Home

Light Transport in Tissue Index matching, no incident diffuse light, both media scattering If two slabs with the same index of refraction are juxtaposed, then the boundary conditions at the interface z=z0 are continuity of the first two moments of the radiance $$\varphi_{d}^{(1)} (\mathbf{r})=\varphi_{d}^{(2)}(\mathbf{r}) \qquad\mathrm{at}\qquad z=z_0$$ (4.61) $$\mathbf{F}_{d}^{(1)}(\mathbf{r})\cdot\hat\mathbf{z}=\mathbf{... ...}(\mathbf{r})\cdot\hat\mathbf{z} \qquad\mathrm{at}\qquad z=z_0$$ (4.62) This is the boundary condition required for multi-layered tissues in which there is no index of refraction difference from one medium to another. Equation (4.62) simplifies to $${1\over\mu_{tr}^{(1)}} {\partial\varphi_d^{(1)}(\mathbf{r})\... ...(2)}(\mathbf{r})\over\partial z} \qquad\mathrm{at}\qquad z=z_0$$ (4.63) where the superscripts 1 and 2 denote either the upper or lower medium respectively.

S. A. Prahl."Light Transport in Tissue," PhD thesis, University of Texas at Austin, 1988.