Analysis of photoacoustic waveforms using the Method of Moments

In many ways, the analysis of waveforms from pulsed-laser photoacoustics is analogous to the analysis of timeresolved fluorescence data obtained from single-photon counting techniques. We have shown previously that the Method of Moments can be used to analyze photoacoustic data (E.W. Small et al., Fluorescence Detection III, E.R. Menzel, ed., SPIE Proceedings 1054, pp. 36-53, 1989). Difficulties arose in attempts to analyze the magnitude of very fast decays, those with lifetimes less than the digitization channel width. While these decays may often be regarded as an error such as scatter in the case of fluorescence, they represent important fast relaxation processes in the case of photoacoustics, and their magnitude must be accurately determined. We present here three approaches to making the Method of Moments more applicable to photoacoustic waveform analysis. One approach involves using the method required for measuring a scatter component in a fluorescence decay. Other approaches include using a Cheng-Eisenfeld filter to fix a lifetime in order to recover its amplitude, and analyzing for MDO (moment index displacement 0), which is intrinsically sensitive to short lifetimes. The relative merits of the techniques are evaluated, and a successful approach to analyzing noisy synthetic data of up to three components is demonstrated. Preliminary studies on the performance of the Method of Moments in handling nonrandom errors in photoacoustic data are also shown.