 3-d steerable filters," Opt. Express 17, 6829-6848 (2009). [CrossRef] [PubMed]
  7. P. Sarder, and A. Nehorai, "Deconvolution methods for 3-d fluorescence microscopy images," IEEE Signal Process. Mag. 23, 32-45 (2006). [CrossRef]
  8. E. Cuche, P. Marquet, and C. 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. C. Depeursinge, P. Jourdain, B. Rappaz, P. Magistretti, T. Colomb, and P. Marquet, "Cell biology explored with digital holographic microscopy," Biomed. Opt. p. BMD58 (2008).
  10. C. J. Sheppard, "Fundamentals of superresolution," Micron 38, 165-169 (2007). [CrossRef]
  11. D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, "One-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 2353-2359 (1997). [CrossRef] [PubMed]
  12. A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. G. Martinez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999). [CrossRef]
  13. Z. Zalevsky, and D. Mendlovic, Optical superresolution, vol. 91 (Springer, 2004).
  14. E. N. Leith, D. Angell, and C. P. Kuei, "Superresolution by incoherent-to-coherent conversion," J. Opt. Soc. Am. A 4, 1050-1054 (1987). [CrossRef]
  15. R. Gerchberg, and W. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).
  16. V. Mico, Z. Zalevsky, C. Ferreira, and J. García, "Superresolution digital holographic microscopy for three-dimensional samples," Opt. Express 16, 19260-19270 (2008). [CrossRef]
  17. G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, "Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms," Appl. Opt. 46, 993-1000 (2007). [CrossRef] [PubMed]
  18. V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002). [CrossRef] [PubMed]
  19. M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberle, "High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples," Opt. Lett. 34, 79-81 (2009). [CrossRef]
  20. M. G. L. Gustafsson, "Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy," J. Microsc. 198, 82-87 (2000). [CrossRef] [PubMed]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  22. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1987), 6th ed.
  23. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).
  24. Y. Cotte, and C. Depeursinge, "Measurement of the complex amplitude point spread function by a diffracting circular aperture," in "Focus on Microscopy," (2009), Advanced linear and non-linear imaging, pp. TU-AF2-PAR-D.
  25. X. Heng, X. Q. Cui, D. W. Knapp, J. G. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. H. Yang, "Characterization of light collection through a subwavelength aperture from a point source," Opt. Express 14, 10410-10425 (2006). [CrossRef] [PubMed]
  26. A. Marian, F. Charri`ere, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, "On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography," J. Microsc. 225, 156-169 (2007). [CrossRef] [PubMed]
  27. N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, "Suppression of the zero-order term in off-axis digital holography through nonlinear filtering," Appl. Opt. 48, H186-H195 (2009). [CrossRef] [PubMed]
  28. C. J. R. Sheppard, and M. Gu, "Imaging by a high aperture optical-system," J. Mod. Opt. 40, 1631-1651 (1993). [CrossRef]
  29. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, "Fast focus field calculations," Opt. Express 14, 11277-11291 (2006). [CrossRef] [PubMed]
  30. D. E. Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning (Addison-Wesley, 1989).
  31. V. Torczon, "On the convergence of pattern search algorithms," SIAM J. Optim. 7, 125 (1997). [CrossRef]
  32. Y. Cotte, M. F. Toy, E. Shaffer, N. Pavillon, and C. Depeursinge, "Sub-Rayleigh resolution by phase imaging," Opt. Lett. 35, 2176-2178 (2010). [CrossRef] [PubMed]
  33. M. Totzeck, and H. J. Tiziani, "Phase-singularities in 2d diffraction fields and interference microscopy," Opt. Commun. 138, 365-382 (1997). [CrossRef]
  34. C. J. Sheppard, and K. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik (Stuttg.) 107, 79-87 (1997).
  35. H. Guo, S. Zhuang, J. Chen, and Z. Liang, "Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function," Opt. Lett. 31, 2978-2980 (2006). [CrossRef] [PubMed]

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