Abstract

A new, simple, and hardware-only fluorescence-lifetime-imaging microscopy (FLIM) is proposed to implement on-chip lifetime extractions, and their signal-to-noise-ratio based on statistics theory is also deduced. The results are compared with Monte Carlo simulations, giving good agreement. Compared with the commonly used iterative least-squares method or the maximum-likelihood-estimation- (MLE-) based, general purpose FLIM analysis software, our algorithm offers direct calculation of fluorescence lifetime based on the collected photon counts stored in on-chip counters and therefore delivers faster analysis for real-time applications, such as clinical diagnosis. Error analysis considering timing jitter based on statistics theory is carried out for the proposed algorithms and is also compared with MLE to obtain optimized channel width or measurement window and bit resolution of the time-to-digital converters for a given accuracy. A multi-exponential, pipelined fluorescence lifetime method based on the proposed algorithms is also introduced. The performance of the proposed methods has been tested on mono-exponential and four-exponential decay experimental data.

© 2008 Optical Society of America

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References

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  1. W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Wolfgang, Springer, 2005).
    [CrossRef]
  2. R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
    [CrossRef]
  3. R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
    [CrossRef] [PubMed]
  4. V. V. Apanasovich and E. G. Novikov, “Methods of analysis of fluorescence decay curves in pulsed fluorometry (Review),” J. Appl. Spectrosc. 56, 317-327 (1992).
    [CrossRef]
  5. J. Philips and K. Carlsson, “Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging,” J. Opt. Soc. Am. A 20, 368-379 (2003).
    [CrossRef]
  6. Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
    [CrossRef] [PubMed]
  7. P. Hall and B. Sellnger, “Better estimates of exponential decay parameters,” J. Phys. Chem. 85, 2941-2946 (1981).
    [CrossRef]
  8. M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
    [CrossRef] [PubMed]
  9. S. D. Foss, “A method of exponential curve fitting by numerical integration,” Biometrics 26, 815-821 (1970).
    [CrossRef]
  10. J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.
  11. W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
    [CrossRef]
  12. A. Rochas, “Single photon avalanche diodes in CMOS technology,” Ph.D. thesis, (Lausanne, 2003).
  13. C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).
  14. R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61, 30-33 (1989).
    [CrossRef]
  15. A. Draaijer, R. Sanders, and H. C. Gerritsen, “Fluorescence lifetime imaging, a new tool in confocal microscopy,” in Handbook of Biological Confocal Microscopy, J.Pawley, ed. (Plenum, 1995), pp. 491-505.
  16. M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence lifetime measurements?” Chem. Phys. Lett. 200, 199-204 (1992).
    [CrossRef]
  17. J. R. Lakowicz and H. Szmacinski, “Fluorescence lifetime-based sensing of pH, Ca+2, K+ and glucose,” Sens. Actuators B 11, 133-143 (1993).
    [CrossRef]

2005 (1)

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

2004 (1)

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

2003 (2)

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

J. Philips and K. Carlsson, “Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging,” J. Opt. Soc. Am. A 20, 368-379 (2003).
[CrossRef]

2002 (1)

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

2001 (1)

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

1993 (1)

J. R. Lakowicz and H. Szmacinski, “Fluorescence lifetime-based sensing of pH, Ca+2, K+ and glucose,” Sens. Actuators B 11, 133-143 (1993).
[CrossRef]

1992 (2)

V. V. Apanasovich and E. G. Novikov, “Methods of analysis of fluorescence decay curves in pulsed fluorometry (Review),” J. Appl. Spectrosc. 56, 317-327 (1992).
[CrossRef]

M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence lifetime measurements?” Chem. Phys. Lett. 200, 199-204 (1992).
[CrossRef]

1989 (2)

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61, 30-33 (1989).
[CrossRef]

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

1981 (1)

P. Hall and B. Sellnger, “Better estimates of exponential decay parameters,” J. Phys. Chem. 85, 2941-2946 (1981).
[CrossRef]

1970 (1)

S. D. Foss, “A method of exponential curve fitting by numerical integration,” Biometrics 26, 815-821 (1970).
[CrossRef]

Apanasovich, V. V.

V. V. Apanasovich and E. G. Novikov, “Methods of analysis of fluorescence decay curves in pulsed fluorometry (Review),” J. Appl. Spectrosc. 56, 317-327 (1992).
[CrossRef]

Bajzer, Z.

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

Ballew, R. M.

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61, 30-33 (1989).
[CrossRef]

Becker, W.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Wolfgang, Springer, 2005).
[CrossRef]

Bennodorf, K.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Bergmann, A.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Besse, P. A.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

Biskup, C.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Carlsson, K.

Charbon, E.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

Comelli, D.

