OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 4 — Apr. 1, 2009
« Show journal navigation

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

Sucbei Moon, Youngjae Won, and Dug Young Kim  »View Author Affiliations


Optics Express, Vol. 17, Issue 4, pp. 2834-2849 (2009)
http://dx.doi.org/10.1364/OE.17.002834


View Full Text Article

Acrobat PDF (374 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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 ~108 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

Along with the absorption and fluorescence emission spectra, the fluorescence lifetime provides useful spectroscopic information of the fluorescent molecule and its environment. The fluorescence lifetime measurement has become a very useful investigation tool for studying molecular behaviors by taking advantage of this property [1–5

1. 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).

]. Many fluorescent molecules are sensitive to specific ions of the local environment so that they can play useful roles of molecular ion sensors. And the fluorescence lifetime can also be used to measure the Förster (or fluorescence) resonance energy transfer (FRET) in a quantitative manner to investigate nanometric phenomena [5–8

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

]. Various applications of the lifetime measurements have been developed based on those principles for studying molecular mechanisms in biology, biophysics and diagnostics. In studying such a complicated biological system, fluorescence lifetime imaging microscopy (FLIM) techniques are preferably used to obtain spatially resolved lifetime information as a lifetime image. FLIM can easily visualize complicated molecular phenomena with a powerful spatial resolving capability. In those applications, it has been shown that the lifetime information has various advantages over the conventional methodologies based on fluorescence intensity in accuracy and specificity.

F=ΔττN
(1)

where 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

1. 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).

,9

9. K. Cralsson and J. Philip, “Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques,” Proc. SPIE 4622, 1605–7422 (2002).

,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]

]. Because of the fundamental shot noise, 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.

Lifetime measurement methods can be classified into three major groups by their physical implementation schemes: frequency-domain methods, time-domain methods and single-photon counting (SPC) methods [1

1. 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).

,3

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

,9

9. K. Cralsson and J. Philip, “Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques,” Proc. SPIE 4622, 1605–7422 (2002).

]. The SPC methodology is basically a time-domain approach but uses very different kinds of detection devices to those of the other two groups which are based on acquiring analog signals of fluorescence intensity directly. Analog methods usually exhibit worse accuracy and poorer photon economy compared to the SPC-based methods because of the worse temporal resolution and the lower noise immunity of the analog techniques. For analog methods, the performances can be enhanced by increasing the modulation and detection frequency or adopting wide-band measurement techniques such as using multiple frequencies in the frequency-domain method or using a high-speed digitizer in the time-domain method. But the technical difficulties increase the costs of implementations to achieve such an enhancement.

Several approaches have been developed to achieve higher measurement speeds in the SPC-based lifetime measurement methods. By the help of the recent progress in electronics, the TCSPC instrument has reached nearly the theoretical limit of photon counting rates with a short dead time. The state-of-the-art TCSPC unit now can handle up to ~106 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

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

]. Further enhancements are possible by utilizing multiple TCSPC units for a single measurement system [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]

,15

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]

]. As an alternative approach, the 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

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]

]. Because the arrival time of a photon is determined by discrete temporal gates instead of a real delay, the photon economy of this time-gating SPC is not as good as the conventional TCSPC and can vary widely by the ratio of the lifetime to the gate width. All of those SPC-based techniques are unlikely to obtain even higher measurement speeds far beyond 107 detected photon counts per second or 104 lifetime acquisitions per second for N≥1,000 to fulfill the speed requirement of the real-time FLIM imaging applications.

In this report, we propose a new high-speed fluorescence lifetime measurement method that exhibits a high accuracy and precision, aiming at the confocal or multi-photon FLIM applications. In our method, an analog fluorescence intensity signal is acquired in the time domain and the lifetime is determined by taking the mean temporal delay of the fluorescence intensity signal. Because our 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

Lifetime analysis based on a mean delay is not a totally new concept by itself but has been used in the TCSPC scheme as one of optional data analysis methods [13

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

]. The key point of our AMD method is that the fluorescence lifetime is determined directly from a measured analog signal taking advantage of the deconvolution-like characteristic of the mean delay. The effect of the finite bandwidth of the detection device can be eliminated effectively by this property. Thus the analog fluorescence signal can be acquired by using a relatively narrow-bandwidth photodetector and digitizing electronics without any concern of signal distortion. This solves the problem of implementation costs in two aspects: the costs of a high-resolution photodetector and those of signal processing electronics. In this section, the basic principles and the characteristics of the AMD method are introduced, starting from a classical linear time-invariant system model for an analog temporal waveform of fluorescence intensity.

