The geometric transfer function for slant-hole collimators

In this paper we provide a complete description of the geometric response properties of slant-hole (SH) collimators by deriving the SH collimator geometric transfer function (GTF). In doing so, we follow a method first used by Metz et al. (1980) and later employed by Tsui and Gullberg (1990) to derive the GTF for conventional parallel- and converging-hole collimators, respectively. After deriving the GTF for SH collimators, we validate the result via simulation and experimental studies. In the simulations, the Monte-Carlo N-Particle (MCNP) software package is used to simulate the images obtained from a point source with a variety of SH collimators with different design parameters. Results of these simulations are then compared to those obtained from theoretical derivations. Also, the theoretical results are compared to experimental results obtained from point source images obtained using a 4-segment SH collimator in our laboratory. We found that the theoretical formulation is highly accurate in predicting the GTF of SH collimators from their design parameters. The theoretical formulation will be useful for both the design of SH collimators with specific imaging properties, and the modeling and compensation of the image degrading effects of the SH collimator GTF in an iterative reconstruction algorithm.