Mathematical modeling of the solid angle function, part III: transmission through a diffusive plane

Abstract

In a series of papers we have developed various mathematical models for the solid angle centered at a scintillation point and subtended by a circular photomultiplier tube (PMT) in a gamma camera. In this third paper, the scintillation crystal, where the gamma ray is converted to visible light, shows a very diffusive plane in the PMT direction. The media on each side of the boundary are homogeneous. We develop a full mathematical model for the PMT response. This model depends on several physical parameters. They can be set up according to the kind of diffusion occurring at the interface. We also show that the direct and refracted solid angles are particular cases of the diffusive model. Then, for computational purposes, we approximate the model to bring its four-level integral representation to a two-level one. Numerical results show the effectiveness of our mathematical model of the solid angle function transmitted through a diffusive plane.