To apply these results to subsurface scattering for rendering, it is clear that the solution must account for the presence of a surface. We will now switch to the simplest kind of geometric setup that satisfies this requirement: a semi-infinite half space, i.e., a medium that fills all space below a planar surface of infinite lateral extent. The region above is modeled as a dielectric without any kind of scattering (i.e., a vacuum).

For simplicity, we assume that the boundary is located at z = 0 with a normal of n = (0, 0, − 1) so that positive values on the z axis correspond to points inside the medium. Let η denote the relative index of refraction over the boundary. We are still interested in the fluence rate due to ...

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