Electron diffraction tomography (EDT) data are in many ways similar to X-ray diffraction data. However, they also present certain specifics. One of the most noteworthy is the specific rocking curve observed for EDT data collected using the precession electron diffraction method. This double-peaked curve (dubbed 'the camel') may be described with an approximation based on a circular integral of a pseudo-Voigt function and used for intensity extraction by profile fitting. Another specific aspect of electron diffraction data is the high likelihood of errors in the estimation of the crystal orientation, which may arise from the inaccuracies of the goniometer reading, crystal deformations or crystal movement during the data collection. A method for the refinement of crystal orientation for each frame individually is proposed based on the least-squares optimization of simulated diffraction patterns. This method provides typical angular accuracy of the frame orientations of less than 0.05 . These features were implemented in the computer program PETS 2.0. The implementation of the complete data processing workflow in the program PETS and the incorporation of the features specific for electron diffraction data is also described. electron crystallography 514 L. Palatinus et al. Structure refinement from PED Acta Cryst. (2019). B75, 512-522 electron crystallography Acta Cryst. (2019). B75, 512-522 L. Palatinus et al. Structure refinement from PED 517 electron crystallography Acta Cryst. (2019). B75, 512-522 L. Palatinus et al. Structure refinement from PED 521

It is shown that a properly designed transversal groove machined into the surface of a single-crystal monochromator may concentrate (focus) the diffracted radiation meridionally. From this result and from previous papers on the Bragg-diffraction inclined lens it follows that a properly designed depression fabricated into the surface of a single-crystal monochromator should provide two-dimensional focusing of a diffracted synchrotron radiation beam.

One of the factors influencing the focus size in diffractive–refractive optics is the quality of diffracting surface. If the surface is uneven, as it is when the silicon crystal surface is only etched, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown theoretically that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam such that it causes a significant broadening of the focus. In this case a mechanical–chemical polishing is necessary. This has been verified by us earlier in a preliminary experiment with synchrotron radiation. In this work the new experiment with the same crystals is performed using double crystal (+, −) arrangement and a laboratory x-ray source (CuKα radiation). We compared two samples; one of them is mechanically–chemically (MC) polished and thus the diffracting surface is almost perfect; the other is only etched. This experiment allows a better comparison of the result with the theory. The difference between the measured rocking curve widths for the etched and MC polished crystals (10″) roughly agrees with theory (7″), which supports the correctness of the theoretical approach.

One of the factors influencing the focus size in diffractive-refractive optics is the quality of diffracting surface. If the surface is uneven, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam, such that it causes a significant broadening of the focus. In this case a mechanical-chemical polishing is necessary.

The possibility of concentrating a synchrotron X-ray beam using diffraction by a single crystal with a properly designed transverse groove on its surface, suggested earlier, has been studied experimentally. Here, the ®rst experimental demonstration of this effect is reported, performed on beamline BM5 at the ESRF. The experimental result con®rms the theoretical model.