Abstract
A linear programming (LP) method is applied to the analysis of multiexponential decay (in other words, to the Laplace inversion problem). This LP method is first tested on computer generated data (with and without noise) and then applied to the analysis of intensity correlation functions as measured by light beating spectroscopy. These examples show that the distribution of exponentials describing the multiexponential decay (i.e., its Laplace transform) can be correctly recovered by the LP method even when this distribution displays fine structures (e.g., close delta peaks superimposed on smooth distributions). A statistical study of the sequences of residuals is proposed which leads to an evaluation of the ‘‘goodness of fit’’ and to a practical choice of the maximum resolution retrievable for the exponential distribution. The capabilities of the LP method are discussed in view of the results previously obtained by other methods such as cumulants analysis or various least-squares procedures.
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