Source-detector geometrical efficiency

Abstract

By the use of simple analytical spherical-trigonometry a mathematical expression of a solid angle subtended by a point to a plane triangle is deduced. Generalizing, solid angles subtended by a non-axial point source to a circular disk detector and a circular disk source to a circular disk detector are deduced into rigid mathematical expressions very easily computed, for the first time. Results were compared with previous tabulations. By this method, with some mathematical manipulations, solid angles could be deduced for detectors of different geometrical shapes, e.g. rectangular, elliptical, spherical and cylindrical.