Verification test of Monte Carlo codes for biomedical optics applications with arbitrary accuracy

The Monte Carlo method is a gold standard for ``solving'' the radiative transport equation even in complex geometries and distributions of the optical properties. The exact analytical benchmark provided by the law of the invariant total mean pathlength spent by light injected with uniform Lambertian illumination inside non-absorbing scattering media is used to verify Monte Carlo codes developed for biomedical optics applications. The correctness of an MC code can be assessed with a one-sample t-test. Further, the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium. The results obtained show that the accuracy of the estimated average pathlength can be progressively increase as the number of simulated trajectories increases. The method can be applied in total generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatch between the medium and the external region and between different regions of the medium. The proposed verification method is especially reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this contribution, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. This method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.