Determination of $g$ and $\mu$ Using Multiply Scattered Light in Turbid Media

We propose an inversion scheme to reconstruct the scattering coefficient $\mu$ and the anisotropy factor $g$ that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.

Figure 1

The steady state number density ${\varphi }_{+}(r)$ and ${\varphi }_{-}(r)$ as a function of distance from the source $r$. The open circles denote the Monte Carlo results, and the solid lines are the analytical curves. The dotted lines are the usual diffusion theory for the collimated source, and the dot-dashed lines are the predictions for an isotropic source. The parameters are $\mu =5{\mathrm{cm}}^{-1}$ and $g=0.2$ (top) and $g=0.9$ (bottom, using $f=0.81$ and $\tilde{g}=0.47$).

Figure 2

Impact of a measurement error on the inverted scattering coefficient $\mu$ as a function of the location of the second detector $r_2$. The predicted value for $\mu$ was obtained from the inversion using the exact value for ${\varphi }_{-}(r_1)$ and an “inaccurate” value of ${\varphi }_{-}(r_2)$ containing an error of 1% compared to the exact value. The exact value of $\mu$ is $5{\mathrm{cm}}^{-1}$ and $g=0.2$. The four distances $r_1$ are measured in centimeters.