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Cotlet, M.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Cubeddu, R.

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

D'Andrea, C.

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Daujotyte, D.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

De Schryver, F. C.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Demas, J. N.

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61, 30-33 (1989).
[CrossRef]

Draaijer, A.

A. Draaijer, R. Sanders, and H. C. Gerritsen, “Fluorescence lifetime imaging, a new tool in confocal microscopy,” in Handbook of Biological Confocal Microscopy, J.Pawley, ed. (Plenum, 1995), pp. 491-505.

Dryden, D. T. F.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Fang, Q.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.

Foss, S. D.

S. D. Foss, “A method of exponential curve fitting by numerical integration,” Biometrics 26, 815-821 (1970).
[CrossRef]

Gensch, T.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Gerritsen, H. C.

A. Draaijer, R. Sanders, and H. C. Gerritsen, “Fluorescence lifetime imaging, a new tool in confocal microscopy,” in Handbook of Biological Confocal Microscopy, J.Pawley, ed. (Plenum, 1995), pp. 491-505.

Grazulis, S.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Hall, P.

P. Hall and B. Sellnger, “Better estimates of exponential decay parameters,” J. Phys. Chem. 85, 2941-2946 (1981).
[CrossRef]

Hofkens, J.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Jo, J. A.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.

Jones, A. C.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Kelbauskas, L.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Klimasauskas, S.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Klöcker, N.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Köllner, M.

M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence lifetime measurements?” Chem. Phys. Lett. 200, 199-204 (1992).
[CrossRef]

Lakowicz, J. R.

J. R. Lakowicz and H. Szmacinski, “Fluorescence lifetime-based sensing of pH, Ca+2, K+ and glucose,” Sens. Actuators B 11, 133-143 (1993).
[CrossRef]

Magennis, S. W.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Marcu, L.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.

Maus, M.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Myers, A. C.

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

Neely, R. K.

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Niclass, C.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

Novikov, E. G.

V. V. Apanasovich and E. G. Novikov, “Methods of analysis of fluorescence decay curves in pulsed fluorometry (Review),” J. Appl. Spectrosc. 56, 317-327 (1992).
[CrossRef]

Papaioannou, T.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.

Philips, J.

Prendergast, F. G.

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

Rochas, A.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

A. Rochas, “Single photon avalanche diodes in CMOS technology,” Ph.D. thesis, (Lausanne, 2003).

Sanders, R.

A. Draaijer, R. Sanders, and H. C. Gerritsen, “Fluorescence lifetime imaging, a new tool in confocal microscopy,” in Handbook of Biological Confocal Microscopy, J.Pawley, ed. (Plenum, 1995), pp. 491-505.

Schaffer, J.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Sedarous, S. S.

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

Seidel, C. A. M.

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

Sellnger, B.

P. Hall and B. Sellnger, “Better estimates of exponential decay parameters,” J. Phys. Chem. 85, 2941-2946 (1981).
[CrossRef]

Szmacinski, H.

J. R. Lakowicz and H. Szmacinski, “Fluorescence lifetime-based sensing of pH, Ca+2, K+ and glucose,” Sens. Actuators B 11, 133-143 (1993).
[CrossRef]

Taroni, P.

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Valentini, G.

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Wolfrum, J.

M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence lifetime measurements?” Chem. Phys. Lett. 200, 199-204 (1992).
[CrossRef]

Zimmer, T.

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Anal. Chem. (2)

M. Maus, M. Cotlet, J. Hofkens, T. Gensch, F. C. De Schryver, J. Schaffer, and C. A. M. Seidel, “An experimental comparison of the maximum likelihood estimation and nonlinear least-squares fluorescence lifetime analysis of single molecules,” Anal. Chem. 73, 2078-2086 (2001).
[CrossRef] [PubMed]

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61, 30-33 (1989).
[CrossRef]

Biometrics (1)

S. D. Foss, “A method of exponential curve fitting by numerical integration,” Biometrics 26, 815-821 (1970).
[CrossRef]

Biophys. J. (1)

Z. Bajzer, A. C. Myers, S. S. Sedarous, and F. G. Prendergast, “Padé-Laplace method for analysis of fluorescence intensity decay,” Biophys. J. 56, 79-93 (1989).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence lifetime measurements?” Chem. Phys. Lett. 200, 199-204 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, “Toward a 3-D camera based on single photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 769-802 (2004).

