Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond

In this article we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we study a Volterra integral equation of the second kind that describes the shape transformation of propagating stress waves in the paraxial approximation of the underlying wave-equation. Expanding the optoacoustic convolution kernel in terms of a Fourier-series, a best fit to a pair of observed near-field and far-field signals allows to obtain a sequence of expansion coefficients that describe a given “apparative” setup. The resulting effective kernel is used to solve the optoacoustic source reconstruction problem using a Picard-Lindelöf correction scheme. We verify the validity of the proposed inversion protocol for synthetic input signals and explore the feasibility of our approach to also account for the shape transformation of signals beyond the paraxial approximation including the inversion of experimental data stemming from measurements on melanin doped PVA hydrogel tissue phantoms.