The Pade–Laplace Extrapolated Approximation of the Multi-Exponential Decay Kinetics of Molecular Fluorescence

Abstract

A method was proposed for multi-exponential approximation of the fluorescence decay kinetics. Unlike the well-known Prony technique, the method is suitable for analyzing large-scale experimental data arrays. The method differs from the Pade–Laplace approximation applied previously in that the Pade coefficients are calculated more accurately. The exponential parameters can be found if the following four conditions are satisfied: (1) there are no more than eight exponentials in the kinetic curve, (2) τa 4h, and (4) the noise level is kept below a critical value. It is noteworthy that the critical value depends on the sum N of exponentials, i.e., the greater the sum N is, the lower the noise level is. T is the time domain for which the kinetic curve has been measured; h = T/n; n is the number of points that represent the kinetic curve; τa = max (τ1, τ2, …, τN); τi = min (τ1, τ2, …, τN); τk is the time constant for the kth exponential; and k = 1, 2, …, N.