2.1 Classical deconvolution

The formation of the photo-electron signal of fluorescence intensity can be understood as a linear time-invariant (LTI) process or simply, a linear process. For a fluorescence lifetime measurement, the signal formation consists of two parts: the fluorescence emission and the photodetection process. Each process can be denoted by an integral convolution operation in the linear system analysis. For a linear process, the output waveform 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

ie(t)=γ{Iex(t)Ψτ(t)Ipd(t)},
(2)

where ie(t) is the detected photocurrent, γ is the net conversion coefficient of an excitation photon to a detected photoelectron; Iex(t) is the intensity of an excitation pulse; Ψτ(t) is the exponential probability decay of fluorescence emission; and Ipd(t) is the impulse response of a photodetector. The integral convolution is represented by ⊗. The normalized fluorescence emission rate Ψτ is characterized by the fluorescence lifetime τ for a single exponential decay so that it is represented by Ψτ(t) = exp(-t/τ)/τ for t≥0 and Ψτ(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 ie(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.

Lifetime measurement can be performed in the modulation frequency domain as well as in the time domain. The frequency-domain methodology may be more practical due to its property of easy deconvolution. Note that the difficulty of extracting an accurate lifetime from an acquired signal arises from the fact that the desired signal of fluorescence emission rate Ψτ(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, iirf(t) can be measured by using photon emission or reflection phenomena of virtually zero lifetime so that

iirf(t)ie(t)|τ=0=γ{IexIpd(t)}.
(3)

The signal distortion caused by the system imperfection (iirfδ(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, Ψτ(t) can be retrieved in principle by

Ψτ(t)=1{{ie}(f){iirf}(f)}
(4)

where 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.

Under the assumption of a single exponential fluorescence decay, the Fourier transform of Eq. (2) yields a simple algebraic relation of the phase components and the lifetime or that of the amplitude components and the lifetime [1

1. 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).

]. The phase fluorometry takes advantage of this deconvolutional property, in which the convolution relation changes to a simple relation of the phase components in the frequency domain. In the phase fluorometry methods, the lifetime τf is determined by subtracting the IRF phase from the signal phase as

τf=12πftan(ϕ(f)ϕirf(f))
(5)

where ϕ and ϕirf 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.

2.2 AMD lifetime determination

The principle of deconvolution suggests an advantage of transforming the acquired signal into a certain domain where the convolution changes to a simple algebra. It can be generalized to the AMD method. A domain of statistical values can play such a role of deconvolution domain [23

23. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).

]. 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.

Fig. 1. Schematic timing plots of excitation, fluorescence emission and photodetection processes that occur serially in time. For a detected photoelectron, the final temporal delay is a summation of various random variables of time delays.

The arrival time of the final photoelectron at the signal acquisition instrument, Te, can be expressed by a summation of those delays defined in the above as

Te=(tex+Tex)+(Tre+Tfl+tfl)+(Tpd).
(6)

Three terms of the right-hand side in Eq. (6) correspond to the three major steps i.e. the physical processes of excitation, fluorescence emission and photodetection, respectively. And the PDFs of Te, Tex, (Tre+Tfl) and Tpd 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 Te to ie(t), Tex to Iex(t), (Tre + Tfl) to Ψτ(t), and Tpd to Ipd(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.

The lifetime can be determined accurately in a mean-delay domain by a deconvolutional process with pre-determined information of the 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, Te0 is represented by

Te0Te|Tre=0Tfl=0=(tex+Tex)+(tfl)+(Tpd).
(7)

And the mean value of Te0 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 T is denoted by 〈T〉. So, the IRD is denoted by 〈Te0〉. It is well known that the operation of taking an expected value is a linear operation [23

23. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).

