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Theoretical Prediction of the Geometric Transfer Function for Focused Collimators

The University of Chicago and The Franklin McLean Memorial Research Institute, Chicago, Illinois

Correspondence: For reprints contact: Charles E. Metz, Box 429, Dept. of Radiology, The University of Chicago, 950 E. 59th St., Chicago, Ill. 60637.

ABSTRACT

The transfer function describing spatial resolution characteristics of a focused collimator used in conventional scanning can be described by the weighted sum of three terms representing contributions of geometrically collimated, penetrating, and scattered radiation. The present work has shown 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, has shown that the predicted transfer functions are accurate to within a few percent over a broad range of spatial frequencies and collimator-to-source distances. Thus the theoretical approach appears to provide a powerful tool for the designing of focused collimators.