## Analog mean-delay method for high-speed fluorescence lifetime measurement

Optics Express, Vol. 17, Issue 4, pp. 2834-2849 (2009)

http://dx.doi.org/10.1364/OE.17.002834

Acrobat PDF (374 KB)

### Abstract

We present a new high-speed lifetime measurement scheme of analog mean-delay (AMD) method which is suitable for studying dynamical time-resolved spectroscopy and high-speed fluorescence lifetime imaging microscopy (FLIM). In our lifetime measurement method, the time-domain intensity signal of a fluorescence decay is acquired as an analog waveform. And the lifetime information is extracted from the mean temporal delay of the acquired signal. Since this method does not rely on the single-photon counting technique, the signals of multiple fluorescence photons can be acquired simultaneously. The measurement speed can be increased easily by raising the fluorescence intensity without a photon-rate limit. We have investigated various characteristics of our method in lifetime accuracy and precision as well as measurement speed. It has been found that our method can provide excellent measurement performances in various aspects. We have demonstrated a high-speed measurement with a high photon detection rate of ~10^{8} photons per second with a nearly shot noise-limited photon economy. A fluorescence lifetime of 3.2 ns was accurately determined with a standard deviation of 3% from the data acquired within 17.8 μs at a rate of 56,300 lifetime determinations per second.

© 2009 Optical Society of America

## 1. Introduction

5. E. A. Jares-Erijman and T. M. Jovin, “FRET imaging,” Nat. Biotechnol. **21**, 1387–1395 (2003). [CrossRef] [PubMed]

*τ*,

*Δτ*and

*N*are the lifetime, the standard deviation of the measured lifetimes and the number of detected photons involved with a lifetime determination, respectively [1,9,10

10. H. C. Gerritsen , M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc. **206**, 218–224 (2002). [CrossRef] [PubMed]

*F*is always larger than one for all the lifetime measurements in general. The number of photons required for a given signal-to-noise ratio (SNR) is proportional to the square of

*F*. Therefore, a sufficiently low figure of merit is indispensable for a sensitive measurement of fluorescence lifetime.

3. Klaus Suhling, Paul M. W. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. **4**, 13–22 (2005). [CrossRef]

^{6}photon counts per second [12

12. W. Becker, A. Bergmann, M.A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. **63**, 58–66 (2003). [CrossRef] [PubMed]

13. W. Becker and A. Bergmann, “Timing stability of TCSPC experiments,” Proc. SPIE **6372**, 637209 (2006). [CrossRef]

12. W. Becker, A. Bergmann, M.A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. **63**, 58–66 (2003). [CrossRef] [PubMed]

15. D. McLoskey, D. J. S. Birch, A. Sanderson, K. Suhling, E. Welch, and P. J. Hicks, “Multiplexed single-photon counting. I. A time-correlated fluorescence lifetime camera,” Rev. Sci. Instrum. **67**, 2228–2237 (1996). [CrossRef]

*time-gating SPC*method has been introduced for higher measurement speeds, which can detect more than one photon for a fluorescence decay being separated by intervals larger than the impulse response of the photodetector [10

10. H. C. Gerritsen , M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc. **206**, 218–224 (2002). [CrossRef] [PubMed]

17. C. J. de Grauw and H. C. Gerritsen, “Multiple time-gate module for fluorescence lifetime imaging,” Appl. Spectrosc. **55**, 670–678 (2001), http://www.opticsinfobase.org/as/abstract.cfm?URI=as-55-6-670. [CrossRef]

^{7}detected photon counts per second or 10

^{4}lifetime acquisitions per second for

*N*≥1,000 to fulfill the speed requirement of the real-time FLIM imaging applications.

