Detector solid angle formulas for use in x-ray energy dispersive spectrometry

With the advent of silicon drift X-ray detectors, a range of new geometries has become possible in electron optical columns. Because of their compact size, these detectors can potentially achieve high geometrical collection efficiencies; however, using traditional approximations detector solid angle calculations rapidly break down and at times can yield nonphysical values. In this article we present generalized formulas that can be used to calculate the variation in detection solid angle for contemporary Si(Li) as well as new silicon drift configurations.