Smoothing of X-ray diffraction data and K[alpha]2 elimination using penalized likelihood and the composite link model

X-ray diffraction scans consist of series of counts; these numbers obey Poisson distributions with varying expected values. These scans are often smoothed and the K[alpha]2 component is removed. This article proposes a framework in which both issues are treated. Penalized likelihood estimation is used to smooth the data. The penalty combines the Poisson log-likelihood and a measure for roughness based on ideas from generalized linear models. To remove the K[alpha] doublet the model is extended using the composite link model. As a result the data are decomposed into two smooth components: a K[alpha]1 and a K[alpha]2 part. For both smoothing and K[alpha]2 removal, the weight of the applied penalty is optimized automatically. The proposed methods are applied to experimental data and compared with the Savitzky-Golay algorithm for smoothing and the Rachinger method for K[alpha]2 stripping. The new method shows better results with less local distortion. Freely available software in MATLAB and R has been developed. [PUBLICATION ABSTRACT]