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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. 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 ($\beta, \gamma$), $\varGamma-q^2$ linearity ($R^2=0.99904$), and consistency with the Einstein-Stokes law. Key parameter sensitivity analysis reveals some points below. 1) Optimal aperture matching ($r/\sigma=1$) balances coherence and photon flux; 2) Mechanical vibrations with $\Delta x/s=1500$ induce periodic oscillations in $g_2(q,\tau)$, 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. 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. -
Keywords:
- X-ray photon correlation spectroscopy /
- Monte Carlo simulation /
- speckle dynamics /
- full optical path simulation
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图 1 模拟数据在不同散射矢量q处的空间相干因子β和拉伸指数γ
Figure 1. Simulated spatial coherence factor β and stretching exponent γ at different scattering vectors q
图 2 模拟数据在不同步长s时的空间相干因子β和拉伸指数γ
Figure 2. Simulated spatial coherence factor β and stretching exponent γ at different step lengths s
图 3 弛豫率与散射矢量的拟合: $ \varGamma=D\cdot q^2 $, 其中$ D= $$ 3.63\times10^{-4} $ nm2/s
Figure 3. Fitting of relaxation rate to scattering vector: $ \varGamma=D\cdot q^2 $, where $ D=3.63\times 10^{-4} $ nm2/s
图 4 模拟衍射的光路图与SAXS图样
Figure 4. Simulated diffraction light path diagram and SAXS pattern
图 5 弛豫率与步长平方的拟合: $ \varGamma=k\cdot s^2 $, 其中$ k= $$ 5.93\times 10^4/{\mathrm{s}} $
Figure 5. Fitting of relaxation rate versus the square of step length: $ \varGamma=k\cdot s^2 $, where $ k=5.93\times 10^4 $/s
图 6 光阑孔径对于关联函数的影响
Figure 6. The effect of pinhole size on the correlation function
图 7 光子计数噪声(泊松噪声)对于实验散斑衬度的影响
Figure 7. The effect of photon counting noise (Poisson noise) on the correlation function
图 8 光强波动对于实验散斑衬度的影响
Figure 8. The effect of light intensity fluctuation on the correlation function
图 9 机械振动对于关联函数的影响
Figure 9. The effect of mechanical vibration on the correlation function
表 1 不同距离处放置机械泵对样品台振动振幅的影响
Table 1. Effect of mechanical pump at different distances on sample stage vibration amplitude
Distance/m Horizontal/nm Frequency/Hz Steady 723 24.378 2 1538 24.326 1 2129 24.240 0.5 2785 24.220 Steady 755 24.166 
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