Combining advanced characterization techniques with machine learning principles: DFXM and darfix
GARRIGA FERRER J. 1, RODRÍGUEZ-LAMAS R. 1, YILDIRIM C. 1, FAVRE-NICOLIN V. 1, DETLEFS C. 1
1 ESRF, Grenoble, France
Dark-field X-ray microscopy (DFXM) is a non-destructive full-field imaging technique that maps the 3D structure, orientation and strain of deeply embedded crystalline elements, such as grains or domains. An X-ray objective lens is placed along the diffracted beam to form direct-space images, affording a spatial resolution on the order of 100 nm, while maintaining a working distance between the sample and X-ray objective lens that is in the cm-range. Darfix is a Python package specifically designed for the analysis of DFXM data, that can also be used in a larger scope like rocking curve imaging. It provides the essential tools for fast processing and visualization of the acquired images, either imported as library components or accessed through a graphical user interface. Blind source separation (BSS) comprises all techniques that try to decouple a set of source signals from a set of their mixtures. The choice of the technique depends on the assumptions on the data. In DFXM, diffracting elements can be interpreted as source signals, where each element forms an image with a corresponding rocking curve and reciprocal space map. darfix implements several machine learning techniques for BSS to identify and isolate the elements: Principal Component Analysis (PCA), Non-negative Independent Component Analysis (NICA), Non-negative Matrix Factorization (NMF), and NICA-NMF. Since our data images are always positive, we can assume the non-negativity of the sources as an important parameter, nevertheless, the eigenvalues of the principal components in PCA can be used to estimate the number of true components present in the data. NICA imposes the non-negativity and independence of the sources, but it does not require the mixing coefficients to be non-negative, which can lead to nonphysical results. NMF constrains the non-negativity for both sources and mixing elements but doesn’t give a unique solution. This last setback can be solved by initializing NMF with the factorization given by NICA. DFXM has been used to observe defects such as dislocations and their formation/evolution under external forces. Dislocations are defects that are present in the crystalline lattice and that usually look like a line of dots. Their density and distribution are essential in materials science and extensive work has resolved that they spatially organize during plastic deformation into hierarchical networks. A deep learning algorithm is being developed to detect, and if possible classify, this dislocations from a given dataset obtained using the DFXM technique. This algorithm is to be included in darfix in a future release. In this work we present some examples on standard data acquired by DFXM and the post processing analysis using the tools provided in darfix, focusing on the use of the implemented machine learning techniques.