A Note on Smoothness Priors and Nonlinear Regression

Accurate data processing for neutron Laue diffractometers

The factors affecting the accuracy of structural refinements from image-plate neutron Laue diffractometers are analysed. From this analysis, an improved data-processing method is developed which optimizes the intensity corrections for exposure scaling, wavelength distribution, absorption and extinction corrections, and the wavelength/spatial/time dependence of the image-plate detector efficiencies. Of equal importance is an analysis of the sources of uncertainty in the final corrected intensities, without which bias of the merged intensities occurs, due to the dominance of measurements with small statistical errors though potentially large systematic errors. A new aspect of the impact of detector crosstalk on the counting statistics of area detectors is reported and shown to be significant for the case of neutron Laue diffraction. These methods have been implemented in software which processes data from the KOALA instrument at ANSTO and the now decommissioned VIVALDI instrument at ILL (Grenoble, France). A comparison with earlier data-analysis methods shows a significant improvement in accuracy of the refined structures.