Abstract

We demonstrate a method to improve the measurement sensitivity of two-photon frequency-domain lifetime measurements in poor signal to background conditions. This technique uses sinusoidal modulation of the two-photon excitation source and detection of the second harmonic of the modulation frequency that appears in the emission. Additionally, we present the mathematical model which describes how the observed phase shift and amplitude demodulation factor of two-photon phosphorescence emission are related to the phosphorescence lifetime and modulation frequency. We demonstrate the validity of the model by showing the existence of new frequency terms in the phosphorescence emission generated from the quadratic nature of two-photon absorption and by showing that the phase shift and demodulation match theory for all frequency components.

© 2010 OSA

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  1. R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
    [CrossRef] [PubMed]
  2. E. B. van Munster and T. W. J. Gadella, “Fluorescence lifetime imaging microscopy (FLIM),” Adv. Biochem. Eng. Biotechnol. 95, 143–175 (2005).
    [PubMed]
  3. M. Y. Berezin and S. Achilefu, “Fluorescence lifetime measurements and biological imaging,” Chem. Rev. 110(5), 2641–2684 (2010).
    [CrossRef] [PubMed]
  4. H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
    [CrossRef] [PubMed]
  5. J. M. Vanderkooi and D. F. Wilson, “A new method for measuring oxygen concentration in biological systems,” Adv. Exp. Med. Biol. 200, 189–193 (1986).
    [PubMed]
  6. W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
    [CrossRef]
  7. R. D. Shonat and A. C. Kight, “Oxygen tension imaging in the mouse retina,” Ann. Biomed. Eng. 31(9), 1084–1096 (2003).
    [CrossRef] [PubMed]
  8. A. D. Estrada, A. Ponticorvo, T. N. Ford, and A. K. Dunn, “Microvascular oxygen quantification using two-photon microscopy,” Opt. Lett. 33(10), 1038–1040 (2008).
    [CrossRef] [PubMed]
  9. E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
    [CrossRef] [PubMed]
  10. J. R. Lakowicz, “Principles of Fluorescence Spectroscopy,” in Principles of Fluorescence Spectroscopy, 3 ed. (Springer Science + Business Media, LLC, New York, NY, 2006), pp. 171,192–194.
  11. D. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Applied Spectroscopy … (1984).
  12. J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
    [CrossRef]
  13. E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
    [CrossRef] [PubMed]
  14. P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
    [CrossRef]
  15. A. Esposito, H. C. Gerritsen, and F. S. Wouters, “Optimizing frequency-domain fluorescence lifetime sensing for high-throughput applications: photon economy and acquisition speed,” J. Opt. Soc. Am. A 24(10), 3261–3273 (2007).
    [CrossRef]
  16. R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
    [CrossRef]
  17. P. Tian and W. S. Warren, “Ultrafast measurement of two-photon absorption by loss modulation,” Opt. Lett. 27(18), 1634–1636 (2002).
    [CrossRef]
  18. J. Van Houten and R. Watts, “Temperature dependence of the photophysical and photochemical properties of the tris (2, 2'-bipyridyl) ruthenium (II) ion in aqueous solution,” J. Am. Chem. Soc (1976).
  19. R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
    [CrossRef] [PubMed]
  20. I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
    [CrossRef] [PubMed]
  21. L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
    [CrossRef] [PubMed]

2010

M. Y. Berezin and S. Achilefu, “Fluorescence lifetime measurements and biological imaging,” Chem. Rev. 110(5), 2641–2684 (2010).
[CrossRef] [PubMed]

2008

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

A. D. Estrada, A. Ponticorvo, T. N. Ford, and A. K. Dunn, “Microvascular oxygen quantification using two-photon microscopy,” Opt. Lett. 33(10), 1038–1040 (2008).
[CrossRef] [PubMed]

2007

2005

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

E. B. van Munster and T. W. J. Gadella, “Fluorescence lifetime imaging microscopy (FLIM),” Adv. Biochem. Eng. Biotechnol. 95, 143–175 (2005).
[PubMed]

2004

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

2003

W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
[CrossRef]

R. D. Shonat and A. C. Kight, “Oxygen tension imaging in the mouse retina,” Ann. Biomed. Eng. 31(9), 1084–1096 (2003).
[CrossRef] [PubMed]

R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
[CrossRef] [PubMed]

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

2002

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
[CrossRef] [PubMed]

P. Tian and W. S. Warren, “Ultrafast measurement of two-photon absorption by loss modulation,” Opt. Lett. 27(18), 1634–1636 (2002).
[CrossRef]

1996

L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
[CrossRef] [PubMed]

1995

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

1990

R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
[CrossRef]

1986

J. M. Vanderkooi and D. F. Wilson, “A new method for measuring oxygen concentration in biological systems,” Adv. Exp. Med. Biol. 200, 189–193 (1986).
[PubMed]

1985

J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
[CrossRef]

Achilefu, S.

