Inverse scattering theory of Fourier transform infrared photoacoustic spectroscopy

Abstract

A new inverse scattering theory is introduced for the reconstruction of optical density profiles in materials by constant scan rate (FTIR) photoacoustic spectroscopy. From the photoacoustic data, the inverse problem reconstructs the heat flux profile induced in the sample by light absorption, assuming the sample is thermally homogeneous. The inverse reconstruction uses a stable multilinear least-squares analysis based on the newly developed expectation minimum method of Power and Prystay. A depth dependence of the optical density is obtained from the heat flux profile and the sample's measured optical transmission. This new method exhibits robustness to the major experimental errors encountered in constant scan rate FTIR photoacoustic spectroscopy, and exhibits good reconstructive fidelity on heat flux profiles of arbitrary depth dependence. Zero-order Tikhonov regularization was used as a reference method, and also yielded good results for profiles which varied continuously with depth. In the presence of flux discontinuities, the expectation minimum method gave superior reconstructions.