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The Method of Moments is one of a series of closely related transform methods which have been developed primarily for the deconvolution and analysis of fluorescence decay data. The main distinguishing feature of the Method of Moments is that it has been designed to be robust with respect to several important nonrandom errors of instrumental origin. The historical development of the method is reviewed here. Several new extensions are also described, including a statistical theory, an improved global analysis, and a method for analyzing continuous distributions of lifetimes. The new statistical theory is the first to incorporate a combined treatment of exponential depression and moment index displacement, both necessary components of the Method of Moments. In comparisons with the more commonly used least squares iterative reconvolution (LSIR) approach, it is shown that, in analyses of ideal synthetic data with random noise, the Method of Moments gives deviations in recovered parameters which are slightly greater but essentially comparable to those found by the data fitting method. Real experimental data also contain nonrandom errors. In the presence of certain such errors, decay parameters recovered by the Method of Moments will be unaffected, whereas the least squares method may yield incorrect results, unless care is taken to fit all of the data errors. An example of the improved global analysis application of the Method of Moments is shown in which two rhodamine dyes with very close lifetimes are distinguished based on spectral data. Also, the use of the distribution analysis method is illustrated with the binding of the intercalating dye ethidium bromide to DNA and nucleosome core particles. At very low ionic strength the width and location of the lifetime distribution shows a time dependence, indicating time-dependent changes in the environment of the probe. Finally, examples of Method of Moments analyses are shown for a totally different kind of data, photoacoustic waveforms. Multiexponential decays can be resolved. A new version of the Method of Moments program (which runs under either DOS or OS/2 operating systems) will soon be available on request.
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