Curvature correction and Mie scattering in Monte Carlo analysis of propagating focused Gaussian beam in scattering media
We introduce curvature correction to set the photon-step size and initial photon distribution in the focusing lens aperture to account for the effect of the radius of curvature of a Gaussian beam propagated towards a scattering medium. It improves the accuracy of the Monte Carlo simulation results with decreasing step size s and increasing number of steps Ns. In the absence of scattering, the axial beam distribution approaches the prediction of the scalar diffraction theory for a given numerical aperture NA, s, and Ns based on the Linfoot's criteria. Mie scattering theory is employed to calculate the particle radius, density, and phase distribution needed for a desired degree of scattering and anisotropy. Ray-tracing algorithms are used to determine the scattering events. We discuss how the simulation performs for random scattering media consisting of spherical scatterers based on the obtained axial intensity and mean free path, and explore its behavior in periodic media.