Topic 2: The inverse OA problem
Here, our aim is to solve the optoacoustic (OA) source reconstruction problem in order to invert OA signals to inintial stress profiles and to infer the optical properties of the underlying material. Therefore we consider the OA problem in the paraxial approximation where the source reconstruction is achieved by the inverse solution of a Volterra integral equation.
The figure below illustrates an exemplary solution of the OA source reconstruction problem using a Picard-Lindelöff iteration scheme for synthetic input data (solid blue curve). As evident from the figure, the inverted signal (solid red curve) compares well to the true initial stress profile (solid black curve). The intermediate auxiliary stress profiles (dashed gray lines) feature a pronounced rarefaction dip that shifts outwards upon iteration. The iteration procedure is stopped as soon as the Chebychev-norm between two subsequent auxiliary profiles decreases below a fixed threshold.
In our numerical studies we also analyzed the effects of noise, detector-to-sample distance and finite detector size on the OA signals and the reconstructed initial stress profiles, see here.