INVERSE SCATTERING-THEORY OF FOURIER-TRANSFORM INFRARED PHOTOACOUSTIC-SPECTROSCOPY

A new inverse scattering theory is introduced for the reconstruction o f optical density profiles in materials by constant scan rate (FTIR) p hotoacoustic spectroscopy. From the photoacoustic data, the inverse pr oblem reconstructs the heat flux profile induced in the sample by ligh t absorption, assuming the sample is thermally homogeneous. The invers e reconstruction uses a stable multilinear least-squares analysis base d on the newly developed expectation minimum method of Power and Pryst ay. A depth dependence of the optical density is obtained from the hea t flux profile and the sample's measured optical transmission. This ne w method exhibits robustness to the major experimental errors encounte red in constant scan rate FTIR photoacoustic spectroscopy, and exhibit s good reconstructive fidelity on heat flux profiles of arbitrary dept h dependence. Zero-order Tikhonov regularization was used as a referen ce method, and also yielded good results for profiles which varied con tinuously with depth. In the presence of flux discontinuities, the exp ectation minimum method gave superior reconstructions.