Abstract

We investigate the photon efficiency of frequency-domain fluorescence lifetime imaging microscopy, using both theoretical and Monte Carlo methods. Our analysis differs from previous work in that it incorporates the data fitting process used in real experiments, allows for the arbitrary choice of excitation and gain waveforms, and calculates lifetimes as well as associated F-values from higher harmonics in the data. Using our analysis, we found different photon efficiencies to those previously reported and were able to propose optimal excitation and gain waveforms. Additionally, we suggest measurement protocols that lead to further improvement in photon efficiency. We compare our results to other techniques for lifetime imaging and consider the implications of our higher-harmonic analysis for multi-exponential lifetime determination.

© 2008 Optical Society of America

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  1. J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, K. W. Berndt, and M. Johnson, "Fluorescence lifetime imaging," Anal. Biochem. 202, 316-330 (1992).
    [CrossRef] [PubMed]
  2. K. Suhling, "Fluorescence lifetime imgaging," in Methods Express, Cell Imaging, D.Stephens, ed. (Scion, 2006), pp. 219-245.
  3. W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, "Fluorescence lifetime imaging by time-correlated single-photon counting," Microsc. Res. Tech. 63, 58-66 (2004).
    [CrossRef]
  4. W. Becker, H. Hickl, C. Zander, K. H. Drexhage, M. Sauer, S. Siebert, and J. Wolfrum, "Time-resolved detection and identification of single analyte molecules in microcapillaries by time-correlated single-photon counting (TCSPC)," Rev. Sci. Instrum. 70, 1835-1841 (1999).
    [CrossRef]
  5. K. Dowling, S. C. W. Hyde, J. C. Dainty, P. M. W. French, and J. D. Hares, "2-D fluorescence lifetime imaging using a time-gated image intensifier," Opt. Commun. 135, 27-31 (1997).
    [CrossRef]
  6. A. D. Elder, J. H. Frank, J. Swartling, X. Dai, and C. F. Kaminski, "Calibration of a wide-field frequency-domain fluorescence lifetime microscopy system using light emitting diodes as light sources," J. Microsc. 224, 166-180 (2006).
    [CrossRef]
  7. Q. S. Hanley, V. Subramaniam, D. J. Arndt-Jovin, and T. M. Jovin, "Fluorescence lifetime imaging: multi-point calibration, minimum resolvable differences, and artifact suppression," Cytometry 43, 248-260 (2001).
    [CrossRef] [PubMed]
  8. 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.
  9. C. J. de Grauw and H. C. Gerritsen, "Multiple time-gate module for fluorescence lifetime imaging," Appl. Spectrosc. 55, 670-678 (2001).
    [CrossRef]
  10. 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]
  11. M. Kölner and J. Wolfrum, "How many photons are necessary for fluorescence lifetime measurements?" Chem. Phys. Lett. 200, 199-204 (1992).
    [CrossRef]
  12. J. Philip and K. Carlsson, "Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging," J. Opt. Soc. Am. 20, 368-379 (2003).
    [CrossRef]
  13. K. Carlsson and J. Philip, "Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques," Proc. SPIE 4622, 70-78 (2002).
    [CrossRef]
  14. A. Esposito, T. Oggierc, H. C. Gerritsen, F. Lustenberger, and F. S. Wouters, "All-solid-state lock-in imaging for wide-field fluorescence lifetime sensing," Opt. Express 13, 9812-9821 (2005).
    [CrossRef] [PubMed]
  15. P. C. Schneider, and R. M. Clegg, "Rapid acquisition, analysis, and display of fuorescence lifetime-resolved images for real-time applications," Rev. Sci. Instrum. 68, 4107-4119 (1997).
    [CrossRef]
  16. F. R. Boddeke, "Quantitative fluorescence microscopy," Ph.D. dissertation (Technische Universiteit Delft, 1998).
  17. K. Beers, Numerical Methods for Chemical Engineering: Applications in MAT-LAB (Cambridge U. Press, 2006).
  18. A. Squire, P. J. Verveer, and P. I. H. Bastiaens, "Multiple frequency fluorescence lifetime imaging microscopy," J. Microsc. 197, 136-149 (2000).
    [CrossRef] [PubMed]
  19. A. D. Elder, S. M. Matthews, J. Swartling, K. Yunus, J. H. Frank, C. M. Brennan, A. C. Fisher, and C. F. Kaminski, "Application of frequency-domain fluorescence lifetime imaging microscopy as a quantitative analytical tool for microfluidic devices," Opt. Express 14, 5456-5467 (2006).
    [CrossRef] [PubMed]

