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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 10 — Apr. 1, 2007
  • pp: 1819–1829

Gaussian approximations of fluorescence microscope point-spread function models

Bo Zhang, Josiane Zerubia, and Jean-Christophe Olivo-Marin  »View Author Affiliations

Applied Optics, Vol. 46, Issue 10, pp. 1819-1829 (2007)

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We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D–3D paraxial–nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L 1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(110.0180) Imaging systems : Microscopy
(180.1790) Microscopy : Confocal microscopy
(180.2520) Microscopy : Fluorescence microscopy
(180.6900) Microscopy : Three-dimensional microscopy

ToC Category:
Optical microscopy techniques and technology

Original Manuscript: June 2, 2006
Manuscript Accepted: September 15, 2006
Published: March 13, 2007

Virtual Issues
Vol. 2, Iss. 5 Virtual Journal for Biomedical Optics

Bo Zhang, Josiane Zerubia, and Jean-Christophe Olivo-Marin, "Gaussian approximations of fluorescence microscope point-spread function models," Appl. Opt. 46, 1819-1829 (2007)

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  1. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).
  2. C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, "Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera," J. Cell Sci. 101, 415-425 (1992). [PubMed]
  3. G. J. Schütz, H. Schindler, and T. Schmidt, "Single-molecule microscopy on model membranes reveals anomalous diffusion," Biophys. J. 73, 1073-1080 (1997). [CrossRef] [PubMed]
  4. M. K. Cheezum, W. F. Walker, and W. H. Guilford, "Quantitative comparison of algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001). [CrossRef] [PubMed]
  5. A. Santos and I. T. Young, "Model-based resolution: applying the theory in quantitative microscopy," Appl. Opt. 39, 2948-2958 (2000). [CrossRef]
  6. D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with super-resolution: application to the analysis of chromosome movement," J. Microsc. 208, 49-64 (2002). [CrossRef] [PubMed]
  7. F. Rooms, W. Philips, and D. S. Lidke, "Simultaneous degradation estimation and restoration of confocal images and performance evaluation by colocalization analysis," J. Microsc. 218, 22-36 (2005). [CrossRef] [PubMed]
  8. J. C. G. Blonk, A. Don, H. van Aalst, and J. J. Birmingham, "Fluorescence photobleaching recovery in the confocal scanning light microscope," J. Microsc. 169, 363-374 (1993). [CrossRef]
  9. K. Braeckmans, L. Peeters, N. N. Sanders, S. C. D. Smedt, and J. Demeester, "Three-dimensional fluorescence recovery after photobleaching with the confocal scanning laser microscope," Biophys. J. 85, 2240-2252 (2003). [CrossRef] [PubMed]
  10. G. J. Streekstra and J. van Pelt, "Analysis of tubular structures in three-dimensional confocal images," Network Comput. Neural Syst. 13, 381-395 (2002). [CrossRef]
  11. J.-A. Conchello, "Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images," J. Opt. Soc. Am. A 15, 2609-2619 (1998). [CrossRef]
  12. L. J. van Vliet, "Grey-scale measurements in multi-dimensional digitized images," Ph.D. dissertation (Delft University, The Netherlands, 1993).
  13. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, "A study of Gaussian approximations of fluorescence microscopy PSF models," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 6090, 60900K (2006).
  14. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).
  15. L. Tao and C. Nicholson, "The three-dimensional point spread functions of a microscope objective in image and object space," J. Microsc. 178, 267-271 (1995). [CrossRef] [PubMed]
  16. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).
  17. D. R. Sandison, R. M. Williams, K. S. Wells, J. Strickler, and W. W. Webb, "Quantitative fluorescence confocal laser scanning microscopy (CLSM)," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed., 2nd ed. (Plenum, 1995), pp. 39-53.
  18. M. Petrán, M. Hadravský, J. Benes, R. Kucera, and A. Boyde, "The tandem scanning reflected light microscope. Part 1-The principle and its design," in Proceedings of the Royal Microscopical Society (Blackwell, 1985), Vol. 20, pp. 125-129.
  19. J.-A. Conchello and J. W. Lichtman, "Theoretical analysis of a rotating-disk partially confocal scanning microscope," Appl. Opt. 33, 585-596 (1994). [CrossRef] [PubMed]
  20. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1967).

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