![]() These subsidiary maxima are much weaker than the principal – Bragg – maximum and their extent ( i.e. In Bragg coherent diffraction imaging (BCDI) and Bragg ptychography the intensity distributions at, and around, Bragg peaks, that is, the intensity at the Bragg positions as well as the secondary (or subsidiary) interference fringes, are employed to obtain a high-spatial-resolution image of the diffracting crystal with high strain sensitivity (Stagl et al., 2014 ). elastic) scattering for low- Z elements in the 10–20 keV range. This is why Compton scattering is usually neglected in X-ray diffraction experiments on single crystals, even if the total scattering cross section of Compton scattering can already be of the same order of magnitude as that of Rayleigh ( i.e. Already for small crystals with few thousands lattice points, the incoherent contribution is insignificant with respect to the coherent part. The contribution due to Compton scattering, being incoherent, only contributes as I inc ∝ N and the ratio of the incoherent/coherent contribution scales as 1/ N. We include the subscript `coh' to stress that interference effects can only arise from the coherently scattered photons (Rayleigh scattering). For a crystal with N lattice points illuminated with a monochromatic X-ray beam, at those points satisfying Bragg's law, in the kinematical approximation the maximum intensity is proportional to the square of the total number of lattice points, i.e. These directions are determined by Bragg's law. Due to the periodic arrangement of the atoms or molecules within the crystal into a space lattice, diffraction only occurs at very specific directions, for which the spherical wavelets scattered by each lattice point interfere constructively. In conventional X-ray crystallography, the angles and intensities of the beams diffracted by a crystal are measured. Notwithstanding, Compton scattering can often be ignored. The Compton scattered photons lose their phase relationship with the incoming photons. However, even in the absence of external influences or vibrations, the coherence may be degraded via the interaction with the sample through quantum effects such as Compton scattering, in which the incoming photon transfers part of the momentum and energy to electrons. Finally, special attention has also been given to the characterization of the incoming wavefront to disentangle the contributions of the incoming wavefield and the sample scattering function (Kewish et al., 2010 Schropp et al., 2010 Mastropietro et al., 2011 Björling et al., 2020 ). This is justified in terms of conservation of the phase space and considers that the experimental X-ray system is closed, without external influences (Nugent, 2010 ). It has been argued that, in the absence of vibrations or instabilities, the coherence properties of the radiation cannot be degraded during the propagation through optical components (Nugent et al., 2003 ). The propagation of the X-ray beam through optical components of hard X-ray beamlines and the apparent loss of coherence sometimes observed has also been discussed (Vartanyants & Robinson, 2003 Nugent et al., 2003 ). For this reason, the use of coherence preserving optics is especially important (Paganin, 2006 ). Partial coherence, as widely discussed in the literature (Sinha et al., 1998 Whitehead et al., 2009 Nugent, 2010 ), washes out interference effects and thus compromises the inversion process or the achievable spatial resolution. For these techniques, markedly for inverse microscopy, coherence propagation and preservation are very important issues, as they can affect in a strong way the inversion's outcome. Techniques exploiting coherence have been developed and employed in different ways to study the morphology and strain of materials using inverse microscopy approaches, or the dynamics, using photon correlation spectroscopy (Nugent, 2010 ). ![]() In the last decade, the use of the coherence properties of X-rays produced at third-generation synchrotron radiation sources has markedly increased.
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