Direct calculation with a finite-element method of the Laplace transform of the distribution of photon time of flight in tissue

Reconstruction methods for optical tomographic imaging require the development of models of light transport in highly scattering materials. While the simulation of the full temporal response function arising from a short source light pulse is computationally expensive, there are methods to evaluate efficiently certain transforms of the temporal profile. We previously presented methods to obtain directly the Mellin Transform, which is related to the moments of the temporal intensity distribution; We introduce a similar method to calculate directly the Laplace transform. This method provides an addtional, largely independent measurement type that can be combined with the moments to improve image quality in optical tomography, in particular with respect to the simultaneous reconstruction of absorption and scattering distribution.