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Register a new userA ray-trace analysis of X-ray multilayer Laue lenses for nanometer focusing
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Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for X-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Braggs law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions are provided of the fourth-order series expansions of the wavefront aberrations and transmissions of both axi-symmetric lenses and pairs of crossed lenses that each focuses in only one dimension like a cylindrical lens. We find that aplanatic zone-plate designs, whereby aberrations are corrected over a large field of view, can be achieved by axi-symmetric lenses but not the crossed lenses. We investigate the performance of 1 nm-resolution lenses with focal lengths of about 1 mm and show their fields of view are mainly limited by the acceptance angle of Bragg diffraction, and that aberrations can limit the performance of lenses with longer focal lengths. We apply the ray-tracing formalism for a tolerancing analysis of imperfect lenses and examine some strategies for the correction of their aberrations.
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We propose a novel data-driven approach for analyzing synchrotron Laue X-ray microdiffraction scans based on machine learning algorithms. The basic architecture and major components of the method are formulated mathematically. We demonstrate it through typical examples including polycrystalline BaTiO$_3$, multiphase transforming alloys and finely twinned martensite. The computational pipeline is implemented for beamline 12.3.2 at the Advanced Light Source, Lawrence Berkeley National Lab. The conventional analytical pathway for X-ray diffraction scans is based on a slow pattern by pattern crystal indexing process. This work provides a new way for analyzing X-ray diffraction 2D patterns, independent of the indexing process, and motivates further studies of X-ray diffraction patterns from the machine learning prospective for the development of suitable feature extraction, clustering and labeling algorithms.
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