Theoretical prediction of the geometric transfer function for focused collimators

The transfer function describing spatial resolution characteristics of a focused collimator used in conventional scanning can be described by the weighted sum of 3 terms representing contributions of geometrically collimated, penetrating, and scattered radiation. The present work showed that the geometric component of the transfer function of a single hole or multihole focused collimator with round holes packed in an hexagonal array can be expressed in the form of a rather simple equation involving trigonometric functions, first order Bessel functions, and the physical dimensions of the collimator. This expression is applicable for any collimator to source distance and takes into account the directional dependence of geometric resolution due to hole packing geometry. Fourier transformation of line spread functions measured using a thin walled line source of ¹²⁵I in air, in which case scatter and septal penetration can be neglected, showed that the predicted transfer functions are accurate to within a few % over a broad range of spatial frequencies and collimator to source distances. The theoretical approach appears to provide a powerful tool for the designing of focused collimators.