]. 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

TeTe0=Tre+TflTfl=τ
(8)

is derived from Eq. (6) and Eq. (7). Here, we have neglected 〈Tre〉 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, 〈Tfl〉 is the fluorescence lifetime of 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 〈Te0〉. In an integral form for the time-domain signals of ie(t) and iirf(t), Eq. (8) is rewritten as

τ=TeTe0=(tie(t)dtie(t)dt)(tiirf(t)dtiirf(t)dt)
(9)

where ie(t) and iirf(t) are the acquired fluorescence signal and the IRF signal, respectively, which are the measured PDFs of Te and Te0 as defined in Eq. (2) and Eq. (3). In Eq. (9), all the integrations are definite integrations for an integration range of (t0, t1) by which both ie(t) and iirf(t) are bounded. Our AMD method of fluorescence lifetime measurement determines the lifetime by using Eq. (9) with acquired analog signals of ie(t) and iirf(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 (Tex, Tpd≠0) because of this deconvolutional property.

2.3 Precision of the AMD method

The precision of the AMD method can be analyzed by the basic principles of the statistics. The standard deviation of the measured lifetimes, denoted by Δτ, can be obtained from the variance of the mean delays, Δτ2. It is the variance of the expected value of the temporal delay τ for the PDF of fluorescence emission Ψτ(t). The variance of an expected value is the variance of the random variable divided by the number of the statistical samples [23

23. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).

]. 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

Δτ2=σ2[Tfl]=σ2[Tfl]N=τ2N
(10)

since Tfl has a PDF of an exponential decay distribution Ψτ(t) of which variance is the square of the expected value i.e. τ2. From Eq. (1) and Eq. (10), the figure of merit for our AMD method is 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.

Δttts2=σ2[(iTpdi)]
(11)

when the photodetector generates a set of photoelectrons, T1pd, T2pd, ⋯ TMpd for a single fluorescence photon. Because there are always a large number of photoelectrons (M>104) 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 Δτ2 can be derived in the same way as that of Eq. (10). It is given by Δttts 2/N for N detected fluorescence photons.

Amplitude noises of a high-gain photodetector also need to be considered to estimate the practical precision performance. As it is difficult to estimate the amount of the amplitude noises exactly, only a rough outline will be discussed in this estimation. Dark counts are usually the most dominant source of amplitude noises for a PMT. Here, the dark counts are defined collectively as all the high-amplitude noise pulses of which amplitudes are comparable to those of a single-photon response. For simplicity, let us assume that the dark counts have the same amplitude as that of the photon count and they are spread uniformly in time. When the total number of dark counts in a pulse period or a measurement period Tm is denoted by Nd, the effective number of dark counts found in the integration window is Nde = Ndε in average. Here, ε is the duty ratio of the integration window width ΔTw ≡ {t1-t0} to the pulse period Tm so that ε = ΔTw/Tm. We introduce a dark-count ratio RdNd/N that measures the relative noise power. Thus the effective number of the dark counts is Nde = NRdε inside the integration window. For the condition of a low dark-count rate i.e. Rd≪1 or NNd, the variance of the measured lifetime is derived as

Δτ2=σ2[(i=1NTei+j=1NdeTdj)(N+Nde)]
=(Nσ2[Te]+Ndeσ2[Td])(N+Nde)2
σ2[Te]N+1N(Rdε12ΔTw2)
(12)

where i and j are positive-integer indices; Tei or Te is the random time delay of a signal photon count; Tdj or Td is the random time delay of a noisy dark count; and ΔTw is the time width of the integration window, respectively. The variance of a uniform distribution function is 1/12 of the width ΔTw. 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.

The precision of the AMD method is determined by summing those error sources: the duration of the excitation pulse, the TTS of the photodetector, dark-count effect and the intrinsic random error caused by the fluorescence emission. Summing up all those partial variances, the variance of the measured mean delay is

Δτ2=1N(τ2+Δtex2+Δttts2+Rdε12ΔTw2)
(13)

when error sources other than mentioned in the above are neglected. Therefore, more practical estimation of the figure of merit, F′ for the AMD method is given by

F=1+1τ2{Δtex2+Δttts2+(Rd12ΔTwTm)ΔTw2}
(14)

as a function of fluorescence lifetime 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 ΔTw. It is important to take an integration window as small as possible, to obtain a good precision performance of a low figure of merit.

