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Light Transport in Tissue Glass slide -- no incident diffuse light In many experiments to measure optical properties the scattering material is sandwiched between glass (or quartz) slides. The slides provide support for thin tissues and a smooth reproducible boundary. Unfortunately, the index of refraction of the slide is usually not equal to that of the tissue or that of the environment. This section shows how internal reflection from the glass slide is incorporated into the boundary conditions. To incorporate a glass slide in the boundary conditions, Equation (B.21) should be used to calculate the reflection coefficient $r'(\mu)$ rather that the usual Fresnel reflection equation. Thus two new reflection coefficients R1glass and R2glass may be defined analogous to Equation (4.42) $${R_1^{\mathrm{glass}}\over2} \int_0^1r'(\mu)\mu\,d\mu = -\int_{-1}^0 r'(\mu)\mu\,d\mu$$ = $${R_2^{\mathrm{glass}}\over3} \int_0^1r'(\mu)\mu^2\,d\mu = \int_{-1}^0 r'(\mu)\mu^2\,d\mu$$ = (4.55) The analysis of the index mismatch section follows with Atop replaced by $$A_{\mathrm{top}}^{\mathrm{glass}} = {1+R_2^{\mathrm{glass}}\... ...{glass}} = {1+R_2^{\mathrm{glass}}\over1-R_1^{\mathrm{glass}}}$$ (4.56) Values for $A^{\mit glass}$ may be calculated using the polynomial approximations (B.52)-(B.57) in Appendix B. The boundary conditions for the top and bottom of the slab follow from Equations (4.45) and (4.48) $$\varphi_d(\mathbf{r})-A_{\mathrm{top}}^{\mathrm{glass}}h{\pa... ...op}}^{\mathrm{glass}}Q(\mathbf{r}) \qquad\mathrm{at}\qquad z=0$$ (4.57) $$\varphi_d(\mathbf{r})+A_{\mathrm{bottom}}^{\mathrm{glass}}h{... ...om}}^{\mathrm{glass}}Q(\mathbf{r}) \qquad\mathrm{at}\qquad z=d$$ (4.58) Equations (4.57) and (4.58) are appropriate for a slab of tissue sandwiched between glass slides.

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