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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 9 — Jul. 6, 2010

Automatic deconvolution in 4Pi-microscopy with variable phase

Giuseppe Vicidomini, Roman Schmidt, Alexander Egner, Stefan W. Hell, and Andreas Schönle  »View Author Affiliations

Optics Express, Vol. 18, Issue 10, pp. 10154-10167 (2010)

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4Pi-microscopy doubles the aperture of the imaging system by coherent addition of the wavefronts for illumination and/or detection through opposing objective lenses. This improves the axial resolution 3–7 fold, but the raw data usually features ghost images which have to be removed by image reconstruction. This straightforward procedure is sometimes precluded by imperfect alignment of the instrument or a specimen with strong variations of its refractive index, because the image formation process now depends on the space-variant phase difference between the counter-propagating wavefronts. Here we present a computationally fast method of parametric blind deconvolution that allows for automatic and robust simultaneous estimation of both the object and the phase function in such cases. We verify the performance of our approach on both synthetic and real data. Because the method does not require a-priori knowledge of the phase function it is a major step towards reliable 4Pi-imaging and automatic image restoration by non-expert users.

© 2010 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(180.2520) Microscopy : Fluorescence microscopy
(180.6900) Microscopy : Three-dimensional microscopy
(100.1455) Image processing : Blind deconvolution

ToC Category:

Original Manuscript: March 26, 2010
Revised Manuscript: April 22, 2010
Manuscript Accepted: April 22, 2010
Published: April 29, 2010

Virtual Issues
Vol. 5, Iss. 9 Virtual Journal for Biomedical Optics

Giuseppe Vicidomini, Roman Schmidt, Alexander Egner, Stefan Hell, and Andreas Schönle, "Automatic deconvolution in 4Pi-microscopy with variable phase," Opt. Express 18, 10154-10167 (2010)

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  1. S. W. Hell, "Double-scanning confocal microscope," European Patent (ISSN 0491289) (1990).
  2. C. Cremer and T. Cremer, "Considerations on a laser-scanning-microscope with high resolution and depth of field," Microsc. Acta 81(1), 31-44 (1978). [PubMed]
  3. S. W. Hell and A. Schonle, "Nanoscale resolution in far-field fluorescence microscopy," in Science of Microscopy, P. W. Hawkes and J. C. H. Spence, eds., (Springer, 2007), pp. 790-834. [CrossRef]
  4. M. Nagorni and S. W. Hell, "Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts," J. Opt. Soc. Am. A 18(1), 36-48 (2001). [CrossRef]
  5. G. Vicidomini, S. W. Hell, and A. Schonle, "Automatic deconvolution of 4Pi-microscopy data with arbitrary phase," Opt. Lett. 34(22), 3583-3585 (2009). [CrossRef] [PubMed]
  6. C. M. Blanca, J. Bewersdorf, and S. W. Hell, "Determination of the unknown phase difference in 4Pi-confocal microscopy through the image intensity," Opt. Commun. 206(4-6), 281-285 (2002). [CrossRef]
  7. S. W. Hell, C. M. Blanca, and J. Bewersdorf, "Phase determination in interference-based superresolving microscopes through critical frequency analysis," Opt. Lett. 27(11), 888-890 (2002). [CrossRef]
  8. D. Baddeley, C. Carl, and C. Cremer, "4Pi microscopy deconvolution with a variable point-spread function," Appl. Opt. 45(27), 7056-7064 (2006). [CrossRef] [PubMed]
  9. T. Staudt, M. C. Lang, R. Medda, J. Engelhardt, and S. W. Hell, "2,2prime-Thiodiethanol: A new water soluble mounting medium for high resolution optical microscopy," Microsc. Res. Tech. 70, 1-9 (2007). [CrossRef]
  10. M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).Q1 [CrossRef]
  11. M. Schrader, K. Bahlmann, G. Giese, and S. W. Hell, "4Pi-Confocal Imaging in Fixed Biological Specimens," Biophys. J. 75(4), 1659-1668 (1998). [CrossRef] [PubMed]
  12. J. Enderlein, "Theoretical study of detection of a dipole emitter through an objective with high numerical aperture," Opt. Lett. 25(9), 634-636 (2000). [CrossRef]
  13. B. Richards and E. Wolf, "Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959). [CrossRef]
  14. M. Bertero, P. Boccacci, G. Desiderà, and G. Vicidomini, "Image deblurring with Poisson data: from cells to galaxies," Inverse Probl. 25, 123006 (2009). [CrossRef]
  15. A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153(4-6), 211-217 (1998). [CrossRef]
  16. A. Egner, S. Verrier, A. Goroshkov, H.-D. Soling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004). [CrossRef] [PubMed]
  17. G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, "Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy," J. Microsc. 234(1), 47-61 (2008). [CrossRef]
  18. L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974). [CrossRef]
  19. W. H. Richardson, "Bayesian-Based Iterative Method of Image Restoration," J. Opt. Soc. Am. 62(1), 55-59 (1972). [CrossRef]
  20. C. Kelley, Iterative Method for Optimization, (SIAM, Philadelphia, 1999) Vol. 18.
  21. D. L. Donoho and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization," Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197-2202 (2003). [CrossRef]
  22. H. Lantéri, M. Roche, O. Cuevas, and C. Aime, "A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints," Signal Process. 81, 945-974 (2001). [CrossRef]
  23. I. Csiszár "Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problem," Ann. Stat. 19, 2032-2066 (1991). [CrossRef]

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