*F*=6 under normal operation conditions [1]. The analog time-domain method is more straightforward in its concept and has been popular in many applications. But its accuracy is critically limited by the temporal resolution of the time-domain measurement means. Without using expensive high-speed detection devices such as a streak camera [16

16. R. V. Krishnan, H. Saitoh, H. Terada, V. E. Centonze, and B. Herman, “Development of a multiphoton fluorescence lifetime imaging microscopy system using a streak camera,” Rev. Sci. Instrum. **74**, 2714–2721 (2003). [CrossRef]

3. Klaus Suhling, Paul M. W. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. **4**, 13–22 (2005). [CrossRef]

4. P. Herman, H.-J. Lin, and J. R. Lakowicz, “Lifetime-based imaging” in *Biomedical Photonics Handbook*,
T. Vo-Dinh, ed. (CRC Press, Boca Raton, 2003). [CrossRef]

8. D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, “High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events,” Opt. Express **15**, 15656–15673 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15656. [CrossRef] [PubMed]

19. J. Requejo-Isidro, J. McGinty, I. Munro, D. S. Elson, N. P. Galletly, M. J. Lever, M. A. A. Neil, G. W. H. Stamp, P. M. W. French, P. A. Kellett, J. D. Hares, and A. K. L. Dymoke-Bradshaw, “High-speed wide-field time-gated endoscopic fluorescence-lifetime imaging,” Opt. Lett. **29,**2249–2251 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-19-2249. [CrossRef]

20. A. Esposito, T. Oggier, H. Gerritsen, F. Lustenberger, and F. Wouters, “All-solid-state lock-in imaging for wide-field fluorescence lifetime sensing,” Opt. Express **13**, 9812–9821 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9812. [CrossRef] [PubMed]

19. J. Requejo-Isidro, J. McGinty, I. Munro, D. S. Elson, N. P. Galletly, M. J. Lever, M. A. A. Neil, G. W. H. Stamp, P. M. W. French, P. A. Kellett, J. D. Hares, and A. K. L. Dymoke-Bradshaw, “High-speed wide-field time-gated endoscopic fluorescence-lifetime imaging,” Opt. Lett. **29,**2249–2251 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-19-2249. [CrossRef]

8. D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, “High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events,” Opt. Express **15**, 15656–15673 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15656. [CrossRef] [PubMed]

11. T. H. Chia, A. Williamson, D. D. Spencer, and M. J. Levene, “Multiphoton fluorescence lifetime imaging of intrinsic fluorescence in human and rat brain tissue reveals spatially distinct NADH binding,” Opt. Express **16**, 4237–4249 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-4237. [CrossRef] [PubMed]

14. A. Schönle, M. Glatz, and S. W. Hell, “Four-dimensional multiphoton microscopy with time-correlated single-photon counting,” Appl. Opt. **39**, 6306–6311 (2000), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-34-6306. [CrossRef]

16. R. V. Krishnan, H. Saitoh, H. Terada, V. E. Centonze, and B. Herman, “Development of a multiphoton fluorescence lifetime imaging microscopy system using a streak camera,” Rev. Sci. Instrum. **74**, 2714–2721 (2003). [CrossRef]

18. E.-S. Kwak, T. J. Kang, and D. A. Vanden Bout, “Fluorescence lifetime imaging with near-field scanning optical microscopy,” Anal. Chem. **73**, 3257–3262 (2001). [CrossRef] [PubMed]

*analog mean-delay (AMD) method*does not rely on the photon-counting technique but uses analog signals, the signals of multiple fluorescence photons can be detected simultaneously without any limit. The measurement speed can be enhanced easily by increasing the fluorescence intensity and can reach the excitation rate in theory. The accuracy of our AMD method is independent of the response time of the photodetector or the electronics used in the system. By the theoretical and experimental investigations, we have also found that our AMD method has an excellent photon economy that is comparable to that of the conventional TCSPC. These results suggest that our AMD method is very suitable for high-speed applications of lifetime measurements for its good performances of accuracy, precision and measurement speed.

## 2. Theory of operation

13. W. Becker and A. Bergmann, “Timing stability of TCSPC experiments,” Proc. SPIE **6372**, 637209 (2006). [CrossRef]

### 2.1 Classical deconvolution

*g*(

*t*) is represented by the input function

*f*(

*t*) convolved with the characteristic function of the system,

*h*(

*t*), known as the impulse response function where

*t*is the coordinate variable of time. This well-known relation is expressed as

*g*(

*t*) =

*f*(

*t*)⊗

*h*(

*t*)= ∫

^{+∞}

_{-∞}

*f*(

*t*′)∙

*h*(

*t*-

*t*′)

