Quantitative point source photoacoustic inversion formulas for scattering and absorbing media

We present here an expression for the photoacoustic contribution of an optical point source in a diffusive and absorbing medium. By using this measurement as a reference, we present a direct inversion formula that recovers the absorption map quantitatively, at the same time accounting for instrumental factors such as the source strength, the shape of the optical pulse, and the impulse response and finite size of the transducers. We further validate this expression through accurate numerical simulations showing that the absorption map is recovered quantitatively in the presence of a rotating geometry. We finally discuss how the presented solutions for point sources within the photoacoustic problem enable the use of concurrent fluorescence and ultrasound measurements as appropriate for a hybrid tomographic system. The proposed system could retrieve absorption information using photoacoustic measurements, and use these data to more accurately describe the fluorescence problem and improve reconstruction fidelity.