Comparison of two methods for calculating slit-length collimation corrections in small angle X-ray scattering

The methods of Lake [Acta Cryst. (1967) 23, 191] and Schmidt [Acta Cryst. (1965) 19, 938] for calculating slit-length collimation corrections in small angle X-ray scattering have been compared in a number of tests. The tests showed that under most conditions neither method introduces errors larger than the expected uncertainty in present-day scattering data and that slit-length corrections are relatively insensitive to small changes or errors in the weighting function. Neither method is extremely sensitive to random errors in the measured intensity but the effect of these errors is somewhat smaller with Schmidt's method than with Lake's. Three cases were found in which one of the correction methods should be avoided or used with caution: with Schmidt's method errors are produced in the outer part of the scattering curve if the angular increment is too large - a criterion has been developed for determining acceptable increments; if Lake's method is used in an angular region in which a scattering curve has subsidiary maxima or minima, more iterations may be necessary than are required for monotonically decreasing scattering curves; the usual form of Lake's method, which was developed to converge rapidly with curves which have a zero-angle maximum, was sometimes found to give appreciable errors for curves with a pronounced minimum at zero scattering angle. When the latter type of curve is corrected by this method, precautions should be taken to ensure that the collimation correction is not introducing errors.