2006

A. D. Elder, J. H. Frank, J. Swartling, X. Dai, and C. F. Kaminski, "Calibration of a wide-field frequency-domain fluorescence lifetime microscopy system using light emitting diodes as light sources," J. Microsc. 224, 166-180 (2006).
[CrossRef]

A. D. Elder, S. M. Matthews, J. Swartling, K. Yunus, J. H. Frank, C. M. Brennan, A. C. Fisher, and C. F. Kaminski, "Application of frequency-domain fluorescence lifetime imaging microscopy as a quantitative analytical tool for microfluidic devices," Opt. Express 14, 5456-5467 (2006).
[CrossRef] [PubMed]

2005

2004

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, "Fluorescence lifetime imaging by time-correlated single-photon counting," Microsc. Res. Tech. 63, 58-66 (2004).
[CrossRef]

2003

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

2002

K. Carlsson and J. Philip, "Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques," Proc. SPIE 4622, 70-78 (2002).
[CrossRef]

2001

Q. S. Hanley, V. Subramaniam, D. J. Arndt-Jovin, and T. M. Jovin, "Fluorescence lifetime imaging: multi-point calibration, minimum resolvable differences, and artifact suppression," Cytometry 43, 248-260 (2001).
[CrossRef] [PubMed]

C. J. de Grauw and H. C. Gerritsen, "Multiple time-gate module for fluorescence lifetime imaging," Appl. Spectrosc. 55, 670-678 (2001).
[CrossRef]

2000

A. Squire, P. J. Verveer, and P. I. H. Bastiaens, "Multiple frequency fluorescence lifetime imaging microscopy," J. Microsc. 197, 136-149 (2000).
[CrossRef] [PubMed]

1999

W. Becker, H. Hickl, C. Zander, K. H. Drexhage, M. Sauer, S. Siebert, and J. Wolfrum, "Time-resolved detection and identification of single analyte molecules in microcapillaries by time-correlated single-photon counting (TCSPC)," Rev. Sci. Instrum. 70, 1835-1841 (1999).
[CrossRef]

1997

K. Dowling, S. C. W. Hyde, J. C. Dainty, P. M. W. French, and J. D. Hares, "2-D fluorescence lifetime imaging using a time-gated image intensifier," Opt. Commun. 135, 27-31 (1997).
[CrossRef]

P. C. Schneider, and R. M. Clegg, "Rapid acquisition, analysis, and display of fuorescence lifetime-resolved images for real-time applications," Rev. Sci. Instrum. 68, 4107-4119 (1997).
[CrossRef]

1992

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, K. W. Berndt, and M. Johnson, "Fluorescence lifetime imaging," Anal. Biochem. 202, 316-330 (1992).
[CrossRef] [PubMed]

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

1989

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]

Anal. Biochem.

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, K. W. Berndt, and M. Johnson, "Fluorescence lifetime imaging," Anal. Biochem. 202, 316-330 (1992).
[CrossRef] [PubMed]

Anal. Chem.

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]

Appl. Spectrosc.

Chem. Phys. Lett.

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

Cytometry

Q. S. Hanley, V. Subramaniam, D. J. Arndt-Jovin, and T. M. Jovin, "Fluorescence lifetime imaging: multi-point calibration, minimum resolvable differences, and artifact suppression," Cytometry 43, 248-260 (2001).
[CrossRef] [PubMed]

J. Microsc.

A. D. Elder, J. H. Frank, J. Swartling, X. Dai, and C. F. Kaminski, "Calibration of a wide-field frequency-domain fluorescence lifetime microscopy system using light emitting diodes as light sources," J. Microsc. 224, 166-180 (2006).
[CrossRef]

A. Squire, P. J. Verveer, and P. I. H. Bastiaens, "Multiple frequency fluorescence lifetime imaging microscopy," J. Microsc. 197, 136-149 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

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

Microsc. Res. Tech.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, "Fluorescence lifetime imaging by time-correlated single-photon counting," Microsc. Res. Tech. 63, 58-66 (2004).
[CrossRef]

Opt. Commun.

K. Dowling, S. C. W. Hyde, J. C. Dainty, P. M. W. French, and J. D. Hares, "2-D fluorescence lifetime imaging using a time-gated image intensifier," Opt. Commun. 135, 27-31 (1997).
[CrossRef]

Opt. Express

Proc. SPIE

K. Carlsson and J. Philip, "Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques," Proc. SPIE 4622, 70-78 (2002).
[CrossRef]

Rev. Sci. Instrum.

