Possible improvements in the precision and accuracy of small‐angle X‐ray scattering measurements

The sensitivity of small‐angle X‐ray scattering (SAXS) measurements to random statistical errors (precision) and to systematic errors (accuracy) is addressed in this paper. Equations are drafted that serve as a basis for algorithms for reaching a reasonable compromise between the duration of a SAXS measurement and the precision of excess scattering intensity when the background scattering is taken into account. As a measure of precision, the relative deviation at each angle is considered. An example of the algorithm for the optimization of SAXS measurements is shown and discussed in sufficient detail to allow direct application. A new mode of measurement that uses a remotely controlled sample changer is proposed, which increases the accuracy of the excess scattering intensity by lowering its sensitivity to long‐time‐scale variations in the experimental conditions. The idea is that the scattering intensity of the sample and that of the background are measured immediately one after another at every angle. With computer simulations, this new mode is compared with conventional procedures, where the whole scattering curves of the sample and the background are measured separately. The new method is found to be especially useful when the higher‐angle region of the small‐angle scattering function is of interest. The relative deviation for measurements made using the new method grows with increasing scattering angle, finally reaching a value comparable to the amplitude of long‐time‐scale primary‐beam fluctuations. With conventional measurements, the growth of the relative deviation appears much sooner and its final value is at least twice as high. The full advantages of our method can be realized when measurements are recorded by step scanning. Nevertheless, users of position‐sensitive detectors may find some of the ideas presented here useful for improving their measurements.