Developing the Techniques for Solving the Inverse Problem in Photoacoustics

Abstract

In this work, theoretically/mathematically simulated models are derived for the photoacoustic (PA) frequency response of both volume and surface optically-absorbing samples in a minimum volume PA cell. In the derivation process, the thermal memory influence of both the sample and the air of the gas column are accounted for, as well as the influence of the measurement chain. Within the analysis of the TMS model, the influence of optical, thermal, and elastic properties of the sample was investigated. This analysis revealed that some of the processes, characterized by certain sample properties, exert their dominance only in limited modulation frequency ranges, which are shown to be dependent upon the choice of the sample material and its thickness. Based on the described analysis, two methods are developed for TMS model parameter determination, i.e., sample properties which dominantly influence the PA response in the measurement range: a self-consistent procedure for solving the exponential problems of mathematical physics, and a well-trained three-layer perceptron with back propagation, based upon theory of neural networks. The results of the application of both inverse problem solving methods are compared and discussed. The first method is shown to have the advantage in the number of properties which are determined, while the second one is advantageous in gaining high accuracy in the determination of thermal diffusivity, explicitly. Finally, the execution of inverse PA problem is implemented on experimental measurements performed on macromolecule samples, the results are discussed, and the most important conclusions are derived and presented.