Analysis of photoacoustic waveforms using the nonlinear least squares method

Pulsed-laser photoacoustics is a technique which measures photoinduced enthalpic and volumetric changes on the nano- and microsecond timescales. Analysis of photoacoustic data generally requires deconvolution for a sum of exponentials, a procedure which has been developed extensively in the field of time-resolved fluorescence decay. Initial efforts to adapt an iterative nonlinear least squares computer program, utilizing the Marquardt algorithm, from the fluorescence field to photoacoustics indicated that significant modifications were needed. The major problem arises from the wide range of transient decay times which must be addressed by the photoacoustic technique. We describe an alternative approach to numerical convolution with exponential decays, developed to overcome the problems. Instead of using an approximation method (Simpson's rule) for evaluating the convolution integral, we construct a continuous instrumental response function by quadratic fitting of the discrete data and evaluate the convolution integral directly, without approximations. The success and limitations of this quadratic-fit convolution program are then demonstrated using simulated data. Finally, the program is applied to the analysis of experimental data to compare the resolution capabilities of two commercially available transducers. The advantages of a broadband, heavily damped transducer are shown for a standard organic photochemical system, the quenching of the triplet state of benzophenone by 2,5-dimethyl-2,4-hexadiene.