*dt*′ in an integral form. The final signal of the detected fluorescence response is determined by the two convolution operations in the analog fluorescence signal measurement. Due to the commutative property of the convolution operation, the final electrical signal can be represented by the convolution of three functions: the intensity profile of excitation light as an input function, the exponential decay function of a fluorescence emission and the impulse response of the photodetector as the impulse response functions of the fluorescence emission and photodetection processes, respectively. The acquired photocurrent signal is represented by

*i*(

_{e}*t*) is the detected photocurrent,

*γ*is the net conversion coefficient of an excitation photon to a detected photoelectron;

*I*(

_{ex}*t*) is the intensity of an excitation pulse; Ψ

_{τ}(

*t*) is the exponential probability decay of fluorescence emission; and

*I*(

_{pd}*t*) is the impulse response of a photodetector. The integral convolution is represented by ⊗. The normalized fluorescence emission rate Ψ

_{τ}is characterized by the fluorescence lifetime

*τ*for a single exponential decay so that it is represented by Ψ

_{τ}(

*t*) =

*exp*(-

*t*/

*τ*)/

*τ*for

*t*≥0 and Ψ

_{τ}(

*t*)=0 for

*t*<0. The fluorescence lifetime

*τ*is the characteristic time constant of the decay function as well as the time average of the function, which is called the mean lifetime. A lifetime measurement method has a way of extracting the lifetime value of

*τ*from the acquired raw signal of

*i*(

_{e}*t*). In general, the fluorescence decay may consist of multiple decays with multiple lifetime components. But the mean lifetime of a single value is usually of the prime interest in most of the applications.

_{τ}(

*t*) is contaminated by the convolution processes: The molecule is excited by an excitation pulse of a non-zero duration and the analog signal is detected by a photodetector of a finite impulse response. Because the convolution process is an analytic process, the inverse process called as

*deconvolution*can not be done easily in the time domain. The Fourier analysis of a linear system suggests that such a deconvolution process can be performed with ease in the frequency domain. The signal processing in practice can be done by either Fourier-transforming the acquired time-domain signal or measuring the response directly in the frequency domain as the phase fluorometer does. The deconvolution process requires the knowledge of the system characteristic known as

*instrumental response function*(IRF) defined in the time domain or

*instrumental transfer function*(ITF) defined in the frequency domain

*i.e.*the Fourier conjugate of the IRF. This function of IRF,

*i*(

_{irf}*t*) can be measured by using photon emission or reflection phenomena of virtually zero lifetime so that

*i*≠

_{irf}*δ*(

*t*)) can be compensated in the deconvolutional signal processing by using the knowledge of the IRF for a measurement system. For an analog time-domain method, the actual fluorescence emission rate, Ψ

_{τ}(

*t*) can be retrieved in principle by

*f*is the frequency reciprocal to

*t*, ℑ represents the Fourier transform, and ℑ

^{-1}represents the inverse transform, respectively. The major drawback of this approach is clearly observed in Eq. (4). Because the IRF is band-limited in practice, the measured response is divided by zero at the outside of the valid frequency range. And the SNR consequently decreases after the deconvolution process. In terms of implementation costs, this method requires a time-domain acquisition device of a high sampling rate and a high temporal resolution for measuring short lifetimes. And the digital Fourier transform (DFT) is a computationally heavy process and may be improper for real-time calculations.

*τ*is determined by subtracting the IRF phase from the signal phase as

_{f}*ϕ*and

*ϕ*denote the phase of the fluorescence signal and that of the IRF with respect to the excitation moment, respectively. For a multi-frequency measurement, the multiple lifetimes obtained as a function of frequency can be averaged to make a single measured value of enhanced precision. So, the effect of the measurement system can be neutralized by measuring the relative phase shift of a fluorescence signal by this manner.

_{irf}### 2.2 AMD lifetime determination

*deconvolution*domain [23]. The convolution of probability distribution functions (PDFs) corresponds to a summation operation of the corresponding random variables and consequently, that of the corresponding expected values. We could take advantage of this property for a simplified deconvolution and determining the lifetime from a degraded analog signal.

