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.
References
[1]
Hebden, J.C.; Hall, D.J.; Firbank, M.; Delpy, D.T. Time-resolved optical imaging of a solid tissue-equivalent phantom. Appl. Opt. 1995, 34, 8038–8047.
[2]
Paciaroni, M.; Linne, M.; Hall, T.; Delplanque, J.P.; Parker, T. Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray. At. Sprays 2006, 16, 51–69.
[3]
Sobol, I.M. The Monte Carlo Method; The University of Chicago Press: Chicago, IL, USA, 1967.
[4]
Berrocal, E.; Sedarsky, D.L.; Paciaroni, M.E.; Meglinski, I.V.; Linne, M.A. Laser light scattering in turbid media part i: Experimental and simulated results for the spatial intensity distribution. Opt. Express 2007, 15, 10649–10665.
[5]
Boas, D.A.; Culver, J.P.; Stott, J.J.; Dunn, A.K. Three dimensional monte carlo code for photon migration through complex heterogeneous media including the adult human head. Opt. Express 2002, 10, 159–170.
[6]
Zaccanti, G. Monte-carlo study of light-propagation in optically thick media—Point-source case. Appl. Opt. 1991, 30, 2031–2041.
[7]
Fang, Q.Q.; Boas, D.A. Monte carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units. Opt. Express 2009, 17, 20178–20190.
[8]
Kokhanovsky, A.A. Analytical solutions of multiple light scattering problems: A review. Meas. Sci. Technol. 2002, 13, 233–240.
[9]
Contini, D.; Martelli, F.; Zaccanti, G. Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Theory. Appl. Opt. 1997, 36, 4587–4599, doi:10.1364/AO.36.004587.
[10]
Gandjbakhche, A.H.; Bonner, R.F.; Nossal, R. Scaling relationships for anisotropic random-walks. J. Stat. Phys. 1992, 69, 35–53.
[11]
Gandjbakhche, A.H.; Nossal, R.; Bonner, R.F. Scaling relationships for theories of anisotropic random-walks applied to tissue optics. Appl. Opt. 1993, 32, 504–516.
[12]
Gandjbakhche, A.H.; Weiss, G.H.; Bonner, R.F.; Nossal, R. Photon path-length distributions for transmission through optically turbid slabs. Phys. Rev. E 1993, 48, 810–818.
[13]
Sun, X.; Li, X.; Ma, L. A closed-form method for calculating the angular distribution of multiply scattered photons through isotropic turbid slabs. Opt. Express 2011, 19, 22932–23937.
[14]
Moon, J.A.; Reintjes, J. Image-resolution by use of multiply scattered-light. Opt. Lett. 1994, 19, 521–523.
