“…This improvement was obtained mainly by making the capillary length equal to twice the focal distance, which is the optimized length for best focusing as discussed in this paper. With further refinements of the glass puller control system, capillary profile accuracy has also been significantly improved, enabling us to make dozens of capillaries with total divergence controlled very well at various values (from 2 to 8 mrad) for a variety of applications at CHESS, such as microcrystallography, microbeam X-ray standing wave (Kazimirov et al, 2004), scanning microspectroscopy (Bilderback et al, 2002), microbeam hightemperature high-pressure diffraction with diamond anvil cells and confocal X-ray fluorescence (Woll et al, 2005). Optical formulae are developed below to easily explain SBC focusing properties even without numerical coding, which helps both beamline scientists and users to choose capillary parameters to best fit their applications.…”