Publicly available polarized-light MC algorithms developed by Ramella-Roman et al.^{19} were used to simulate the propagation and collection of polarized light. The implementation of this algorithm to track photons as functions of polarization, radius, $\theta c$, and maximum depth travelled ($z$) has been described in detail by Turzhitsky et al.^{17} Reflection, refraction, and alteration of the Stokes vector at the sample/environment interface was computed using Snell’s Law and the Stokes formalism of the Fresnel equations.^{20} To employ the Whittle-Matérn model described in the previous section, we used a phase function derived from Eq. (1). First, the spectral density $\Phi $ at spatial frequency $\kappa $ can be calculated from the Fourier transform of $Bn(r)$ yielding Display Formula
$\Phi n(\kappa )=dn2lc3\Gamma (m)(1+\kappa 2lc2)\u2212m\pi 3/2|\Gamma [m\u2212(3/2)]|.$(4)
Then, following the derivation of Moscoso et al.,^{21} the phase function for incident light with initial Stokes vector $[IoQoUoVo]$ can be written as Display Formula$F(\theta ,\varphi )=\pi 4k4\Phi n(2k\u2009sin\theta 2)[(1\u2212cos2\u2009\theta )Io+(cos2\u2009\theta \u22121)(Qo\u2009cos\u20092\varphi +Uo\u2009sin\u20092\varphi )],$(5)
where $\theta $ is the angle of scattering and $\varphi $ is the angle of rotation into the scattering plane.