Method based on matrix optics for vibration evaluation of the X-ray beamline systems

The vibrations of X-ray optics play a crucial role in determining the stability of synchrotron radiation light sources and modern X-ray free-electron (X-FELs). Therefore, it is of great importance to perform the numerical analysis of vibrations in X-ray beamline design. This paper presents a method based on matrix optics, which can be used to rapidly analyze the degradation of beam performance, such as stability, beam size, and coherence, caused by the vibrations of optical elements. The analytical results derived from matrix optics are in good agreement with the ray-tracing simulations performed using SHADOW3. The proposed method can analytically describe the impact of vibrations on the beam quality, facilitating rapid optical vibration evaluation in complex beamline configurations and establishing quantitative stability specifications for critical optical elements.