Development of a vibration mode propagation method to perform wave-optics simulation of beamline vibration

Fourth-generation synchrotron radiation (SR) sources offer dramatically enhanced coherence, pushing the requirements for beamline stability to new extremes, particularly in spatial resolution for imaging, temporal resolution for dynamic studies, and X-ray nanoprobes. Therefore, the beamline must possess high stability while effectively propagating coherent photons during optical design. For fourth-generation SR sources with significantly enhanced coherence, wave-optics simulations must be incorporated into optical design processes. Here, we present the development of a vibration mode propagation (VMP) method for beamline vibration simulation. By utilizing vibration modes instead of wavefront vibrations and propagating them through the method developed in this work, the VMP method enables computational speeds up to 40 times faster than the brute-force method in actual beamline models of fourth-generation SR sources, and high-efficiency, fully wave-optics simulation of vibration is achieved. Furthermore, by integrating the VMP method with coherent mode decomposition, we extend its application to partially coherent SR beams, enabling a comprehensive analysis of vibration decoherence, position vibration, and the vibration impact of experimental sampling frequency.