*T*, can be expressed by a summation of those delays defined in the above as

_{e}*i.e.*the physical processes of excitation, fluorescence emission and photodetection, respectively. And the PDFs of

*T*,

_{e}*T*, (

_{ex}*T*+

_{re}*T*) and

_{fl}*T*correspond to the temporal shapes of the finally detected electric pulse, excitation light pulse, fluorescence decay and the impulse response of the photodetector, respectively. Thus they have one-to-one relationships of

_{pd}*T*to

_{e}*i*(

_{e}*t*),

*T*to I

_{ex}*(*

_{ex}*t*), (

*T*+

_{re}*T*) to Ψ

_{fl}_{τ}(

*t*), and

*T*to

_{pd}*I*(

_{pd}*t*), in Eq. (2) and Eq. (6). Note that the analog signals acquired in practice are not exact PDFs but histograms with random errors. They are not distinguished in this paper for simplicity.

*instrumental response delay*(IRD) that corresponds to the IRF given by Eq. (3). The IRF is measured in keeping the optical and electric paths identical to those of the fluorescence signal acquisitions. For a photoelectron of the IRF, the final delay,

*T*is represented by

_{e}^{0}*T*will be called the IRD of the measurement system, which contains the mean-delay information of the measurement system. In this paper, the mean value of a random variable

_{e}^{0}*T*is denoted by 〈

*T*〉. So, the IRD is denoted by 〈

*T*〉. It is well known that the operation of taking an expected value is a linear operation [23]. Thus subtracting the IRD from the mean value of the temporal delays of the detected photoelectrons given by Eq. (6) yields the mean temporal delay of the fluorescence emission as

_{e}^{0}*T*〉 because the relaxation delay is on the order of picoseconds, much smaller than the fluorescence lifetime that is usually on the order of nanoseconds. The mean delay of fluorescence emission, 〈

_{re}*T*〉 is the fluorescence lifetime of

_{fl}*τ*for the case of single exponential decays. For the case of multi-exponential decays, it is the intensity-weighted average of multiple lifetimes. Thus the lifetime is determined by obtaining the mean delay of the fluorescence signal with respect to the IRD of 〈

*T*〉. In an integral form for the time-domain signals of

_{e}^{0}*i*(

_{e}*t*) and

*i*(

_{irf}*t*), Eq. (8) is rewritten as

*i*(

_{e}*t*) and

*i*(

_{irf}*t*) are the acquired fluorescence signal and the IRF signal, respectively, which are the measured PDFs of

*T*and

_{e}*T*as defined in Eq. (2) and Eq. (3). In Eq. (9), all the integrations are definite integrations for an integration range of (

_{e}^{0}*t*,

_{0}*t*) by which both

_{1}*i*(

_{e}*t*) and

*i*(

_{irf}*t*) are bounded. Our AMD method of fluorescence lifetime measurement determines the lifetime by using Eq. (9) with acquired analog signals of

*i*(

_{e}*t*) and

*i*(

_{irf}*t*). In this method, an accurate fluorescence lifetime is measured in the mean-delay domain where the effect of the IRF can be easily eliminated by calibrating its systematic mean delay of the IRD. The accuracy of the AMD method is no more hampered by the system imperfection (

*T*,

_{ex}*T*≠0) because of this deconvolutional property.

_{pd}### 2.3 Precision of the AMD method

*Δτ*, can be obtained from the variance of the mean delays,

*Δτ*. It is the variance of the expected value of the temporal delay

^{2}*τ*for the PDF of fluorescence emission Ψ

_{τ}(

*t*). The variance of an expected value is the variance of the random variable divided by the number of the statistical samples [23]. In denoting the variance of a random variable

*T*with

*σ*

^{2}[

*T*], the variance of a fluorescence lifetime measured with

*N*detected photons can be represented by

*T*has a PDF of an exponential decay distribution Ψ

_{fl}_{τ}(

*t*) of which variance is the square of the expected value

*i.e. τ*. From Eq. (1) and Eq. (10), the figure of merit for our AMD method is

^{2}*F*= 1 in the case of the ideal condition of exciting the molecules with an impulse-like pulse and detecting the signal with negligibly small noises and timing jitters. Hence, the theoretical performance of the AMD method is the same with that of the TCSPC scheme in their photon economies.

