Theory of Optimum Drilled Scintillation Collimators for X-Ray Astronomy

In order to study unambiguously the X-ray spectra from single celestial X-ray sources located amid several closely spaced sources, some form of angular collimation must be used on an X-ray telescope flown at balloon altitudes or higher. A popular design featuring high background rejection consists of closely spaced holes drilled through a block of scintillator material. The present paper explores several general cross-sectional geometries for these holes, presenting features in mathematical and graphical form such as transmission efficiency; angular resolution; residual detector area after collimation; and optimum spacing between detector and collimator. The influence of the hole shape on collimator "leakage" and on signal to background ratio is discussed. Collimator geometries to fulfill specific needs are deduced from the curves. A symmetric "hourglass" hole shape is shown to provide most nearly an optimum compromise of desirable features.