Improved estimation of the detector response function for converging beam collimators

Converging beam collimator geometries offer improved tradeoffs between resolution and noise for single photon emission computed tomography (SPECT). The major factor limiting the resolution in SPECT is the collimator-detector response blurring. In order to compensate for this blurring it is useful to be able to calculate the collimator response function. A previous formulation presented a method for calculating the response for parallel and converging beam collimators that assumed that the shape of the holes did not change over the face of the collimator. However, cast collimators are fabricated using pins with a constant cross-section (shape perpendicular to the pin axis). As a result, due to the angulation of the pins, the holes made by these pins have shapes on the front and back faces of the collimator that change with position. This change in hole shape is especially pronounced when the angle between the collimator hole and the collimator normal is large, as is the case for half-fan-beam or short-focal-length collimators. This paper presents a derivation of a modification to the original method that accounts for the change in shape of the collimator holes. The method has been verified by comparing predicted line spread functions to experimentally measured ones for a collimator with a maximum hole angle of 35 degrees with respect to the normal. This formulation is useful for predicting the response of fan-beam collimators in the design process and for use in detector response compensation algorithms.