OSA's Digital Library

Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 8 — Aug. 1, 2011
  • pp: 2216–2230

Realistic 3D coherent transfer function inverse filtering of complex fields

Yann Cotte, Fatih M. Toy, Cristian Arfire, Shan Shan Kou, Daniel Boss, Isabelle Bergoënd, and Christian Depeursinge  »View Author Affiliations

Biomedical Optics Express, Vol. 2, Issue 8, pp. 2216-2230 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (2629 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a novel technique for three-dimensional (3D) image processing of complex fields. It consists in inverting the coherent image formation by filtering the complex spectrum with a realistic 3D coherent transfer function (CTF) of a high-NA digital holographic microscope. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of a scattering object field. Experimental reconstructions in phase and amplitude are presented under non-design imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample or illumination rotation.

© 2011 OSA

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.5070) Image processing : Phase retrieval
(100.6890) Image processing : Three-dimensional image processing
(110.0180) Imaging systems : Microscopy
(180.6900) Microscopy : Three-dimensional microscopy
(090.1995) Holography : Digital holography

ToC Category:
Image Reconstruction and Inverse Problems

Original Manuscript: April 4, 2011
Revised Manuscript: June 29, 2011
Manuscript Accepted: June 30, 2011
Published: July 8, 2011

Yann Cotte, Fatih M. Toy, Cristian Arfire, Shan Shan Kou, Daniel Boss, Isabelle Bergoënd, and Christian Depeursinge, "Realistic 3D coherent transfer function inverse filtering of complex fields," Biomed. Opt. Express 2, 2216-2230 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009). [CrossRef] [PubMed]
  2. C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical-system,” J. Mod. Opt. 40, 1631–1651 (1993). [CrossRef]
  3. S. Frisken Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 8(10), 1601–1613 (1991). [CrossRef]
  4. R. Arimoto and J. M. Murray, “A common aberration with water-immersion objective lenses,” J. Microsc. 216, 49–51 (2004). [CrossRef] [PubMed]
  5. M. Born and E. Wolf, Principles of Optics , 7th ed. (Cambridge University Press, 1999).
  6. A. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4(4), 336–350 (1982). [CrossRef] [PubMed]
  7. 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]
  8. Y. Cotte, M. F. Toy, N. Pavillon, and C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields,” Opt. Express 18(19), 19462–19478 (2010). [CrossRef] [PubMed]
  9. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).
  10. A. Marian, F. Charrière, 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]
  11. Y. Cotte and C. Depeursinge, “Measurement of the complex amplitude point spread function by a diffracting circular aperture,” in Focus on Microscopy , Advanced linear and non-linear imaging, pp. TU–AF2–PAR–D (2009).
  12. F. Montfort, F. Charrire, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position,” J. Opt. Soc. Am. A 23(11), 2944–2953 (2006). [CrossRef]
  13. T. Latychevskaia, F. Gehri, and H.-W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 18(21), 22527–22544 (2010). [CrossRef] [PubMed]
  14. P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006). [CrossRef]
  15. J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999). [CrossRef] [PubMed]
  16. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009). [CrossRef] [PubMed]
  17. 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]
  18. 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]
  19. I. Bergoend, C. Arfire, N. Pavillon, and C. Depeursinge, “Diffraction tomography for biological cells imaging using digital holographic microscopy,” in Laser Applications in Life Sciences , SPIE vol. 7376 (2010).
  20. J. Braat, “Analytical expressions for the wave-front aberration coefficients of a tilted plane-parallel plate,” Appl. Opt. 36(32), 8459–8467 (1997). [CrossRef]
  21. S. S. Kou and C. J. Sheppard, “Imaging in digital holographic microscopy,” Opt. Express 15(21), 13,640–13,648 (2007). [CrossRef]
  22. S. S. Kou and C. J. R. Sheppard, “Image formation in holographic tomography: high-aperture imaging conditions,” Appl. Opt. 48(34), H168–H175 (2009). [CrossRef] [PubMed]
  23. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14(10), 4300–4306 (2006). [CrossRef] [PubMed]
  24. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. II. transmission and cross-polarization effects,” Appl. Opt. 35(3), 515–531 (1996). [CrossRef] [PubMed]
  25. D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31(18), 3518–3523 (1992). [CrossRef] [PubMed]
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  27. Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008). [CrossRef] [PubMed]
  28. Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Computational adaptive optics for live three-dimensional biological imaging,” Proc. Natl. Acad. Sci. U.S.A. 98(7), 3790–3795 (2001). [CrossRef] [PubMed]
  29. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979). [CrossRef]
  30. J. G. McNally, C. Preza, J.-A. Conchello, and L. J. Thomas, “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11(3), 1056–1067 (1994). [CrossRef]

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