Heuristic model for ballistic photon detection in collimated transmittance measurements

An heuristic model for ballistic photon detection in continuous-wave measurements of collimated transmittance through a slab is presented. The model is based on the small angle approximation and the di usion equation and covers all the ranges of optical thicknesses of the slab from the ballistic to the di usive regime. The performances of the model have been studied by means of comparisons with the results of gold standard Monte Carlo simulations for a wide range of optical thicknesses and two types of scattering functions. For a non-absorbing slab and field of view of the receiver less than 3◦ the model shows errors less than 15% for any value of the optical thickness. Even for an albedo value of 0.9, and field of view of the receiver less than 3◦ the model shows errors less than 20%. These results have been verified for a large set of scattering functions based on the Henyey-Greenstein model and Mie theory for spherical scatterers. The latter has also been used to simulate the scattering function of Intralipid, a di usive material widely used as reference standard for tissue simulating phantoms. The proposed model represents an e ective improvement compared to the existing literature.