M. Y. Berezin and S. Achilefu, “Fluorescence lifetime measurements and biological imaging,” Chem. Rev. 110(5), 2641–2684 (2010).
[CrossRef] [PubMed]

Alcala, J.

J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
[CrossRef]

Barry, N.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

Berezin, M. Y.

M. Y. Berezin and S. Achilefu, “Fluorescence lifetime measurements and biological imaging,” Chem. Rev. 110(5), 2641–2684 (2010).
[CrossRef] [PubMed]

Berland, K. M.

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Breusegem, S.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

Briñas, R. P.

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

Clegg, R. M.

R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
[CrossRef] [PubMed]

Dong, C. Y.

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Dunn, A. K.

Dunphy, I.

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
[CrossRef] [PubMed]

Esposito, A.

Esteves da Silva, J. C. G.

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

Estrada, A. D.

Ford, T. N.

Freeman, R.

R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
[CrossRef]

French, T.

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Gadella, T. W. J.

E. B. van Munster and T. W. J. Gadella, “Fluorescence lifetime imaging microscopy (FLIM),” Adv. Biochem. Eng. Biotechnol. 95, 143–175 (2005).
[PubMed]

Gerritsen, H. C.

Gilliland, D.

R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
[CrossRef]

Gohlke, C.

R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
[CrossRef] [PubMed]

Gonçalves, H. M. R.

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

Gratton, E.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
[CrossRef]

Hochstrasser, R. M.

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

Holub, O.

R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
[CrossRef] [PubMed]

Ince, C.

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

Jameson, D.

J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
[CrossRef]

Jorge, P. A. S.

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

Kight, A. C.

R. D. Shonat and A. C. Kight, “Oxygen tension imaging in the mouse retina,” Ann. Biomed. Eng. 31(9), 1084–1096 (2003).
[CrossRef] [PubMed]

Koch, C. J.

L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
[CrossRef] [PubMed]

Lo, L. W.

L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
[CrossRef] [PubMed]

Lytle, F.

R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
[CrossRef]

Maule, C. D.

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

Mik, E. G.

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

Mycek, M.-A.

W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
[CrossRef]

Ponticorvo, A.

Raat, N. J.

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

Ruan, Q.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

Shonat, R. D.

R. D. Shonat and A. C. Kight, “Oxygen tension imaging in the mouse retina,” Ann. Biomed. Eng. 31(9), 1084–1096 (2003).
[CrossRef] [PubMed]

So, P. T. C.

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Sutin, J.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

Tian, P.

Troxler, T.

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

Urayama, P.

W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
[CrossRef]

van Leeuwen, T. G.

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

van Munster, E. B.

E. B. van Munster and T. W. J. Gadella, “Fluorescence lifetime imaging microscopy (FLIM),” Adv. Biochem. Eng. Biotechnol. 95, 143–175 (2005).
[PubMed]

Vanderkooi, J. M.

J. M. Vanderkooi and D. F. Wilson, “A new method for measuring oxygen concentration in biological systems,” Adv. Exp. Med. Biol. 200, 189–193 (1986).
[PubMed]

Vinogradov, S. A.

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
[CrossRef] [PubMed]

Warren, W. S.

Wilson, D. F.

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
[CrossRef] [PubMed]

L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
[CrossRef] [PubMed]

J. M. Vanderkooi and D. F. Wilson, “A new method for measuring oxygen concentration in biological systems,” Adv. Exp. Med. Biol. 200, 189–193 (1986).
[PubMed]

Wouters, F. S.

Yu, W. M.

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Zhong, W.

W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
[CrossRef]

Adv. Biochem. Eng. Biotechnol.

E. B. van Munster and T. W. J. Gadella, “Fluorescence lifetime imaging microscopy (FLIM),” Adv. Biochem. Eng. Biotechnol. 95, 143–175 (2005).
[PubMed]

Adv. Exp. Med. Biol.

J. M. Vanderkooi and D. F. Wilson, “A new method for measuring oxygen concentration in biological systems,” Adv. Exp. Med. Biol. 200, 189–193 (1986).
[PubMed]

Anal. Biochem.

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, “Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence,” Anal. Biochem. 310(2), 191–198 (2002).
[CrossRef] [PubMed]

L. W. Lo, C. J. Koch, and D. F. Wilson, “Calibration of oxygen-dependent quenching of the phosphorescence of Pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems,” Anal. Biochem. 236(1), 153–160 (1996).
[CrossRef] [PubMed]

Anal. Chem.

