Recovery Of Fluorescence Lifetime Distributions Generated By Heterogeneous Systems

ABSTRACT The Maximum Entropy Method and a new Exponential Series Method are described and tested for the recovery of underlying fluorescence lifetime distributions from digital fluorescence decay data. These two numerical techniques are applied to two heterogeneous systems, the intramolecular quenching in 1,3-di(l-pyrenyl)propane and the cupric ion quenching of pyrene in a sodium dodecyl sulfate micellar system. In the former, the short lifetime region is characterized by a broad distribution, which as the temperature is lowered, shifts dramatically to long lifetimes. In the micellar system, a lifetime distribution following the predicted Poisson distribution is recovered at each of five cupric ion concentrations, a result that supports the model of quencher ions distributed in the micelles according to Poisson statistics. 1. INTRODUCTION The recovery of shapes of distributions of fluorescence lifetimes from fluorescence decay data presents a non-trivial problem in numerical analysis. Similar problems arise in light scattering1, image recovery in astrophysics2, tomography^, etc. While methods involving the minimization of Chi-squared (x2) are commonly used, the maximum entropy method (MEM) has recently gained popularity as the method of choice1"7. Inherent in the method theoretically is a 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. Up to 200 terms can be used in the trial function in the present version of MEM.The MEM maximizes the functionQ « S - XC (1) whereS - - E ak*n(ak/atot) (2)atot - £ ak np (Y - E E