Quartic collimator design for high-energy gamma rays

In a gamma ray detection system, the only rays that need to be shielded from a detector are those that could have entered unwanted. Gamma rays that could not have encountered the detector do not need shielding. This simple optimization principle leads to a quartic shape for a full aperture collimator of minimal volume for a generic detector. Both cylindrical and spherical cases are derived, and the results compare very favorably with other common configurations and collimator shapes, such as standard cylindrical apertures and parallel-hole masks. For one example of collimating 2.615 MeV gamma rays, a quartic collimator reduces the required volume by over 70% from a standard cylindrical collimator.