Abstract
Past work has demonstrated the value of a random walk theory (RWT) to solve multiple-scattering problems arising in numerous contexts. This paper’s goal is to investigate the application range of the RWT using Monte Carlo simulations and extending it to anisotropic media using scaling laws. Meanwhile, this paper also reiterates rules for converting RWT formulas to real physical dimensions, and corrects some errors which appear in an earlier publication. The RWT theory, validated by the Monte Carlo simulations and combined with the scaling law, is expected to be useful to study multiple scattering and to greatly reduce the computation cost.
Highlights
Multiple-scattering represents a fundamental scientific problem, with implications in a wide spectrum of practical applications ranging from biological imaging [1] to dense spray diagnostics [2].multiple-scattering problems usually are complicated and have to be solved numerically, which is computationally costly and often does not provide intuitive understanding of the problem
In the case of isotropic scattering, random walk expressions can be related to real macroscopic variables by equating the random walk theory (RWT) lattice unit to the real displacement divided by the rms scattering length, while expressing the total photon path length in terms of the mean distance traveled on each step of the walk
Panel (a) and (b) of Figure 3 show the results obtained for isotropic media, and it can seen that Equation (1) agrees well with the Monte Carlo simulation even for relative small OD (L is defined as OD/ 2 in these figures)
Summary
Multiple-scattering represents a fundamental scientific problem, with implications in a wide spectrum of practical applications ranging from biological imaging [1] to dense spray diagnostics [2]. These expressions address the computational limitation of numerical techniques, and provide physical insights into the underlying phenomena They have been validated by extensive comparisons against Monte Carlo simulations, and have been found to be useful for a range of practical applications such as the estimation of signal levels and the design of imaging optics. In the case of isotropic scattering, random walk expressions can be related to real macroscopic variables by equating the RWT lattice unit to the real displacement divided by the rms (root mean square) scattering length (equivalent to dividing the macroscopic scattering coefficient by 2 ), while expressing the total photon path length in terms of the mean distance traveled on each step of the walk In this communication we consider transmittance through slabs and provide corrections to some previouslyderived RWT equations [12] that contain typographical errors. We derive the transmittance expression for isotropic scattering media without absorption and demonstrate an unusual scaling law for anisotropic scattering that arises by using a mixture of rms step lengths and mean path lengths within the RWT formulation [12]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
