Reconvolution analysis

Single-photon silicon APDs possess a quantum efficiency ofca. 20-40% between 700 and 900 nm which compares very favorably with ca. 3% at best expected from an S20R or SI photocathode over this range. The lack of late-pulsing in an APD response as compared with a linear focused photomultiplier also has some virtues in the reconvolution analysis of fluorescence decay curves. 

In this work the main aspect has been concerned with the problem of electronic energy relaxation in polychro-mophoric ensembles of aromatic horaopolymers in dilute, fluid solution of a "good" solvent. In this morphological situation microscopic EET and trapping along the contour of an expanded and mobile coil must be expected to induce rather complex rate processes, as they proceed in typically low-dimensional, nonuniform, and finite-size disordered matter. A macroscopic transport observable, i.e., excimer fluorescence, must be interpreted, therefore, as an ensemble and configurational average over a convolute of individual disordered dynamical systems in a series of sequential relaxation steps. As a consequence, transient fluorescence profiles should exhibit a more complicated behavior, as it can be modelled, on the other hand, on the basis of linear rate equations and multiexponential reconvolution analysis. 

There are several analytical procedures available for derivation of relaxation information from time-resolved anisotropy experiments, the merits of which have been discussed at length elsewhere [25,112,114]. The salient points are covered here direct analysis of r(t) using a function such as Equation 2.31 is the most straightforward method but can become particularly problematic if the motion under study is comparable to the width of the excitation pulse [25,112,114]. Furthermore, as r(t) can suffer contamination from the polarizing effects of stray excitation from the source, particularly in weakly fluorescent samples, other methods are required to overcome such artifacts. Impulse reconvolution [115] allows mathematical removal of the instrumental pulse from the experimental data and involves an analysis of s(t) by a statistically adequate model function (e.g., Eq. 2.8). The best fit to s(t) is... 

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]. 

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