*T*,

^{1}_{pd}*T*, ⋯

^{2}_{pd}*T*for a single fluorescence photon. Because there are always a large number of photoelectrons (M>10

^{M}_{pd}^{4}) for a fluorescence photon, the TTS is independent of the impulse response of the photodetector and should be measured for sets of photoelectrons as Eq. (11). The contribution to the total variance

*Δτ*can be derived in the same way as that of Eq. (10). It is given by

^{2}*Δt*

_{tts}^{2}/

*N*for

*N*detected fluorescence photons.

*T*is denoted by

_{m}*N*, the effective number of dark counts found in the integration window is

_{d}*N*=

_{d}^{e}*N*∙

_{d}*ε*in average. Here,

*ε*is the duty ratio of the integration window width

*ΔT*≡ {

_{w}*t*-

_{1}*t*} to the pulse period

_{0}*T*so that

_{m}*ε*=

*ΔT*/

_{w}*T*. We introduce a dark-count ratio

_{m}*R*≡

_{d}*N*/

_{d}*N*that measures the relative noise power. Thus the effective number of the dark counts is

*N*=

_{d}^{e}*N*∙

*R*∙

_{d}*ε*inside the integration window. For the condition of a low dark-count rate

*i.e. R*≪1 or

_{d}*N*≫

*N*, the variance of the measured lifetime is derived as

_{d}*i*and

*j*are positive-integer indices;

*T*or

_{e}^{i}*T*is the random time delay of a signal photon count;

_{e}*T*or

_{d}^{j}*T*is the random time delay of a noisy dark count; and

_{d}*ΔT*is the time width of the integration window, respectively. The variance of a uniform distribution function is 1/12 of the width

_{w}*ΔT*. In the last line of Eq. (12), the first term of the right-hand side represents the intrinsic variance of the fluorescence photon signal and the second term corresponds to the contribution of the dark counts.

_{w}*F′*for the AMD method is given by

*τ*to be measured from Eq. (1) and Eq. (13). This photon economy characteristic is similar to that of the TCSPC. But it may degrade further due to other amplitude noises that are almost absent in the case of single-photon counting. Note that the figure of merit in Eq. (14) depends on ~3/2’th power of the window width

*ΔT*. It is important to take an integration window as small as possible, to obtain a good precision performance of a low figure of merit.

_{w}## 3. Experiment

*ΔT*for a given dark-count rate as Eq. (14) suggests. The optimization of the width of the integration needs to be carefully concerned in the implementation of the AMD method.

_{w}*t*,

_{0}*t*) in Eq. (9) is defined by an integration window of a finite width in our signal processing. Shorter the window width is, larger the deterministic error may reside in the obtained mean delay. On the contrary, the amount of random errors is roughly proportional to the window width

_{1}*ΔT*as Eq. (13) and Eq. (14) suggest. Care is needed to find the optimal size of the integration window. Fortunately, the amount of the final deterministic error is negligibly small for the case of narrow-bandwidth acquisitions when the fluorescence lifetime is much smaller than the width of the system impulse response. The deterministic error found in the delay of the fluorescence signal is almost the same as that of the IRF for that case because their shapes are very similar to each other. Thus those deterministic errors are canceled out in the final relative mean delay of the measured lifetime. This issue of optimal window size will be discussed again in the next section.

_{w}## 4. Results and discussion

^{TM}(Invitrogen) and CY5 (Amersham Biosciences). It is known that Alexa Fluor 633 has a relatively long lifetime of 3.2 ns in water and CY5 has a short lifetime of 1.0 ns in phosphate buffered saline (PBS) [22

22. ISS, Inc, “Lifetime data of selected fluorophores,” http://www.iss.com/resources/fluorophores.html.

^{3}in average for a single lifetime determination. Each fluorescence waveform was acquired by averaging 48 measured pulses to obtain this number of photons. Since we operated the pulse laser at a repetition rate of 2.7 MHz or a pulse period of 370 ns, it takes 17.8 μs to acquire a signal dataset. In total, the average photon detection rate was 6.8×10

^{7}detected photons per second. For the narrow-bandwidth case (100 MS/s), the iterative algorithm was used for mean-delay determination. The number of iterations was set to be 10, which was sufficiently large for convergence. The width of the integration window was 1.24 times the FWHM of the IRF (Δ

*T*=56 ns). For the wide-bandwidth case (2,000 MS/s), a fixed integration window of a sufficiently large width (Δ

_{w}*T*≈8∙

_{w}*τ*) was used without the iteration algorithm. The lifetime was determined repeatedly 113 times in the same condition. And the whole measurement was repeated for the other fluorophore, CY5 as well.

*F*= 1.2), almost reaching the theoretical limit. It is significantly degraded for a short lifetime of 0.9 ns (

*F*= 2.5) but shows an acceptable level of precision. On the other hand, we have observed that the figure of merit obtained for CY5 (

*τ*= 0.9 ns) was

*F*= 1.6 in the case of the wide-bandwidth acquisition (2,000 MS/s) for

*ΔT*= 8 ns. Therefore, it is believed that the long integration window of 56 ns in the 100-MS/s case had caused the increase in

_{w}*F*. As Eq. (14) suggests, increasing the integration window width

*ΔT*results in the increase in the figure of merit for a given dark-count rate. It implies that the photon economy might be enhanced by using a photodetector of a low noise count rate.

_{w}*τ*for various window widths. And the speed of the convergence was also evaluated by introducing

*effective number of iterations*,

*N*. This is defined as the number of iterations required for Δ

_{iter}*τ*to reach 110% of the final value that was obtained after 20 iterations. Thus

*N*can be understood as a minimum number of iterations for an optimized precision. Fig. 4 shows the effect of the window width

_{iter}*ΔT*for the iterative algorithm of mean-delay determination on the standard deviation

_{w}*Δτ*and the minimum number of iterations

*N*. It is clear that a smaller number of iterations are required for a wide window width. Hence, a wider integration window is preferred in terms of computing speed. Fig. 4 also shows that the precision of calculated mean delay is optimized for a window width which is approximately the width of the IRF. It must be obvious that a significant amount of photon signal is lost for a very narrow window, and additional noise counts are included for an excessively wide window.

_{iter}## 5. Conclusion

^{5}measurements per second. The photon detection rate achieved in the experiment was on the order of ~10

^{8}detected photons per second. In theory, the measurement speed can be increased up to the repetition rate of a pulsed excitation light just by increasing the excitation power. This high measurement speed can enable fast image acquisitions in FLIM, which can visualize the fast-varying dynamic features of a biological sample. Even though the practically achievable measurement rate might be limited by the finite power of the excitation source or by the photobleaching effect of fluorophores, the absence of the maximum photon rate would be still beneficial. In a TCSPC-based FLIM system, cautious operating conditions must be satisfied in order to optimize both the photon counting rate and the accuracy performance. We have also shown that the accuracy and precision of our AMD method are comparable with those of the TCSPC method. For a long fluorescence lifetime of a few nanoseconds, the figure of merit can nearly reach the theoretical limit. An additional benefit of our AMD method is that these attractive features are obtained with low-cost electronic components of low bandwidths and sampling rates.

## Acknowledgments

## References and Links

1. | H. C. Gerristen, A. Draaijer, D. J. van den Heuvel, and A. V. Agronskaia, “Fluorescence lifetime imaging in scanning microscopy” in |

2. | D. Elson, J. Requejo-Isidro, I. Munro, F. Reavell, J. Siegel, K. Suhling, P. Tadrous, R. Benninger, P. Lanigan, J. McGinty, C. Talbot, B. Treanor, S. Webb, A. Sandison, A. Wallace, D. Davis, J. Lever, M. Neil, D. Phillips, G. Stamp, and P. French, “Time-domain fluorescence lifetime imaging applied to biological tissue,” Photochem. Photobiol. Sci. |

3. | Klaus Suhling, Paul M. W. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. |

4. | P. Herman, H.-J. Lin, and J. R. Lakowicz, “Lifetime-based imaging” in |

5. | E. A. Jares-Erijman and T. M. Jovin, “FRET imaging,” Nat. Biotechnol. |

6. | D. K. Nair, M. Jose, T. Kuner, W. Zuschratter, and R. Hartig, “FRET-FLIM at nanometer spectral resolution from living cells,” Opt. Express |

7. | W. Zhong, M. Wu, C. Chang, K. A. Merrick, S. D. Merajver, and M. Mycek, “Picosecond-resolution fluorescence lifetime imaging microscopy: a useful tool for sensing molecular interactions in vivo via FRET,” Opt. Express |