P. C. Schneider, and R. M. Clegg, "Rapid acquisition, analysis, and display of fuorescence lifetime-resolved images for real-time applications," Rev. Sci. Instrum. 68, 4107-4119 (1997).
[CrossRef]

W. Becker, H. Hickl, C. Zander, K. H. Drexhage, M. Sauer, S. Siebert, and J. Wolfrum, "Time-resolved detection and identification of single analyte molecules in microcapillaries by time-correlated single-photon counting (TCSPC)," Rev. Sci. Instrum. 70, 1835-1841 (1999).
[CrossRef]

Other

K. Suhling, "Fluorescence lifetime imgaging," in Methods Express, Cell Imaging, D.Stephens, ed. (Scion, 2006), pp. 219-245.

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.

F. R. Boddeke, "Quantitative fluorescence microscopy," Ph.D. dissertation (Technische Universiteit Delft, 1998).

K. Beers, Numerical Methods for Chemical Engineering: Applications in MAT-LAB (Cambridge U. Press, 2006).

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Figures (11)

Fig. 1
Fig. 1

Schematic showing the processes involved in calculating an F-value for FD-FLIM.

Fig. 2
Fig. 2

Flow diagram showing the process followed by the Monte Carlo simulations.

Fig. 3
Fig. 3

Graph showing the F-value as a function of τ for sinusoidal excitation (modulation depth of 1.0) with sinusoidal gain (modulation depth of 1.0) for phase and modulation lifetimes. Both the theoretical results and Monte Carlo simulation data are shown, which are in good agreement.

Fig. 4
Fig. 4

Graph showing the F-value as a function of τ for Dirac excitation with sinusoidal gain (modulation depth of 1.0) for phase and modulation lifetimes. Both the theoretical and Monte Carlo simulation data sets are shown, and the agreement is excellent.

Fig. 5
Fig. 5

Graph of the F-value as a function of τ for Dirac excitation and sinusoidal excitation with sinusoidal gain (modulation depth of 1.0) and three phase steps.

Fig. 6
Fig. 6

Graph showing the F-value calculated from the first and third harmonics as a function of τ for square excitation with square gain for both phase and modulation lifetimes. The lifetime calculated from the third harmonic has a large F-value, indicating poor measurement quality.

Fig. 7
Fig. 7

Graph showing the F-value as a function of τ for Dirac excitation with square gain for phase and modulation lifetimes. The F-value data from higher harmonics are much better than for the case with square excitation.

Fig. 8
Fig. 8

Diagram explaining the location of “crossing points” and “peaks and troughs” for uneven phase step positioning.

Fig. 9
Fig. 9

Graph showing the phase F-value as a function of τ for Dirac excitation with sinusoidal gain (modulation depths of 1.0). The phase steps were clustered around the “crossing points” or “peaks and troughs” of the detected signal, with spreads of 5° and 10° shown for both phase and modulation lifetimes.

Fig. 10
Fig. 10

Comparison of the optimum F-values calculated for different operating parameters.

Fig. 11
Fig. 11

Graph showing how the mean of phase and modulation lifetimes can produce a lifetime measurement with an F-value better than that for either measurement alone. This is because the two measurements are taken in parallel. The case shown is Dirac excitation with square gain (compare to Fig. 7).

Equations (48)

