Monte Carlo Calculations of the Optical Coupling between Bismuth Germanate Crystals and Photomultiplier Tubes

The high density and atomic number of bismuth germanate (Bi4Ge3O12 or BGO) make it a very useful detector for positron emission tomography. Modern tomograph designs use large numbers of small, closely-packed crystals for high spatial resolution and high sensitivity. However, the low light output, the high refractive index (n=2.15), and the need for accurate timing make it important to optimize the transfer of light to the photomultiplier tube (PMT). We describe the results of a Monte Carlo computer program developed to study the effect of crystal shape, reflector type, and the refractive index of the PMT window on coupling efficiency. The program simulates total internal, external, and Fresnel reflection as well as internal absorption and scattering by bubbles. We show that when internal trapping in clear, polished BGO crystals is reduced by (a) suitable crystal shaping, (b) a PMT window with a high refractive index, or (c) non-absorbing vacuum bubbles, it is possible to transfer more than 60% of the scintillation light to the PMT. This transfer is greatly reduced by internal absorption.