3. Experiment

Fig. 2. Schematic diagram of the experimental setup for fluorescence lifetime measurement.

A schematic diagram of the lifetime measurement system in the AMD method is illustrated in Fig. 2. The measurement system is constructed based on an epi-fluorescence microscope such that the fluorescence photons are collected backward by an objective lens that is simultaneously used for focusing excitation light. In our system, an excitation pulse at a wavelength of 635 nm was generated by a gain-switched semiconductor laser at a repetition rate of 2.7 MHz. The average output power of the laser was 15 μW. And the excitation light was delivered by a single-mode (SM) fiber to the main body of the measurement system.

After passing through a collimator lens, the excitation light passed through a band-pass filter (denoted by laser filter in Fig. 2), an optical beam splitter and an objective lens consecutively before it was launched onto a fluorescence sample. The emitted fluorescence light from the sample was collected by the objective lens and delivered backward to a multimode (MM) fiber via the beam splitter, a long-wavelength pass (LWP) filter, and a fiber-coupling lens. The core of the multimode (MM) fiber acted as a pin-hole and formed a confocal geometry with the core of the single-mode (SM) fiber. The multimode fiber was connected to a PMT. The photoelectronic signal from the PMT was acquired by a signal digitizer after passing through an electric low-pass filter (LPF). In addition, an electrical clock signal from the excitation pulse source (denoted by pulse clock in Fig. 2) was fed to the digitizer to synchronize it with the pulse laser. For the case of IRF measurements, a piece of flat glass plate was used as a sample, which acts as a mirror with a reflectivity of 4%. By removing the LWP filter and attenuating the light to the PMT, the IRF could be acquired successfully without changing the system significantly.

In our measurement system, the duration of the excitation pulse was 0.8 ns in full width at half maxima (FWHM) or 290 ps in standard-deviation duration. The numerical aperture of the objective lens was 0.4. The cut-on wavelength of the LWP filter was 650 nm for filtering out the residual excitation light. The core of the multimode (MM) fiber was 62.5 μm in diameter and formed a relatively loose pin-hole for a high photon collection efficiency. The PMT used in this study was a low-cost head-on type PMT (R7400U-20, Hamamatsu) that uses metal dynodes for electron gains. This PMT was measured to have an impulse response of 1.2 ns in FWHM that corresponds to an electric bandwidth of ~300 MHz. The signal digitizer (DSO6000, Agilent Technologies) used in this study has a maximum sampling rate of 2,000 mega-samples per second (MS/s) but was used intentionally in an operation mode of 100 MS/s for most of our experiments to simulate a low-cost digitizer. The sampling depth was 8 bits and supported 256 amplitude levels. The low-pass filter (LPF) was inserted only for the 100-MS/s sampling operation as an anti-aliasing filter. This filter is designed by the 5th-order Gaussian filter, of which 6-dB bandwidth of electric power transfer was evaluated to be 10 MHz [21

21. A. I. Zverev, Handbook of Filter Synthesis, (John Wiley & Sons, Hoboken, 2005).

]. Thus the electric bandwidth of the photodetection part is switched from ~300 MHz for the 2,000-MS/s case to 10 MHz for the 100-MS/s sampling case. By the Nyquist-Shannon sampling theorem, the full information must have been acquired effectively at those two sampling rates.

4. Results and discussion

The accuracy of our AMD method was evaluated by two different fluorophores: Alexa Fluor 633TM (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.

