Localization of a fluorescent source without numerical fitting

doi:10.1364/OE.16.018714

Localization of a fluorescent source without numerical fitting

Sean Andersson »View Author Affiliations

Optics Express, Vol. 16, Issue 23, pp. 18714-18724 (2008)
http://dx.doi.org/10.1364/OE.16.018714

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Abstract
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Abstract

We present an algebraic solution to the problem of localizing a single fluorescent particle with sub-diffraction-limit accuracy. The algorithm is derived and its performance studied experimentally. Isolated 20 nm fluorescent beads were imaged using a wide-field microscope at two different positions separated by 100 nm and at a range of signal-to-noise ratios (SNR). The data were analyzed using both the new algorithm and the standard approach of fitting the data to a Gaussian profile. Results indicate that the proposed approach is nearly as accurate as Gaussian fitting across a wide range of SNR while executing over 200 times faster. In addition, the new algorithm is able to localize at lower SNR than the fitting method.

OCIS Codes
(100.2960) Image processing : Image analysis
(180.2520) Microscopy : Fluorescence microscopy
(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence

ToC Category:
Microscopy

History
Original Manuscript: August 29, 2008
Revised Manuscript: October 9, 2008
Manuscript Accepted: October 24, 2008
Published: October 29, 2008

Virtual Issues
Vol. 4, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Sean Andersson, "Localization of a fluorescent source without numerical fitting," Opt. Express 16, 18714-18724 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18714

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References

M. Lakadamyali, M. J. Rust, H. P. Babcock, and X. Zhuang, "Visualizing infection of individual influenza viruses," P. Natl. Acad. Sci USA 100, 9280-9285 (2003). [CrossRef]
C. Kural, H. Balci, and P. R. Selvin, "Molecular motors one at a time: FIONA to the rescue," J. Phys. Condens. Matt. 27, S3979-S3995 (2005). [CrossRef]
C. K. Payne, "Imaging gene delivery with fluorescence microscopy," Nanomedicine 2, 847-860 (2007). [CrossRef] [PubMed]
W. E. Moerner, "New directions in single-molecule imaging and analysis," P. Natl. Acad. Sci USA 104, 596-602 (2007). [CrossRef]
C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, "Advances in single-molecule fluorescence methods for molecular biology," Annu. Rev. Biochem. 77, 51-76 (2008). [CrossRef] [PubMed]
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]
A. J. Berglund, M. D. McMahon, J. J. McClelland, and J. A. Liddle, "Fast, bias-free algorithm for tracking single particles with variable size and shape," Opt. Express 16, 064-075 (2008). [CrossRef]
R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002). [CrossRef] [PubMed]
R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2007). [CrossRef]
S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multdim. Syst. Sign. P. 17, 27-57 (2006). [CrossRef]
A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005). [CrossRef] [PubMed]
S. B. Andersson, "Tracking a single fluorescent molecule with a confocal microscope," Appl. Phys. B 80, 809-816 (2005). [CrossRef]
V. Levi, Q. Ruan, and E. Gratton, "3-D particle tracking in a two-photon microscope: application to the study of molecular dynamics in cells," Biophys. J. 88, 2919-2928 (2005). [CrossRef] [PubMed]
S. Bancroft, "An algebraic solution of the GPS pseudorange equations," IEEE T. Aero. Elec. Sys. AES-21, 56-59 (1985). [CrossRef]
T. Sun and S. B. Andersson, "Precise 3-D localization of fluorescent probes without numerical fitting," in Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2007) pp. 4181-4184. [PubMed]
S. B. Andersson, "Precise localization of fluorescent probes without numerical fitting," in Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI) (IEEE, 2007), pp. 252-255.
S. B. Andersson, "Position estimation of fluorescent probes in a confocal microscope," in Proceedings of IEEE Conference on Decision and Control (IEEE, 2007), pp. 4950-4955.
R. Juskaitis, "Measuring the real point spread function of high numerical aperture microscope objective lenses," in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Springer, 2006), pp. 239-250. [CrossRef]
A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Pure and Applied Mathematics (John Wiley and Sons, 1974).
A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

Andersson, S. B.
Babcock, H. P.
Balci, H.
Bancroft, S.
Berglund, A. J.
Buranachai, C.
Cheezum, M. K.
Gratton, E.
Guilford, W. H.
Ha, T.
Ishitsuka, Y.
Joo, C.
Kural, C.
Lakadamyali, M.
Larson, D. R.
Levi, V.
Mabuchi, H.
Moerner, W. E.
Ober, R. J.
Payne, C. K.
Ram, S.
Ruan, Q.
Rust, M. J.
Selvin, P. R.
Thompson, R. E.
Walker, W. F.
Ward, E. S.
Webb, W. W.
Zhuang, X.

Annu. Rev. Biochem.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, "Advances in single-molecule fluorescence methods for molecular biology," Annu. Rev. Biochem. 77, 51-76 (2008). [CrossRef] [PubMed]

Appl. Phys. B

S. B. Andersson, "Tracking a single fluorescent molecule with a confocal microscope," Appl. Phys. B 80, 809-816 (2005). [CrossRef]

Biophys. J.

V. Levi, Q. Ruan, and E. Gratton, "3-D particle tracking in a two-photon microscope: application to the study of molecular dynamics in cells," Biophys. J. 88, 2919-2928 (2005). [CrossRef] [PubMed]
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]
R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002). [CrossRef] [PubMed]
R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2007). [CrossRef]

IEEE T. Aero. Elec. Sys.

S. Bancroft, "An algebraic solution of the GPS pseudorange equations," IEEE T. Aero. Elec. Sys. AES-21, 56-59 (1985). [CrossRef]

J. Phys. Condens. Matt.

C. Kural, H. Balci, and P. R. Selvin, "Molecular motors one at a time: FIONA to the rescue," J. Phys. Condens. Matt. 27, S3979-S3995 (2005). [CrossRef]

Multdim. Syst. Sign. P.

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multdim. Syst. Sign. P. 17, 27-57 (2006). [CrossRef]

Nanomedicine

C. K. Payne, "Imaging gene delivery with fluorescence microscopy," Nanomedicine 2, 847-860 (2007). [CrossRef] [PubMed]

Opt. Express

A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005). [CrossRef] [PubMed]

P. Natl. Acad. Sci USA

W. E. Moerner, "New directions in single-molecule imaging and analysis," P. Natl. Acad. Sci USA 104, 596-602 (2007). [CrossRef]
M. Lakadamyali, M. J. Rust, H. P. Babcock, and X. Zhuang, "Visualizing infection of individual influenza viruses," P. Natl. Acad. Sci USA 100, 9280-9285 (2003). [CrossRef]

Other

A. J. Berglund, M. D. McMahon, J. J. McClelland, and J. A. Liddle, "Fast, bias-free algorithm for tracking single particles with variable size and shape," Opt. Express 16, 064-075 (2008). [CrossRef]
T. Sun and S. B. Andersson, "Precise 3-D localization of fluorescent probes without numerical fitting," in Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2007) pp. 4181-4184. [PubMed]
S. B. Andersson, "Precise localization of fluorescent probes without numerical fitting," in Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI) (IEEE, 2007), pp. 252-255.
S. B. Andersson, "Position estimation of fluorescent probes in a confocal microscope," in Proceedings of IEEE Conference on Decision and Control (IEEE, 2007), pp. 4950-4955.
R. Juskaitis, "Measuring the real point spread function of high numerical aperture microscope objective lenses," in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Springer, 2006), pp. 239-250. [CrossRef]
A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Pure and Applied Mathematics (John Wiley and Sons, 1974).
A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

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