The visualization and analysis of 3D fields of elastic displacements of micro-dimensional defects and dislocation structures in the volume of single crystals are important in the development of new functional materials. For this purpose, the X-ray diffraction tomography (XRDT) method is increasingly being used. We use XRDT to study the real structure of different single crystals, in particular, to visualize the spatial location of dislocation half-loops in Si (111) single crystal obtained by a four-point bending method . The currently used mathematical algorithms of XRDT data processing are the evolution of absorption tomography methods. Thus, there is a motivation to modify already existing algorithms for processing experimental results in order to develop new mathematical software based on them for modeling images of micro-dimensional defects in crystals. The tools of X-ray diffraction theory, as well as modern methods of digital image processing can be used for interpretation of the obtained data.
The specific feature of XRDT measurements is the impossibility to register a direct beam or its analogue (flatfield correction), which could be used to correct the background of the resulting projections. In this work, we propose a statistical method of analyzing diffraction projections to separate the noise component of the background (scattered radiation, dark current of detector, etc.) from the useful signal.
In particular, an approach using antialiasing the background signal with the Hamming's kernel in a 2D implementation has been proposed. It is proposed to use an algorithm for statistical recognition using Kendall’s rank correlation criterion to recognize the boundaries and peaks in the images. Kendall’s statistic and the concordation coefficient are calculated inside the scan window of the specified width. In this case, only image trends, i.e. relative intensity values, are compared.
The results of filtration depend to a large extent on the accuracy of noise dispersion estimation in the raw data. The main quality criterion of the solution is the value of the residual autocorrelation, which should correspond to a sample from a random sequence. The Durbin-Watson autocorrelation criterion  and several semi-empirical criteria based on the analysis of the curvature of the smoothed curve and the relative value of the systematic component in the residues were chosen as the estimation.
The application of developed algorithms and software for effective automatic noise filtering and smoothing of 2D diffraction projections using the criteria of difference autocorrelation significantly improves 3D reconstruction result of the dislocation half-loops in Si (111) single crystal.
This work was supported by Russian Foundation for Basic Research (project 19-02-00556 A) in the part of image processing and the Ministry of Science and Higher Education within the State assignment FSRC “Crystallography and Photonics” RAS in part of applying tomography algorithms.
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