]. In our experiment, those fluorophores were diluted by PBS and were placed on glass plates as sample specimens respectively. Fig. 3 shows the signals acquired at an acquisition rate of 100 MS/s (a), and acquired at 2,000 MS/s (b), respectively, for Alexa Fluor 633. In each graph, a bold blue line represents the detected fluorescence signal and a dashed black line represents the IRF. Both of them have been waveform-averaged for high SNRs. The number of detected photons was approximately 100,000. Herein, the optical power was measured by an optical power meter (8153A, Agilent Technologies). The photon counting rate was calibrated for the PMT with CW irradiation of a laser operating at 635 nm. In this calibration process, the discrimination level for photon counting was set to be 1/3 of the mean amplitude of the pulse peaks for the single-photon response. A detected photon rate was estimated by the optical power in regard to the conversion factor that had been taken by that calibration process.

Fig. 3. Signals acquired at an acquisition rate of 100 MS/s (a), and acquired at 2,000 MS/s (b), respectively, for Alexa Fluor 633. Each pulse is normalized by the peak.

As seen in Fig. 3(b), a characteristic exponential decay curve is obtained by using a high-speed photodetector for an impulse-like excitation. Because of the finite response of the photodetector, the decay curve is slightly spread, being convolved with the IRF. In contrast, the detailed properties of the exponential decay are completely lost in Fig. 3(a) mainly due to the LPF (low-pass filter) installed after the PMT. The shape of the fluorescence response is almost equal to that of the IRF for this narrow-bandwidth case. However, a sufficient amount of information about the fluorescence lifetime is conveyed by the relative temporal delay. In our AMD method, this temporal delay is measured neglecting the other properties of the detected fluorescence signal as explained.

Our AMD method was applied both to the narrow-bandwidth signals acquired at a signal sampling rate of 100 MS/s and the wide-bandwidth signals acquired at 2,000 MS/s. The number of detected photons was 1.2×103 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 6.8×107 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 (ΔTw=56 ns). For the wide-bandwidth case (2,000 MS/s), a fixed integration window of a sufficiently large width (ΔTw≈8∙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.

Table 1. Fluorescence lifetimes obtained by the analog mean-delay method performed at the two different sampling rates and the phase fluorometry method.

table-icon
View This Table

The lifetimes obtained by our AMD method were compared with those of the conventional method of the phase fluorometry explained by Eq. (5). The measured IRFs and the fluorescence signals shown in Fig. 3 were Fourier-transformed to obtain frequency-domain responses. The phase components were extracted from them and the fluorescence lifetimes were calculated with the relative phase shifts by using Eq. (5) as functions of frequency. Single lifetime values averaged over a broad frequency range of 10–150 MHz were used as reference data to be compared to the results of our AMD method. Table 1 summarizes the comparison between the results of the AMD method performed at the two different sampling rates and those of phase fluorometry method. Only Small differences between the measured lifetimes of different methods were observed and successfully demonstrate the accuracy of our AMD method. Furthermore, results in Table 1 show that the results calculated from the narrow-bandwidth signals with a 100-MS/s sampling rate are almost same as those obtained from the wide-bandwidth signals taken at 2000 MS/s. This means that the accuracy of lifetime determinations has little dependency on the bandwidth of the measurement system in our AMD method.

Table 1 also shows the precision performance of our method for the narrow-bandwidth acquisition case (100 MS/s). The figure of merit was very good for a long fluorescence lifetime of 3.2 ns (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 ΔTw = 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 F. As Eq. (14) suggests, increasing the integration window width ΔTw 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.

The effect of the integration window width was further investigated for the case of 100 MS/s. For an IRF signal, the precision of the mean-delay determinations was estimated by the standard deviation Δτ for various window widths. And the speed of the convergence was also evaluated by introducing effective number of iterations, Niter. This is defined as the number of iterations required for Δτ to reach 110% of the final value that was obtained after 20 iterations. Thus Niter can be understood as a minimum number of iterations for an optimized precision. Fig. 4 shows the effect of the window width ΔTw for the iterative algorithm of mean-delay determination on the standard deviation Δτ and the minimum number of iterations Niter. 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.

Fig. 4. Effect of the integration window width ΔTw for the iterative algorithm of mean-delay determination on the standard deviation Δτ and the effective number of iterations Niter. The window width is normalized by the FWHM of the IRF, 45.2 ns.

