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.