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F = N σ τ τ .
t = 2 π T t * , τ = 2 π T τ * ,
f ( t ) = 1 τ exp ( t τ ) , t 0 ,
e ( t ) = 1 + j = 1 J m ex , j sin ( j t ) 2 π ,
2 π q ( t ) = 1 + j = 1 J m ex , j ( 1 + ( j τ ) 2 ) 1 2 ( sin ( j t α j ) ) ,
α j = arctan ( j τ ) .
q k = 0 2 π exp ( i k t ) q ( t ) d t .
q k = { 1 } k = 0 ,
q k = m ex , k ( 1 + ( k τ ) 2 ) ( k k ) { ( i + k τ 2 ) } k 0 .
q ( t ) = exp ( t τ ) τ ( 1 exp ( 2 π τ ) ) , 0 t < 2 π .
q k = 1 1 + i k τ .
E ( g ( t ) ) = 0 2 π g ( t ) p ( t ) d t .
E ( X i ) = 0 2 π ( a + j = 1 J b j sin ( j ( t ϕ i g ) ) ) q ( t ) d t .
E ( X i ) = a + j = 1 J ( b j m ex , j 2 ( 1 + ( j τ ) 2 ) 1 2 ) cos ( j ϕ i g α j ) .
E ( X i ) = a + j = 1 J b j cos ( j ϕ i g ξ j ) ( 1 + ( j τ ) 2 ) 1 2 ,
ξ j = arctan ( 1 j τ ) .
E ( X i 2 ) = 0 2 π ( a + j = 1 J b j sin ( j ( t ϕ i g ) ) ) 2 q ( t ) d t .
E ( X i 2 ) = q 0 a 2 + 2 a j = 1 J ( b j m ex , j 2 ( 1 + ( j τ ) 2 ) 1 2 ) cos ( j ϕ i g α j ) + j = 1 J k = 1 J b j b k 2 R [ exp ( ( j k ) ϕ i g i ) q ( k j ) exp ( ( j + k ) ϕ i g i ) q ( j + k ) ] .
y i = a 1 + j = 1 H a 2 j cos ( j ϕ i g a 3 j ) .
ϕ spl j = a 3 j , m spl j = a 2 j a 1 .
y i = θ 1 + j = 1 H ( θ 2 j x i 1 , j + θ 3 j x i 2 , j ) .
θ ̱ LS = [ ( X T X ) 1 X T ] y ̱ ,
X = ( x ̱ 1 x ̱ 2 x ̱ N ) , x ̱ i = ( 1 x i 1 , 1 x i 2 , 1 x i 1 , H x i 2 , H ) .
θ ̱ LS = ( θ 1 θ 2 1 θ 3 1 θ 2 H θ 3 H ) = ( 1 N i = 1 N y i 2 N i = 1 N y i cos ( ϕ i g ) 2 N i = 1 N y i sin ( ϕ i g ) 2 N i = 1 N y i cos ( H ϕ i g ) 2 N i = 1 N y i sin ( H ϕ i g ) ) .
U j = 2 N i = 1 N N p X i sin ( j ϕ i g ) ,
V j = 2 N i = 1 N N p X i cos ( j ϕ i g ) ,
W = 1 N i = 1 N N p X i .
μ i = N p E ( X i ) , σ i 2 = N p E ( X i 2 ) ,
E ( U j ) = 2 N i = 1 N [ μ i sin ( j ϕ i g ) + E ( σ i Y i sin ( j ϕ i g ) ) ] .
E ( U j ) = 2 N i = 1 N μ i sin ( j ϕ i g ) .
E ( U j 2 ) = 4 N 2 E ( i = 1 N k = 1 N ( μ i μ k + μ i σ k Y k + μ k σ i Y i + σ i σ k Y i Y k ) sin ( j ϕ i g ) sin ( j ϕ i g ) ) .
E ( U j 2 ) = E ( U j ) 2 + 4 N 2 i = 1 N ( σ i 2 ) sin 2 ( j ϕ i g ) .
j τ p j = tan ( ϕ spl j ) .
j τ p j = θ 3 j θ 2 j .
τ m j = ( ( m gain j m ex j 2 m spl j ) 2 1 ) 1 2 .
j τ m j = ( ( θ 1 2 m gain j 2 m ex j 2 4 ( θ 2 j 2 + θ 3 j 2 ) ) 1 ) 1 2 .
1 j τ p j = θ 3 j θ 2 j ,
j τ m j = ( ( θ 1 2 m gain j 2 θ 2 j 2 + θ 3 j 2 ) 1 ) 1 2 .
j τ p j = U j V j = μ u j + σ u j Y u j μ v j + σ v j Y v j ,
U j V j = μ u j μ v j ( 1 + κ u j Y u j κ v j Y v j κ u j κ v j Y u j Y v j + κ v j 2 Y v j 2 + ) .
E ( τ p j ) = 1 j μ u j μ v j ( 1 ρ u v j κ u j κ v j + κ v j 2 + ) ,
j τ m j = ( ( μ w + σ w Y w ) 2 z j ( μ u j + σ u j Y u j ) 2 z j ( μ v j + σ v j Y v j ) 2 z j ( μ u j + σ u j Y u j ) 2 + z j ( μ v j + σ v j Y v j ) 2 ) 1 2 .
z j = 4 m ex j 2 m gain j 2 .
β k j 2 = ( σ k j 2 μ w 2 z j μ u j 2 z j μ v j 2 ) ,
γ k j = ( 2 μ k j σ k j μ w 2 z j μ u j 2 z j μ v j 2 ) ,
δ k j 2 = ( σ k j 2 μ u j 2 + μ v j 2 ) ,
ϵ k j = ( 2 μ k j σ k j μ u j 2 + μ v j 2 ) ,
F = N N p σ τ τ .

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