Validation test of Monte Carlo codes employed in biomedical optics applications

The Monte Carlo (MC) method is a gold standard for "solving" the radiative transport equation even in complex geometries and distributions of optical properties. The exact analytical benchmark provided by the invariant total mean path length law spent by light injected with uniform Lambertian illumination within nonabsorbing scattering media is used to verify Monte Carlo codes developed for biomedical optics applications. The correctness of an MC code can be evaluated with a sample t-test. In addition, the invariance of the mean path length ensures that the expected value is known regardless of the complexity of the medium. The accuracy of the estimated mean path length can progressively increase as the number of simulated trajectories increases. The method can be used regardless of the scattering and geometric properties of the medium, as well as in the presence of refractive index mismatch between the medium and the outer region and between different regions of the medium. The proposed method is particularly reliable for detecting inaccuracies in the treatment of finite media boundaries. The results presented in this contribution, obtained with a standard computer, show a verification of our MC code to the sixth decimal place. This method can provide a fundamental tool for verification of Monte Carlo codes in the geometry of interest without resorting to simpler geometries and uniform distribution of the scattering properties.