Revisiting Becker-Coppens (1974): updated recipes for estimating extinction factors in spherical crystallites

A technical correction and update of the widely used recipes by Becker & Coppens [Acta Cryst. (1974), A30, 129-147], for the estimation of primary and secondary extinction factors in perfect spherical crystallites or grains, is presented. In the original work, these extinction factors were evaluated numerically from a complicated integral, and simplified analytical approximations to these evaluations constituted the provided recipes. However, these original recipes are plagued by issues of numerical precision in general, and even suffer from complete numerical breakdown in the case of strong extinction effects, especially in backwards scattering. Using modern computing capabilities, the numerical evaluations of the integrals are revisited, and improved recipes are provided with consistent precision guarantees for all Bragg angles and levels of extinction. The new recipes are provided both in a `standard' version, believed to be of suitable precision for any actual analysis of diffraction or transmission data, and a `luxury' reference version with even higher precision. The performance of the new recipes is compared with that of the original work, and in order to facilitate easy adoption by the community, reference implementations are provided for C, C++ and Python languages.