Geometrical response modeling in fan-beam collimators. A numerical simulation

Iterative reconstruction algorithms require modeling of the PSF of the collimator in order to correct the loss of resolution in SPECT. In this paper a method of modeling the geometric response of a fan beam collimator is proposed. The geometric PSF is obtained by numerical simulation based on ray tracing techniques. The versatility of the numerical simulation allows one to generate the array of holes with a distance between holes varying as an angular function, thus being suitable for real distributions of holes. The volume of the simulated PSFs was calculated in order to determine the relative sensitivity and Gaussian functions were fitted to obtain the resolution. Functions depending on the intrinsic parameters of the collimator and of the co-ordinates of the source were fitted to the individual PSF. Thus, the method allows one to determine both the spatial resolution and the sensitivity as a function of the source co-ordinates. The validity of the modelisation functions was checked by comparing the predicted results with those obtained from experimental measurements. The authors´ findings show that the predicted values for the relative sensitivity and for the resolution match accurately the experimental values, with a correlation coefficient of 0.997 for sensitivity and 0.996 for resolution