Diagnostics of KB mirrors misalignment using Zernike rectangular polynomials and neural networks.

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 CARNAUBA 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.