OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 27 — Sep. 20, 2006
  • pp: 7056–7064

4Pi microscopy deconvolution with a variable point-spread function

David Baddeley, Christian Carl, and Christoph Cremer  »View Author Affiliations

Applied Optics, Vol. 45, Issue 27, pp. 7056-7064 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (1381 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.

© 2006 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.3190) Image processing : Inverse problems
(180.1790) Microscopy : Confocal microscopy
(180.2520) Microscopy : Fluorescence microscopy

Original Manuscript: December 21, 2005
Manuscript Accepted: March 14, 2006

Virtual Issues
Vol. 1, Iss. 10 Virtual Journal for Biomedical Optics

David Baddeley, Christian Carl, and Christoph Cremer, "4Pi microscopy deconvolution with a variable point-spread function," Appl. Opt. 45, 7056-7064 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, "Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution," Appl. Phys. Lett. 64, 1335-1337 (1994). [CrossRef]
  2. P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, and C. Cremer, "Two-photon excitation 4Pi confocal microscope: Enhanced axial resolution microscope for biological research," Appl. Phys. Lett. 66, 1698-1700 (1995). [CrossRef]
  3. 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, 36-48 (2001). [CrossRef]
  4. M. Schrader, M. Kozubek, S. W. Hell, and T. Wilson, "Optical transfer functions of 4Pi confocal microscopes: theory and experiment," Opt. Lett. 22, 436-438 (1997). [CrossRef] [PubMed]
  5. M. Schrader, S. W. Hell, and H. T. M. van der Voort, "Three-dimensional superresolution with a 4Pi-confocal microscope using image restoration," J. Appl. Phys. 84, 4033-4042 (1998). [CrossRef]
  6. 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, 211-217 (1998). [CrossRef]
  7. M. Schrader, K. Bahlmann, G. Giese, and S. W. Hell, "4Pi-Confocal imaging in fixed biological specimens," Biophys. J. 75, 1659-1668 (1998). [CrossRef] [PubMed]
  8. S. W. Hell, C. M. Blanca, and J. Bewersdorf, "Phase determination in interference-based superresolving microscopes through critical frequency analysis," Opt. Lett. 27, 888-890 (2002). [CrossRef]
  9. 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, 281-285 (2002). [CrossRef]
  10. W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972). [CrossRef]
  11. S. M. Tan, "Aperture synthesis mapping and parameter estimation," Ph.D. dissertation (Mullard Radio Astronomy Observatory, Cavendish Laboratory, Cambridge, 1987).
  12. S. M. Tan, C. Fox, and G. K. Nicholls, "Physics 707 Inverse Problems (Course Notes)," http://www.math.auckland.ac.nz/∼phy707/.
  13. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. (SIAM, 1994). [CrossRef]
  14. R. Heintzmann, "Resolution Enhancement of Biological Light Microscopic Data," Ph.D. dissertation (University of Heidelberg 1999).
  15. C. Stockklausner and N. Klöcker, "Surface expression of inward rectifier potassium channels is controlled by selective Golgi export," J. Biol. Chem. 278, 17000-17005 (2003). [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