Breakdown of the continuum limit approximation to the discrete scattering events and its influence on the electric field autocorrelation functions of transmitted light

摘要

The complexity of modeling light propagation in turbid media can be significantly simplified if one assumes it to be diffusive. This is, however, only valid after the light has traveled a sufficient distance so that the diffusion equation can be employed. So far, there has been no reliable way to determine this distance, despite the fact that the assumption is often applied in optics. The discrete nature of scattering events plays an important role in modeling propagation of weakly scattered light, so a continuum equation such as the diffusion equation cannot be used to describe this process. Electric field autocorrelation functions g1(t) of light transmitted through turbid colloidal samples are measured using diffusing wave spectroscopy and compared to Monte Carlo simulations in order to obtain a better estimation of the continuum limit. The two methods to calculate g1(t) from the simulated photon trajectories are compared; the first assumes the continuum limit by using the path-length distributions of photon trajectories, while the second considers the square momentum transfers and therefore accurately calculates g1(t) even if the detected signal is composed of weakly scattered light. The results of the two methods are used to determine the lengths of the shortest diffuse photon trajectories; they grow with the sample thickness and scattering anisotropy.