Smoothing of X-ray diffraction data and Kα2 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 Kα2 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 Kα doublet the model is extended using the composite link model. As a result the data are decomposed into two smooth components: a Kα1 and a Kα2 part. For both smoothing and Kα2 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 Kα2 stripping. The new method shows better results with less local distortion. Freely available software in MATLAB and R has been developed.

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