Study of the collection solid angle of doubly curved crystals

An approach to obtain a maximum solid angle is the use of curved crystals. Therefore, in order to make these crystals useful in X-ray spectrometry, it is necessary to design them in such a way that they have high solid angle and reflectivity. In this paper, a nearly exact general equation for calculating the solid angle and area factor on the surface of several curved crystal geometries is extracted and compared with the previous results. Wittry and Sun's shortcut method for calculating the solid angle, and also, its trial and error method for maximizing the solid angle and introducing exact point-focusing crystal geometry is reviewed, and it is shown that for some crystal geometries are not responsive. By writing an algorithm for calculating the solid angle and the area factor for ​​all of the crystal geometries, we show that they are in agreement with the results of the analytical method.