An analytical function for absorption correction

A new analytical function is proposed for absorption correction. It is expressed by surface harmonics with polar angles that specify the primary and secondary beam directions. This function has an advantage over Fourier expansion because it is rotationally invariant. Two empirical, methods are used to determine the expansion coefficients. One uses the intensity deviations of equivalent reflections, and the other uses the calculated intensities at the stage of structure refinement. The utility of the analytical function is demonstrated with a model and with actual data.