Full-process simulation of XPCS speckle dynamics based on Monte Carlo method and analysis of key parameter dependencies

<sec>X-ray photon correlation spectroscopy (XPCS) is important for probing mesoscale material dynamics by using synchrotron radiation. However, the complex influences of parameters such as light source properties, beam propagation, and detector response on speckle dynamics are hard to directly observe. In this study, a Monte Carlo-based full optical path numerical model is developed to systematically analyze these effects, thereby aiding experimental optimization.</sec><sec>A simulation framework integrating Brownian dynamics, beam coherence, and detector response is constructed to replicate the entire photon emission-to-detection process. A Fraunhofer diffraction-based speckle generation algorithm reproduces speckle fluctuations via atomic position evolution and phase modulation. Feasibility is validated via Siegert relation fitting (<inline-formula><tex-math id="M2">\begin{document}$\beta, \gamma$\end{document}</tex-math></inline-formula>), <inline-formula><tex-math id="M3">\begin{document}$\varGamma{\text{-}}q^2$\end{document}</tex-math></inline-formula> linearity (<inline-formula><tex-math id="M4">\begin{document}$R^2=0.99904$\end{document}</tex-math></inline-formula>), and consistency with the Einstein-Stokes law.</sec><sec>Key parameter sensitivity analysis reveals some points below. 1) Optimal aperture matching (<inline-formula><tex-math id="M5">\begin{document}$r/\sigma=1$\end{document}</tex-math></inline-formula>) balances coherence and photon flux; 2) Mechanical vibrations with <inline-formula><tex-math id="M6">\begin{document}$\Delta x/s=1500$\end{document}</tex-math></inline-formula> induce periodic oscillations in <inline-formula><tex-math id="M7">\begin{document}$g_2(q,\tau)$\end{document}</tex-math></inline-formula>, masking intrinsic relaxation, which is validated by a 24.658-Hz pump experiment; 3) Poisson noise and intensity fluctuations degrade low-light signal-to-noise ratio, with Poisson noise causing discrete errors and classical noise inducing baseline shifts.</sec><sec>This framework clarifies how source properties, optical parameters, and noise affect experimental results, providing guidance for XPCS optimization and a foundation for extending its applications to high-precision coherent scattering scenarios.</sec>