Improvements to the Chebyshev expansion of attenuation correction factors for cylindrical samples

The accuracy of the Chebyshev expansion coefficients used for the calculation of attenuation correction factors for cylindrical samples has been improved. An increased order of expansion allows the method to be useful over a greater range of attenuation. It is shown that many of these coefficients are exactly zero, others are rational numbers, and others are rational fractions of π⁻¹ The assumptions of Sears [J. Appl. Cryst. (1984), 17, 226–230] in his asymptotic expression of the attenuation correction factor are also examined.