R. Freeman, D. Gilliland, and F. Lytle, “Second harmonic detection of sinusoidally modulated two-photon excited fluorescence,” Anal. Chem. 62(20), 2216–2219 (1990).
[CrossRef]

Anal. Chim. Acta

H. M. R. Gonçalves, C. D. Maule, P. A. S. Jorge, and J. C. G. Esteves da Silva, “Fiber optic lifetime pH sensing based on ruthenium(II) complexes with dicarboxybipyridine,” Anal. Chim. Acta 626(1), 62–70 (2008).
[CrossRef] [PubMed]

Ann. Biomed. Eng.

R. D. Shonat and A. C. Kight, “Oxygen tension imaging in the mouse retina,” Ann. Biomed. Eng. 31(9), 1084–1096 (2003).
[CrossRef] [PubMed]

Bioimaging

P. T. C. So, T. French, W. M. Yu, K. M. Berland, C. Y. Dong, and E. Gratton, “Time-resolved fluorescence microscopy using two-photon excitation,” Bioimaging 3(2), 49–63 (1995).
[CrossRef]

Chem. Rev.

M. Y. Berezin and S. Achilefu, “Fluorescence lifetime measurements and biological imaging,” Chem. Rev. 110(5), 2641–2684 (2010).
[CrossRef] [PubMed]

Instrum. Sci. Technol.

J. Alcala, E. Gratton, and D. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Instrum. Sci. Technol. 14(3), 225–250 (1985).
[CrossRef]

J. Am. Chem. Soc.

R. P. Briñas, T. Troxler, R. M. Hochstrasser, and S. A. Vinogradov, “Phosphorescent oxygen sensor with dendritic protection and two-photon absorbing antenna,” J. Am. Chem. Soc. 127(33), 11851–11862 (2005).
[CrossRef] [PubMed]

J. Appl. Physiol.

E. G. Mik, T. G. van Leeuwen, N. J. Raat, and C. Ince, “Quantitative determination of localized tissue oxygen concentration in vivo by two-photon excitation phosphorescence lifetime measurements,” J. Appl. Physiol. 97(5), 1962–1969 (2004).
[CrossRef] [PubMed]

J. Biomed. Opt.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. 8(3), 381–390 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Phys. D Appl. Phys.

W. Zhong, P. Urayama, and M.-A. Mycek, “Imaging fluorescence lifetime modulation of a ruthenium- based dye in living cells: the potential for oxygen sensing,” J. Phys. D Appl. Phys. 36(14), 1689–1695 (2003).
[CrossRef]

Methods Enzymol.

R. M. Clegg, O. Holub, and C. Gohlke, “Fluorescence lifetime-resolved imaging: measuring lifetimes in an image,” Methods Enzymol. 360, 509–542 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Other

J. Van Houten and R. Watts, “Temperature dependence of the photophysical and photochemical properties of the tris (2, 2'-bipyridyl) ruthenium (II) ion in aqueous solution,” J. Am. Chem. Soc (1976).

J. R. Lakowicz, “Principles of Fluorescence Spectroscopy,” in Principles of Fluorescence Spectroscopy, 3 ed. (Springer Science + Business Media, LLC, New York, NY, 2006), pp. 171,192–194.

D. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Applied Spectroscopy … (1984).

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Fig. 1
Fig. 1

(a) Experimental setup. (b) Rhodamine 6G fluorescence excited by a two-photon excitation source modulated at 300 Hz. The residuals from the best 1f fit clearly demonstrate the presence of the 2f term.

Fig. 2
Fig. 2

Lifetime measurements of ruthenium solution. (a) Time-domain lifetime measurement. (b) Phase shift and demodulation data of 1f component of detected luminescence signal. (c) Phase shift and demodulation of 2f component of detected luminescence signal.

Fig. 3
Fig. 3

Lifetime measurements of porphyrin phosphorescence. (a) Time-domain lifetime measurement. (b) Phase shift and demodulation of 1f component of detected phosphorescence. (c) Phase shift and demodulation of 2f component of detected phosphorescence.

Equations (5)

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d N e ( t ) d t + 1 τ N e ( t ) = 0
d N e ( t ) d t + 1 τ N e ( t ) = c L ( t ) 2
N e ( t ) = c N 0 [ a + b cos ( ω t ) ] 2 e t / τ = c N 0 2 [ 2 a 2 + b 2 + 4 a b cos ( ω t ) + b 2 cos ( 2 ω t ) ] e t / τ = c N 0 τ 2 [ 2 a 2 + b 2 + 4 a b 1 + ω 2 τ 2 cos ( ω t ϕ 1 ) + b 2 1 + 4 ω 2 τ 2 cos ( 2 ω t ϕ 2 ) ]
M 1 ( ω , τ ) = 4 a b ( 2 a 2 + b 2 ) 1 + ω 2 τ 2 4 a b 2 a 2 + b 2 = 1 1 + ω 2 τ 2
M 2 ( ω , τ ) = b 2 ( 2 a 2 + b 2 ) 1 + 4 ω 2 τ 2 b 2 2 a 2 + b 2 = 1 1 + 4 ω 2 τ 2

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