Iterative reconvolution

The fluorescence quenching of Pe and derivatives has been investigated by fluorescence upconversion. Excitation was performed with the frequency-doubled output of a Ti Sapphire amplifier. The instrument response time was around 240 fs with 0.4 mm thick samples. The data were analysed by iterative reconvolution of the instrument response function with trial functions. For most samples, measurements were carried out at three different wavelengths (438, 475, and 490 nm). Global fits were done with all the available data. 

At last, the finite width of the excitation pulse is accounted by a non linear least square iterative reconvolution procedure. Thus, a good precision on r(t) can be achieved if ... 

The decay law G(t) was extracted from the experimental decay curve using nonlinear least-squares iterative reconvolution. The parameters were varied until the xl values were minimised and initially the trial function for G(t) was chosen to be a sum of 10 exponential terms viz... 

Fluorescence decay profiles are analysed as a sum of up to three exponentials by an iterative reconvolution procedure which has been described elsewhere (17-19) and is based on the Marquardt algoritlim. Goodness of fit is judged by inspection of the weighted residuals, autocorrelation function of the weighted residuals, reduced chi-square value and the Durbin-Watson parameter. 

Although deconvolution is a well defined mathematical procedure, its application to fluorescence decay curves is attended with numerous difficulties owing to the cormting enors and instmmental distortions that accompany sin e photon counting data. It is now generally accepted that least squares iterative reconvolution is the most satisfactory method of analysing nanosecond decay data In its simplest... 

Ultrafast transient absorption spectra and kinetics were obtained with a pump-probe apparatus with 1 ps resolution previously described.[30] Solutions with an absorbance of about. 3 at 610 mn (2 mm pathlength cells) were used. Kinetic parameters were obtained by iterative reconvolution of the data with least squares fitting using the Levenberg-Marquardt algorithm. 

The analysis involved deconvolution by iterative reconvolution, background subtraction, and optional correction for shift of the instrument response function. Statistical tests included chi-square, the Durbin-Watson test, the covariance matrix, a runs test, and the autocorrelation function [6]. An alternative form of data analysis involves distributions of lifetimes rather than a series of exponentials. Differentiation of systems obeying a decay law made up of three discrete components from systems where there exists a continuous distribution of lifetimes, or a distribution plus one or more discrete components, is a nontrivial analytical problem. Methods involving the minimization of the chi-square parameter are commonly used, but recently the maximum entropy method (MEM) has gained popularity [7]. Inherent in the MEM method is the theoretical lack of bias and the potential for recovering the coefficients of an exponential series with fixed lifetimes which are free of correlation effects and artificial oscillations. Recent work has compared the MEM with a new version of the exponential series method (ESM) which allows use of the same size probe function as the MEM and found that the two methods gave comparable results [8]. 

The fluorescence decay measurements were obtained from room-temperature, degassed solutions of the polymers in benzene by the technique of time-correlated, single photon counting using a laser-excited time-resolved fluorescence spectrometer described previously [8]. The fluorescence decay analyses required iterative reconvolution with the finite instrumental response function [8]. 

In practice, initial guesses of the fitting parameters (e.g. pre-exponential factors and decay times in the case of a multi-exponential decay) are used to calculate the decay curve the latter is reconvoluted with the instrument response for comparison with the experimental curve. Then, a minimization algorithm (e.g. Marquardt method) is employed to search the parameters giving the best fit. At each step of the iteration procedure, the calculated decay is reconvoluted with the instrument response. Several softwares are commercially available. 

The fluorescence intensity was analyzed by an iterative nonlinear least-squares reconvolution of the instrument response function and biexponential decays of the form... 

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