Estimation of fast fluorescence lifetimes with a single photon counting apparatus and the phase plane method

Abstract

The phase plane deconvolutlon method allows a rapld determlnation of the lifetimes of emlttlng electronically exclted states In the case of single exponentlal decays. We demonstrate that the phase plane method Is also suitable for more complex decays, when there Is a scattered light component or the sample exhibits a decay which Is ai sum of two exponentlals. Under these conditions, this technique Is very useful for the rapid determlnatlon of the parameters of the decays; In partlcular, It Is useful with mini-or mbrocomputers.with the following initial condition: u(0) = 0.By puttingrelationship 6 can be rewritten in the simpler form 1 (8)Relationship 8 can be rewritten as An important problem in many scientific fields is to extract the maximum information from the result of an experimental measurement. In particular, the accurate measurement offluorescence decays, obtained via the single photon counting technique, is crucial in the field of spectroscopy, chemical kinetics, analysis, photochemistry, and photophysics. In practice, the continuous fluorescence response function, u(t), is significantly distorted by the real time profile of the excitating flash, f ( t ) , and by the response function of the electronics, e(t). If z ( t ) is the real fluorescence time profile of the system exicited by a Dirac pulse, then we have the convolution product (eq 1) (the definitions of symbols appear in the Glossary at the end of this paper). (1)The recovery of z(t) from experimental fluorescence time profiles and g(t) == f(t)*e(t) can be achieved by using several techniques of deconvolution as explained previously (1,2). This paper will deal with the recent phase plane technique. THEORYSingle Exponcsntial Decay. Recently Greer, Reed, and Demas ( 3 , 4 ) have described a fast and accurate deconvolution technique: the "phase plane method". This technique allows the measurement of the lifetime, r, of emitting electronically excited states exhibiting the single exponential decaywhere A is a proportionality factor. We can write the convolution product asTaking the derivative of eq 4 leads toIntegration on both sides of this equation leads to (5) -Plotting u(t)/sg(t) vs. su(t)/sg(t) a t several values of the time t should lead to a straight line of slope -1 /~. The value of T is then determined by use of the least-squares fitting method.Biexponential Decay. Now we show here that the same method can also be used in the case of a biexponential decay (10)with zl(t) = Ale-t/TlPutting Ul(t) = g(t)*z,(t) u&) = g(t)*zz(t)the total fluorescence u ( t ) is given by u ( t ) = g(t)*z(t) = u1(t) + UJt)As previously (cf. ref 6), we can write By taking the derivative of these two equations and adding them, we get knowing that

Luminescence lifetime measurements. Elimination of phototube time shifts with the phase plane method

“…The data generation routines perform three major tasks: (1) generation of E(t), (2) generation of D(t) and R(t) from E(t), and (3) the addition of noise to simulate single photon counting (SPC) statistics. E(t) was generated from E(t) = exp(-f/A) -exp(-t/B); t > 0 (8) where the constants A and B are equal to 6.6 ns and 5.5 ns, respectively. This procedure yields a flash of approximately 14 ns fwhm and a general shape typical of actual excitation pulses (1).…”

Construction of an Inexpensive Subnanosecond Fluoriheter Using a Microcomputer

“…With some modification, the deconvolution of a double component system can also be accomplished. 13 In our deconvolution program, baselines were first subtracted from corresponding decay curves, and then baseline compensated curves were normalized. In this way, cross talk signals were effectively eliminated.…”

Pad�-Laplace method for the analysis of time-resolved fluorescence decay curves

“…A favorable characteristic of this problem is the possibility to control the level of noise and the ability to obtain rather dense sampling of the fluorescence intensity decay curve. Many methods of multicomponent decay curve analysis and deconvolution have been applied to this problem: i) The least squares method with iterative reconvolution (LS) (Grinvald and Steinberg 1974; ii) the method of moments (Isenberg and Dyson 1969); iii) the modulating functions method (Valeur and Moirez 1973); iv) the 102 Laplace transform method (Gafni et al 1975); v) the Fourier transform method (Wild 1983); vi) the phase plane method (Demas and Adamson 1971;Jezequel et al 1982); vii) the maximum likelihood method (Hall and Selinger 1981); viii) the global analysis approach (Eisenfeld and Ford 1979;Knutson et al 1983), and most recently ix) the maximum entropy method (Livesey and Brochon 1987). The very fact that so many methods have been used suggests that none of them is completely satisfactory.…”