8. | D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, “High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events,” Opt. Express |

9. | K. Cralsson and J. Philip, “Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques,” Proc. SPIE |

10. | H. C. Gerritsen , M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc. |

11. | T. H. Chia, A. Williamson, D. D. Spencer, and M. J. Levene, “Multiphoton fluorescence lifetime imaging of intrinsic fluorescence in human and rat brain tissue reveals spatially distinct NADH binding,” Opt. Express |

12. | W. Becker, A. Bergmann, M.A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. |

13. | W. Becker and A. Bergmann, “Timing stability of TCSPC experiments,” Proc. SPIE |

14. | A. Schönle, M. Glatz, and S. W. Hell, “Four-dimensional multiphoton microscopy with time-correlated single-photon counting,” Appl. Opt. |

15. | D. McLoskey, D. J. S. Birch, A. Sanderson, K. Suhling, E. Welch, and P. J. Hicks, “Multiplexed single-photon counting. I. A time-correlated fluorescence lifetime camera,” Rev. Sci. Instrum. |

16. | R. V. Krishnan, H. Saitoh, H. Terada, V. E. Centonze, and B. Herman, “Development of a multiphoton fluorescence lifetime imaging microscopy system using a streak camera,” Rev. Sci. Instrum. |

17. | C. J. de Grauw and H. C. Gerritsen, “Multiple time-gate module for fluorescence lifetime imaging,” Appl. Spectrosc. |

18. | E.-S. Kwak, T. J. Kang, and D. A. Vanden Bout, “Fluorescence lifetime imaging with near-field scanning optical microscopy,” Anal. Chem. |

19. | J. Requejo-Isidro, J. McGinty, I. Munro, D. S. Elson, N. P. Galletly, M. J. Lever, M. A. A. Neil, G. W. H. Stamp, P. M. W. French, P. A. Kellett, J. D. Hares, and A. K. L. Dymoke-Bradshaw, “High-speed wide-field time-gated endoscopic fluorescence-lifetime imaging,” Opt. Lett. |

20. | A. Esposito, T. Oggier, H. Gerritsen, F. Lustenberger, and F. Wouters, “All-solid-state lock-in imaging for wide-field fluorescence lifetime sensing,” Opt. Express |

21. | A. I. Zverev, |

22. | ISS, Inc, “Lifetime data of selected fluorophores,” http://www.iss.com/resources/fluorophores.html. |

23. | H. Stark and J. W. Woods, |

24. | S. Moon and D. Y. Kim, “Analog single-photon counter for high-speed scanning microscopy,” Opt. Express |

**OCIS Codes**

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

(170.6920) Medical optics and biotechnology : Time-resolved imaging

(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence

(300.6500) Spectroscopy : Spectroscopy, time-resolved

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: December 18, 2008

Revised Manuscript: February 9, 2009

Manuscript Accepted: February 10, 2009

Published: February 11, 2009

**Virtual Issues**

Vol. 4, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Sucbei Moon, Youngjae Won, and Dug Young Kim, "Analog mean-delay method for high-speed fluorescence lifetime measurement," Opt. Express **17**, 2834-2849 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-4-2834

