We developed methods to characterize hole pattern artifacts and septal penetration and scatter that are important in collimator design, especially for medium energy and high energy photons. We developed ray-tracing code for calculating the geometric and penetration components of the point source response functions (PSRFs) for both parallel-hole and fan-beam collimator designs. We modeled septal penetration and scatter with the MCNP Monte Carlo code and obtained the geometric, penetration and scatter components of the collimator PSRFs. In order to verify the ray-tracing and Monte Carlo methods, we acquired data from a Ga-67 point source at the 93, 185 and 300 keV photon energies and at various distances from the face of a low energy parallel-hole, a medium energy parallel-hole and a low energy fan-beam collimator. The hole pattern artifacts obtained from the ray-tracing and Monte Carlo methods are in good agreement with experiment. The geometric and penetration components from the ray-tracing and Monte Carlo methods also agree. We conclude that the ray-tracing and Monte Carlo methods are useful in the initial design and detailed characterization of medium energy and high energy collimators.