Forward-adjoint fluorescence model: Monte Carlo integration and experimental validation

The adjoint form of the photon transport equation is applied to a generalized fluorescence detection problem, and its accuracy is empirically tested. This approach can be interpreted as mathematically reversing the temporal flow of fluorescent photons; that is, they are tracked from the detector back to potential sites of origin in the scattering medium. The result is a distribution of potential fluorescing sites that, when properly normalized, gives a probability field of the relative importance of the photon starting position and direction to the resulting signal. This adjoint solution can be combined with the temporally forward-derived distribution of absorbed excitation photons to evaluate the fluorescence excitation detection scheme. This bypasses the normal, temporal derivation wherein the fluorescence transport solution is dependent on the result of the excitation transport solution.