Approximations of the measurable quantity in diffuse optical problems: theoretical analysis of model deviations.

Photon density and photon flux are widely used to model the measurable quantity in diffuse optical tomography problems. However, it is not these two quantities that are actually measured, but rather the radiance accepted by the detection system. We provide a theoretical analysis of the model deviations related to the choice of the measurable quantity-either photon density or flux. By using the diffusion approximation to the radiative transfer equation and its solution with extrapolated boundary conditions, an exact analytical expression of the measurable quantity has been obtained. This expression has been employed as a reference to assess model deviation when considering the photon density or the photon flux as the measurable quantity. For the case of semi-infinite geometry and for both continuous wave and time domains, we show that the photon density approximates the measurable quantity better than the photon flux. We also demonstrate that the validity of this approximation strongly depends on the optical parameters.