Forced detection for astigmatic collimation based on circular acceptance cone approximation

Applicability of the circular cone approximation approach is studied for Monte Carlo modeling of astigmatic collimators using forced detection for low-energy photons. A set of analytic formulas for collimator sensitivity and collimator resolution for primary photons is first derived for flat astigmatic collimators with flat detectors. Based on the analytic formulas, a simulation is conducted to evaluate the major-to-minor axis ratio of acceptance cones over a large sphere within the field-of-view of astigmatic collimators. It was observed that the mean and standard deviation of the ratio increase as the smaller focal length of an astigmatic collimator is decreased. In addition, the mean ratio increases as the difference of the astigmatic focal pair is increased. At the extreme focal difference (i.e., fan beam geometry), the ratio achieves a maximum and can be as large as 3.7 for a focal pair of 40 cm and 1.0e+5 cm. Based on these observations, the circular cone approximation was implemented, and a fan beam collimator was simulated. Simulated point source responses are relatively close to experiment data