Welcome to the "Diffraction powder patterns on GPUs" section! Powder diffraction patterns are computed by the means of the Debye scattering equation [1], without any approximation apart those inherent in the use of floating point math [2].
[1] P. Debye, Annal. Phys. (1915) 351, 809.
[2] L. Gelisio, C. L. Azanza Ricardo, M. Leoni and P. Scardi, J. Appl. Cryst. (2010) 43, 647.