Smoothing of X-ray diffraction data andKα2elimination using penalized likelihood and the composite link model

Abstract

X-ray diffraction scans consist of series of counts; these numbers obey Poisson distributions with varying expected values. These scans are often smoothed and theKα2component 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 theKα doublet the model is extended using the composite link model. As a result the data are decomposed into two smooth components: aKα1and aKα2part. For both smoothing andKα2removal, 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 forKα2stripping. The new method shows better results with less local distortion. Freely available software in MATLAB and R has been developed.