Derivation and Validation of a Sensitivity Formula for Slit-Slat Collimation

An analytic formula is derived for the sensitivity of collimators achieving transverse collimation with a slit and axial collimation with a slat assembly whose septa may be parallel or focus on a line. The formula predicts sin(3) phi dependence on the incidence angle and, in the particular case of parallel slats, 1/h dependence on the distance from the slit. More complex expressions for sensitivity that do not diverge at points near the slit or the focal line of the slat assembly are also derived. The predictions of the formulas are checked against simple cases for which solutions are available from direct calculation as well as against Monte Carlo simulation and published experimental data. Agreement is good in all cases analyzed. An approximate penetration model is also introduced: it involves the use of a sensitivity-effective slit width and septal length. Its predictions are compared to simulation results. Agreement was found to be compatible with statistical fluctuation (+/- 0.3%) for geometric sensitivity and better than 3% of total sensitivity in the worst case of septa designed for high-energy (364.5 keV) photons.