J. Appl. Spectrosc. (1)

V. V. Apanasovich and E. G. Novikov, “Methods of analysis of fluorescence decay curves in pulsed fluorometry (Review),” J. Appl. Spectrosc. 56, 317-327 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Chem. (1)

P. Hall and B. Sellnger, “Better estimates of exponential decay parameters,” J. Phys. Chem. 85, 2941-2946 (1981).
[CrossRef]

J. Phys. D (1)

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Nucleic Acids Res. (1)

R. K. Neely, D. Daujotyte, S. Grazulis, S. W. Magennis, D. T. F. Dryden, S. Klimasauskas, and A. C. Jones, “Time-resolved fluorescence of 2-aminopurine as a probe of base flipping in M. Hhal-DNA complexes,” Nucleic Acids Res. 33, 6953-6960 (2005).
[CrossRef] [PubMed]

Proc. SPIE (1)

W. Becker, A. Bergmann, C. Biskup, L. Kelbauskas, T. Zimmer, N. Klöcker, and K. Bennodorf, “High resolution TCSPC lifetime imaging,” Proc. SPIE 4963, 175-184 (2003).
[CrossRef]

Sens. Actuators B (1)

J. R. Lakowicz and H. Szmacinski, “Fluorescence lifetime-based sensing of pH, Ca+2, K+ and glucose,” Sens. Actuators B 11, 133-143 (1993).
[CrossRef]

Other (4)

W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Wolfgang, Springer, 2005).
[CrossRef]

A. Rochas, “Single photon avalanche diodes in CMOS technology,” Ph.D. thesis, (Lausanne, 2003).

A. Draaijer, R. Sanders, and H. C. Gerritsen, “Fluorescence lifetime imaging, a new tool in confocal microscopy,” in Handbook of Biological Confocal Microscopy, J.Pawley, ed. (Plenum, 1995), pp. 491-505.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Novel ultra-fast deconvolution method for fluorescence lifetime imaging microscopy based on the Laguerre expansion technique,” in Proceedings of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2004), pp. 1271-1274.

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Figures (10)

Fig. 1
Fig. 1

Convolution of a single decay and artificial IRFs with different ratios of FWHM over lifetime.

Fig. 2
Fig. 2

Concept of the single-exponential IEM.

Fig. 3
Fig. 3

Q ( x ) and Q ( x ) G ( x ) versus h τ for gate number M = 15 and 255.

Fig. 4
Fig. 4

Precision and accuracy curves for the 15-gate IEM and 2-gate RLD with N c = 2 17 .

Fig. 5
Fig. 5

SNR plot in terms of measurement window and log 2 ( M ) with N c = 2 17 .

Fig. 6
Fig. 6

SNR comparison plot for the IEM, RLD-M, and the MLE with N c = 2 17 .

Fig. 7
Fig. 7

SNR contour plot in terms of τ ( M h ) and log 2 ( M ) .

Fig. 8
Fig. 8

Concept of the pipelined IEM.

Fig. 9
Fig. 9

Measured single-exponential data and fitted and residual data using IEM.

Fig. 10
Fig. 10

Measured 4-exponential data and fitted and residual data using PL-IEM.

Tables (3)

Tables Icon

Table 1 Comparison of Lifetimes (ns) Extracted by the IEM, RLD-M, LSM, and Edinburgh Instruments F900 Software

Tables Icon

Table 2 Comparison of Lifetimes (ns) and Fractional Amplitudes (%) Extracted by PL-IEM and Edinburgh Instruments F900 Software

