The fine alignment of X-ray nano-focusing optics, such as Kirkpatrick-Baez (KB) mirrors, depends strongly on the ability to diagnose the X-ray beam at the focus position. Despite conventional diagnostics techniques (e.g. knife-edge) allowing the measurement of the beam profile with sub-micrometer resolution, they may yield poor accuracy for beams with sizes under 100 nm. With nanometer-resolution phase-recovering techniques like ptychography, information about optical aberrations can be obtained experimentally in the complex-valued wavefront. In this work, we use wave-propagation simulations with Synchrotron Radiation Workshop (SRW) to model the CARNAÚBA beamline at Sirius. The beam phase at the KB mirrors exit pupil is decomposed in terms of Zernike rectangular polynomials. The relevant degrees of freedom (DOF) of the mirrors are scanned, allowing the correlation of the Zernike coefficients with the beam profile at focus. Therefore, the aberrations are classified and quantified for each mirror’s DOF, and alignment tolerances are obtained. We find that each DOF can be described by a unique combination of only three Zernike terms. Additionally, a database with the first 15 Zernike coefficients is created by simulating random alignment states and used to train a simple fully-connected neural network. The neural network was able to determine the alignment states of unknown samples with errors below 3%. The combination of Zernike polynomials and neural networks could potentially lead to single-iteration alignment of KB mirrors using wavefront sensing techniques as a diagnostic tool.
Side-deflecting cylindrical mirrors with sagittal curvature horizontally deflect and focus the beam in the vertical direction. This optical scheme applied to fourth-generation synchrotron light source beamlines has potential advantages leading to nearly aberration-free focus and variable beam size or focus position. We characterize the surface quality of sagittal cylinders in the low spatial frequency range with the long trace profiler (LTP) and the Fizeau interferometer (FZI). In the standard LTP, the sagittal curvature of the cylindrical mirror causes the reflected laser beam to diverge, which consequently shifts the focus out of the detector plane, turning a reliable measurement impossible. Therefore, a positive cylinder lens is placed at Cat's eye position to recollimate the beam. In this paper, we describe the alignment procedure and dene the required accuracy of each degree of freedom for both the cylinder lens and the cylindrical mirror to be characterized. Measurements with the FZI are limited to optics with small curvatures when measuring with a flat reference. We show that measuring a sagittal cylinder slightly out-of-focus overcomes this limitation. Measurements with the FZI also allow to characterize the deformations caused by clamping forces due to fixation. We compare the measured deformation with Finite Element Analysis (FEA) simulation results. We present measured surface height and slope profiles (LTP and FZI) of cylindrical mirrors for SIRIUS beamlines.
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