Deconvolution analytic continuation

If DAS reduces the problem to the monochromatic situation, the other approach proposed by Rundel is a deconvolution technique in which it is assumed that the action spectrum [which, in this case, can be defined as the biological weighting function (BWF) ] is an analytical continuous function e( ), and the predicted system response R to the ith irradiation regime E iX, t) can be expressed as a function, F, of the biologically active irradiance integrated over the irradiation time ... 

The experiments described above produce accurate decay constants only when sir is negligible. The apparent kinetic parameters that are obtained when this is not the case involve all of the k and W values simultaneously. It is not possible under these circumstances to obtain the actual decay constants from these experiments. Experimental methods have been developed, however, that allow extraction of the individual k and W values in the presence of slr. One method applies to the regime where sir is dominant, that is, W > k, whereas the other is applicable when W < k. The latter method has been applied to biopolymer ODMR and involves deconvolution of phosphorescence decays measured during continuous microwave saturation of pairs of triplet sublevels. Microwave saturation creates a pseudo-two-level system whose decays are easily deconvoluted and are amenable to analysis. The analytical development of the microwave-saturated phosphorescence decay method is rather lengthy, so it is not discussed in this chapter. Detailed descriptions of the method may be found elsewhere. 

A non-intrusive method for RTD characterization has been claimed [17], which has been proven already for visualization of velocity fields in microchannels [18]. Aphoto-activated fluorescent dye dissolved in an aqueous solution is introduced continuously into a flow. A defined section of the inlet channel is exposed to a UV pulse to activate the tracer, which turns fluorescent Due to this inside start of the pulse experiment, artifacts from peripheral equipment can be eliminated. The method generates almost ideal input signals, which simplifies the numerical treatment of experimental data. The new approach was found to be superior to various traditional injection methods. The ideal shape of the stimulus signal was demonstrated for an analytically well-defined straight channel and compared with a signal derived from deconvolution of non-ideal input signals [19]. 

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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