Tables Icon

Table 3 Comparison Summary of the IEM, RLD, and MLE

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

f ( t ) = 0 t I ( t τ ) IRF ( τ ) d τ ,
P = D C R L P R = 1 N P ,
P j , k = P 1 e h τ 1 e M h τ e j h τ ( 1 + σ h j , k h ) ,
N j = k = 1 N t P j , k = 1 N p k = 1 N t 1 e h τ 1 e N h τ e j h τ ( 1 + σ h j , k h ) = N p 1 P 0 e j h τ ( N t + σ h j , 0 h N t ) ,
E N j ( 1 + σ N j E N j + σ h j , 0 h N c N p ) ,
τ ( f 0 f M 1 ) = t 0 t M 1 f ( t ) d t = t 0 t M 1 A exp ( t τ ) d t h 3 ( f 0 + 4 f 1 + 2 f 2 + + 4 f M 2 + f M 1 ) ,
τ IEM h 3 ( E N 0 + 4 E N 1 + 2 E N 2 + + 4 E N M 2 + E N M 1 ) E N 0 E N M 1 = h 3 ( 1 + 4 e h τ + e 2 h τ ) j = 0 ( M 3 ) 2 e 2 j h τ 1 e ( M 1 ) h τ = h 3 1 + 4 e h τ + e 2 h τ 1 e 2 h τ = τ 6 6 α + 4 α 2 2 α 3 + 5 6 α 4 3 10 α 5 + 17 180 α 6 + 6 6 α + 4 α 2 2 α 3 + 4 5 α 4 4 15 α 5 + 8 105 α 6 + = τ [ 1 + 1 180 α 4 1 1512 α 6 + O ( α 8 ) ] = τ ( 1 + Δ τ τ ) ,
τ IEM h j = 0 M 1 ( C j N j ) N 0 N M 1 ,
τ = M j = 0 M 1 t j 2 ( j = 0 M 1 t j ) 2 M j = 0 M 1 [ t j ln ( N j ) ] j = 0 M 1 t j j = 0 M 1 ln ( N j ) ,
τ IEM h [ j = 0 M 1 C j E N j ( 1 + σ N j E N j + σ h j h N t ) ] E N 0 ( 1 + σ N 0 E N 0 + σ h 0 h N t ) E N M 1 ( 1 + σ N M 1 E N M 1 + σ h M 1 h N t ) .
τ IEM h ( U + σ u ) V + σ ν h U V ( 1 + σ u U σ ν V ) τ ( 1 + Δ τ τ + σ u U σ ν V ) ,
U = j = 0 M 1 C j E N j , V = E N 0 E N M 1 ,
σ u = j = 0 M 1 C j ( σ N j + E N j σ h j h N t ) ,
σ ν = ( σ N 0 + E N 0 σ h 0 h N t ) ( σ N M 1 + E N M 1 σ h M 1 h N t ) ,
σ u U σ ν V = σ a 2 + σ b 2 ,
σ a = ( C 0 U 1 V ) 2 σ N 0 2 + j = 1 M 2 ( C j U σ N j ) 2 + ( C M 1 U + 1 V ) 2 σ N M 1 2 ,
σ b = 1 h N t [ ( C 0 U 1 V ) 2 σ h 0 2 E N 0 2 + j = 1 M 2 ( C j U σ h j E N j ) 2 + ( C M 1 U + 1 V ) 2 σ h M 1 2 E N M 1 2 ] .
τ IEM = τ [ 1 + 1 180 ( h τ ) 4 1 1512 ( h τ ) 6 + σ a 2 + σ b 2 ] = τ ( 1 + Δ τ τ + σ τ τ ) ,
σ a = 2 Q ( x ) N c ,
Q ( x ) = ( 1 x M ) ( 4 x + 5 x 2 + 5 x M + 1 + 4 x M + 2 ) ( 1 x ) ( 1 x M 1 ) 2 ( 1 + 4 x + x 2 ) 2 ,
σ b = 2 σ h 0 h G ( x ) N c N p ,
G ( x ) = 8 x 2 + 4 x 3 + 2 x 4 + 4 x 5 + 4 x 2 M 1 + 2 x 2 M + 4 x 2 M + 1 + 8 x 2 M + 2 ( 1 + x 2 ) ( 1 x M 1 ) 2 ( 1 + 4 x + x 2 ) 2 ,
Precision σ τ IEM τ IEM = σ a 2 + σ b 2 = 2 N c Q ( x ) + G ( x ) N p σ h 0 2 h 2 ,
Accuracy Δ τ IEM τ IEM = 1 180 ( h τ ) 4 1 1512 ( h τ ) 6 .
Precision = 2 N c Q ( x ) + I L G ( x ) K ̃ σ h 0 2 h 2
Precision = 2 N t K ̃ Q ( x ) I L + σ h 0 2 G ( x ) h 2
g ( x ) = τ { M j = 0 M 1 [ t j ln ( N j ) ] j = 0 M 1 t j j = 0 M 1 ln ( N j ) } + M j = 0 M 1 t j 2 ( j = 0 M 1 t j ) 2 = 0 ,
σ g ( x ) = σ x g ( x ) ,
σ x x = h σ τ τ 2 .
σ τ RLD M τ RLD M = τ C h S ( x ) N c P 0 + 2 C σ h 0 2 N c N p τ 2 ( 1 + τ h ) 2 ,
S ( x ) = 1 ( x 1 1 ) 3 [ ( M 1 ) 2 ( x M 2 1 ) + ( 6 2 M 2 ) ( x M 1 x 1 ) + ( M + 1 ) 2 ( x M x 2 ) ] ,
Precision τ IEM σ τ IEM 2 + Δ τ IEM 2 .
τ IEM , Cal τ IEM [ 1 1 180 ( h τ IEM ) 4 + 1 1512 ( h τ IEM ) 6 ] .
σ τ MLE τ MLE = τ h N c { x ( 1 x ) 2 M 2 x M ( 1 x M ) 2 } , x = e h τ .
I ( t ) = i = 1 4 A i exp ( t τ i ) ,
h = { 2 3 τ , w o calibration 5 3 τ , with calibration } ,

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