Sort: Year | Journal | Reset

### References

- H. C. Gerristen, A. Draaijer, D. J. van den Heuvel, and A. V. Agronskaia, "Fluorescence lifetime imaging in scanning microscopy" in Handbook of Biological Confocal Microscopy, 3rd Ed., J. B. Pawley, ed. (Springer, New York, 2006).
- D. Elson, J. Requejo-Isidro, I. Munro, F. Reavell, J. Siegel, K. Suhling, P. Tadrous, R. Benninger, P. Lanigan, J. McGinty, C. Talbot, B. Treanor, S. Webb, A. Sandison, A. Wallace, D. Davis, J. Lever, M. Neil, D. Phillips, G. Stamp, and P. French, "Time-domain fluorescence lifetime imaging applied to biological tissue," Photochem. Photobiol. Sci. 3, 795-801 (2004). [CrossRef] [PubMed]
- Klaus Suhling, Paul M. W. French, and D. Phillips, "Time-resolved fluorescence microscopy," Photochem. Photobiol. Sci. 4, 13-22 (2005). [CrossRef]
- P. Herman, H.-J. Lin, and J. R. Lakowicz, "Lifetime-based imaging" in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, Boca Raton, 2003). [CrossRef]
- E. A. Jares-Erijman and T. M. Jovin, "FRET imaging," Nat. Biotechnol. 21, 1387-1395 (2003). [CrossRef] [PubMed]
- D. K. Nair, M. Jose, T. Kuner, W. Zuschratter, and R. Hartig, "FRET-FLIM at nanometer spectral resolution from living cells," Opt. Express 14, 12217-12229 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-25-12217. [CrossRef] [PubMed]
- W. Zhong, M. Wu, C. Chang, K. A. Merrick, S. D. Merajver, and M. Mycek, "Picosecond-resolution fluorescence lifetime imaging microscopy: a useful tool for sensing molecular interactions in vivo via FRET," Opt. Express 15, 18220-18235 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18220. [CrossRef] [PubMed]
- D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, "High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events," Opt. Express 15, 15656-15673 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15656. [CrossRef] [PubMed]
- K. Cralsson and J. Philip, "Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques," Proc. SPIE 4622, 70-78 (2002).
- H. C. Gerritsen, M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, "Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution," J. Microsc. 206, 218-224 (2002). [CrossRef] [PubMed]
- T. H. Chia, A. Williamson, D. D. Spencer, and M. J. Levene, "Multiphoton fluorescence lifetime imaging of intrinsic fluorescence in human and rat brain tissue reveals spatially distinct NADH binding," Opt. Express 16, 4237-4249 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-4237. [CrossRef] [PubMed]
- 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 (2003). [CrossRef] [PubMed]
- W. Becker and A. Bergmann, "Timing stability of TCSPC experiments," Proc. SPIE 6372, 637209 (2006). [CrossRef]
- A. Schönle, M. Glatz, and S. W. Hell, "Four-dimensional multiphoton microscopy with time-correlated single-photon counting," Appl. Opt. 39, 6306-6311 (2000), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-34-6306. [CrossRef]
- D. McLoskey, D. J. S. Birch, A. Sanderson, K. Suhling, E. Welch, and P. J. Hicks, "Multiplexed single-photon counting. I. A time-correlated fluorescence lifetime camera," Rev. Sci. Instrum. 67, 2228-2237 (1996). [CrossRef]
- R. V. Krishnan, H. Saitoh, H. Terada, V. E. Centonze, and B. Herman, "Development of a multiphoton fluorescence lifetime imaging microscopy system using a streak camera," Rev. Sci. Instrum. 74, 2714-2721 (2003). [CrossRef]
- C. J. de Grauw and H. C. Gerritsen, "Multiple time-gate module for fluorescence lifetime imaging," Appl. Spectrosc. 55, 670-678 (2001), http://www.opticsinfobase.org/as/abstract.cfm?URI=as-55-6-670. [CrossRef]
- E.-S. Kwak, T. J. Kang, and D. A. Vanden Bout, "Fluorescence lifetime imaging with near-field scanning optical microscopy," Anal. Chem. 73, 3257 -3262 (2001). [CrossRef] [PubMed]
- J. Requejo-Isidro, J. McGinty, I. Munro, D. S. Elson, N. P. Galletly, M. J. Lever, M. A. A. Neil, G. W. H. Stamp, P. M. W. French, P. A. Kellett, J. D. Hares, and A. K. L. Dymoke-Bradshaw, "High-speed wide-field time-gated endoscopic fluorescence-lifetime imaging," Opt. Lett. 29, 2249-2251 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-19-2249. [CrossRef]
- A. Esposito, T. Oggier, H. Gerritsen, F. Lustenberger, and F. Wouters, "All-solid-state lock-in imaging for wide-field fluorescence lifetime sensing," Opt. Express 13, 9812-9821 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9812. [CrossRef] [PubMed]
- A. I. Zverev, Handbook of Filter Synthesis (John Wiley & Sons, Hoboken, 2005).
- ISS, Inc, "Lifetime data of selected fluorophores," http://www.iss.com/resources/fluorophores.html.
- H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).
- S. Moon and D. Y. Kim, "Analog single-photon counter for high-speed scanning microscopy," Opt. Express 16, 13990-14003 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13990. [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.