Maximum entropy method for frequency domain fluorescence lifetime analysis. 1. Effects of frequency range and random noise.

The maximum entropy method (MEM) provides a self-modeling fit to data in which minimization of the χ(2) goodness-of-fit parameter is coupled with maximization of a statistical entropy function. We have found that MEM provides an excellent visual description of the uncertainties, errors, and limitations associated with the distributions which it recovers. To more accurately interpret fluorescence lifetime distributions recovered by the MEM from frequency domain lifetime data, a detailed examination of the effects of frequency range, noise, data set size, and sample heterogeneity was carried out for both simulated and real data. Results clearly demonstrate that the frequency range in which data are collected can affect the number and nature of the fluorescence lifetime components that are recovered by MEM, and the quality of the data at the frequencies that are optimal for a given lifetime is also crucial. Expansion of sufficient data sets to include more frequencies, or more replicates at the same frequencies, provides little improvement over the original data set when the lifetimes are well-windowed by the frequency range. Synergism among multiple components in a sample can affect the recovered distribution, by shifting and splitting poorly windowed components and broadening the recovered peaks for all components. These effects are related to the number of components for which evidence must be found.