Exact PN Method Solutions

The spherical harmonics (PN) solution at the surface of a source-free half-space is investigated to determine conditions for which exact results can be obtained with an approximation of any odd order N. For isotropic scattering, an exact solution for the net current can be obtained if the incident illumination comes from an isotropic plane source, which extends the observation of Garcia and Siewert that an exact solution for the scalar flux can be obtained if the incident illumination is constant with the cosine of the polar angle. An exact solution for the scalar flux at the interface between two isotropic-scattering, halfspace media also can be obtained with a finite N for a spatially uniform source in one half-space.