Coherent or partially coherent X-rays have recently been utilized in beamlines at advanced synchrotron radiation facilities and X-ray free-electron lasers. Wave-optical and ray-tracing calculations are widely employed to predict intensity and phase distributions of X-ray beams when designing new beamlines. Both calculation methods have their respective advantages and disadvantages. In this presentation, we will compare the results of calculations in optical systems that use X-ray focusing mirrors, and introduce a method for combining these two methods. Furthermore, we will discuss the applications of this method for calculating partially coherent X-rays.

Recent upgrades of synchrotron light source facilities towards ultra-low electron beam emittances allow increased photon beam brightness and coherence. New techniques for online modeling and control, taking advantage of modern Machine Learning approaches are required to fully utilize these new photon capabilities. We present recently developed reduced models for x-ray propagation that may enable an array of fast optimization methods for beamline alignment and reconfiguration. In particular, we have extended the analysis of the partially coherent Gaussian Schell model to include physical apertures and expressed it in terms of a Wigner function such that only second moment and centroid propagation is required. We have implemented this formalism within the SHADOW ray tracing code, providing fast, convenient transfer matrix computation down an x-ray beamline and subsequent moment propagation, including beam size, divergence and coherence properties. For the fully coherent case, we are developing tools for efficient Linear Canonical Transforms. On the optimization front, we have used Bayesian Optimization with Gaussian Processes and performed proof of principle automated alignment experiments on the Tender Energy Spectroscopy (TES) beamline at NSLS-II. These software tools are being integrated into the Sirepo web-based simulation framework as well as combined with the Bluesky control software suite in a dedicated package called Sirepo-Bluesky. We present an outlook on the progress we have made thus far, along with a future vision for this work.

We introduce an X-ray Hartmann Wavefront Sensor (HWS) simulation tool developed under the Synchrotron Radiation Workshop (SRW) framework. This metrology package can mimic an in-situ wavefront measurement experiment with a particular beamline optical layout, predict the expected Hartmanngrams, and then give access to the wavefront results under different beamline configurations. From the HWS design point of view, this SRW HWS simulation tool can be used to optimize the wavefront sensor parameters, such as the size and pitch of the Hartmann mask and the distance between the mask and the detector, in a specific X-ray energy range and help to tolerance complicated optical setup. Besides the X-ray HWS simulation in SRW, we also address some initial tests of a hard X-ray HWS under development at NSLS-II. Initial tests can be performed to evaluate the basic functionality of the X-ray HWS, such as the measurement repeatability and sensitivity to beam imperfections. It can provide a comprehensive evaluation of the performance of an X-ray HWS and help to optimize its design and functionality as a diagnostic tool for specific research questions and experimental conditions.

We will discuss the impact of simulation in a Coherent Diffractive Imaging (CDI) beamline currently under construction at NSLS-II. The optical system is designed to efficiently transport brightness from source to sample, while varying the sample illumination beam size and controlling the coherence properties of the beam. Detailed forward simulations of the measured intensity arising from the interaction of a model of the sample and the known x-ray beam can be used to interpret the images provided by the CDI method. Our current activities, plans for the immediate future, and considerations of our future needs will be presented.

SRW is an established wave physics library for X-ray simulations. We present a novel software package, initially forked from existing projects, that permits to use SRW in a convenient way for start-to-end simulation of full beamlines, including full coherence analysis, poly-chromaticity with chromatic aberrations, scanning and vibrations, and automatically generated reports. We demonstrate the capabilities and performance with simulations of coherent imaging experiments of holography and ptychography, including a challenging multi-beam ptychography case.

We will report on partially coherent undulator radiation simulations performed for the Hard X-ray Nanoprobe (HXN) beamline of NSLS-II with electron beam and X-ray optics instabilities taken into consideration. RF BPM and XBPM data were used to estimate values of these positional and angular instabilities for the partially coherent X-ray emission and propagation calculations with SRW code. These calculations allowed us to determine time-varying (due to the instabilities) intensity distributions and other characteristics of the X-ray radiation at important beamline locations, and estimate impacts of the instabilities on experimental data from coherent diffraction imaging experiments at HXN.

Cavity-based x-ray free-electron lasers (CBXFEL) [1-6] will allow use of optical cavity feedback to support generation of fully coherent x-rays of high brilliance and stability by electrons in undulators. CBXFEL optical cavities comprise Bragg-reflecting flat crystal mirrors, which ensure x-rays circulation on a closed orbit, and x-ray refractive lenses, which stabilize the orbit and refocus the x-rays back on the electrons in the undulator. Depending on the cavity design, there are tens of degrees of freedom of the optical elements, which can never be perfectly aligned. Here, we study signatures of misalignment of the optical components and of the undulator source with the purposes of understanding the effects of misalignment on x-ray beam dynamics, understanding misalignment tolerances, and developing cavity alignment procedures. Betatron oscillations of the x-ray beam trajectory are one of the characteristic signatures of cavity misalignment. The studies are performed on an example of a four-crystal rectangular cavity (Fig. 1) using analytical and numerical wave optics as well as ray-tracing techniques [7]. Detailed results of the studies are published in [8]. References [1] Z. Huang and R. D. Ruth, Phys. Rev. Lett. 96, 144801 (2006). [2] K.-J. Kim, Yu. Shvyd’ko and S. Reiche, Phys. Rev. Lett. 100, 244802 (2008). [3] K.-J. Kim and Yu. Shvyd’ko, Phys. Rev. ST Accel. Beams 12, 030703 (2009). [4] G. Marcus et al., Proc. 38th Int. FEL Conf. 10.18429/JACoW-FEL2017-MOP061. [5] H. P. Freund, P.J.M. van der Slot, Yu. Shvyd’ko, New J. Phys. 21, 093028 (2019). [6] G. Marcus et al., Phys. Rev. Lett. 125, 254801 (2020). [7] M. Sanchez del et al., J. Synchrotron Radiat. 18, 708 (2011). [8] P. Qi and Yu. Shvyd’ko, Phys. Rev. Accel. Beams 25 (2022) 050701 Acknowledgements Work at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH11357.