The geometric transfer function component for scintillation camera collimators with straight parallel holes

Abstract

A theoretical approach has been developed that allows the geometric transfer function component for conventional scintillation camera collimators to be predicted in closed form. If transfer function analysis is to be useful in describing imaging system performance, the image of a point source must not depend on source position in a plane parallel to the detection plane. This shift invariance can be achieved by analysis of system response in terms of an effective point spread function, defined as the normalised image of a point source that would be obtained if the camera collimator were uniformly translated (but not rotated) during image formation. The geometric component of the corresponding effective transfer function is shown to be expressed simply by the absolute square of the two-dimensional Fourier transform of a collimator hole aperture, with the spatial frequency plane scaled by a factor which depends on collimator length, source-to-collimator distance, and collimator-to-detection plane distance. Closed form algebraic expression of the geometric transfer function have been obtained for all four common hole shapes (circular, hexagonal, square and triangular). Monte Carlo simulations and experimental measurements have shown these theoretical expressions to be highly accurate.