The signal acquisition is very fast in our AMD method. Collecting a set of data for determining a 3.2-ns fluorescence lifetime with a ±3% random error (±110 ps) was completed in 17.8 μs or 48 pulse periods, in which ~1,200 detected photons were collected. This measurement rate is equivalent to signal acquisitions of a FLIM image composed of 100,000 pixels (~316×316 pixels) in 1.8 seconds. The acquisition speed can be further improved with ease by raising the excitation light intensity that will increase the fluorescence photon rate. For a single-channel TCSPC instrument, it takes longer than 100,000 pulse periods for a single lifetime determination to obtain an equivalent result. Even for 10 times higher excitation pulse rate of 27 MHz that is around the typical pulse rate, 3,700 μs needs to be spent to acquire a single lifetime determination with a TCSPC method. This indicates that the measurement speed of our AMD method is more than 2 orders of magnitude faster than that of the TCSPC scheme.

5. Conclusion

In this report, we have introduced a new fluorescence lifetime measurement scheme of the analog mean-delay (AMD) method for high-speed fluorescence lifetime measurements. The basic characteristics of our method have been investigated in both theory and experiment. Owing to the linear property of mean-delay analysis, the fluorescence lifetime can be accurately extracted from an analog signal which is acquired with a photodetection device whose impulse response is much longer than the lifetime to be measured. We have demonstrated that the measurement of this AMD method is so fast that lifetimes can be determined in a rate of ~105 measurements per second. The photon detection rate achieved in the experiment was on the order of ~108 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.

The most promising application of our AMD method would be the scanning FLIM microscopy such as a laser-scanning confocal microscope, multi-photon excitation microscope or a scanning near-field optical microscope (SNOM). The high-speed FLIM techniques based on gated intensifiers are not easily compatible with those scanning microscopes. The slow TCSPC has mainly been used for those applications so far. Our method can increase the imaging speed in these applications to ~1 frame per second with ease. Of course, the measurement speed, herein, means the signal acquisition speed and does not automatically mean that the lifetime is automatically calculated in real time. But the algorithm used in our method is very easy to be computed. There seems to be little technical difficulty for well-developed digital signal processors to compute the mean delays in real time for a relatively low sampling rate of 100 MS/s that corresponds to 100 MB/s in data rate for 8-bit digitization. Although our AMD method can only deal with a simple lifetime analysis of the single-exponential decay, those various advantages make it suitable for most of the FLIM applications.

Acknowledgments

This work was supported by the Creative Research Initiatives (CRI) Program of Korea Science and Engineering Foundation (KOSEF).

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 Handbook of Biological Confocal Microscopy, 3rd Ed., J. B. Pawley, ed. (Springer, New York, 2006).

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, 795–801 (2004). [CrossRef] [PubMed]

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]

5.

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

6.

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]

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 15, 18220–18235 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18220. [CrossRef] [PubMed]

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]

9.

K. Cralsson and J. Philip, “Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques,” Proc. SPIE 4622, 1605–7422 (2002).

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]

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]

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]

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]

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]

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]

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]

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]

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]

21.

A. I. Zverev, Handbook of Filter Synthesis, (John Wiley & Sons, Hoboken, 2005).

22.

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

23.

H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).

24.

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]

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:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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).
  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, 795-801 (2004). [CrossRef] [PubMed]
  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]
  5. E. A. Jares-Erijman and T. M. Jovin, "FRET imaging," Nat. Biotechnol. 21, 1387-1395 (2003). [CrossRef] [PubMed]
  6. 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]
  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 15, 18220-18235 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18220. [CrossRef] [PubMed]
  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]
  9. 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).
  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]
  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]
  12. 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]
  13. W. Becker and A. Bergmann, "Timing stability of TCSPC experiments," Proc. SPIE 6372, 637209 (2006). [CrossRef]
  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]
  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]
  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]
  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]
  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]
  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]
  21. A. I. Zverev, Handbook of Filter Synthesis (John Wiley & Sons, Hoboken, 2005).
  22. ISS, Inc, "Lifetime data of selected fluorophores," http://www.iss.com/resources/fluorophores.html.
  23. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd Ed., (Prentice-Hall, Upper Saddle River, 2002).
  24. 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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited