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基于散斑技术的同步辐射X射线光子关联谱(XPCS)是研究材料介观尺度动态过程的重要方法, 但实验中的光源特性、光束传输及探测器响应等因素对散斑动力学信号的影响机制复杂, 难以对其中的影响因素进行单独且直接的观测. 为此, 本文旨在通过蒙特卡罗模拟开展全光路数值建模, 系统解析各因素的影响, 为实验设计与优化提供理论支撑. 研究构建了包含布朗粒子动力学、光束相干性及探测器响应的三维仿真框架, 模拟从光子发射到信号采集的全流程. 基于夫琅禾费衍射理论, 开发散斑光场生成算法, 通过原子位置动态演化与相位调制, 复现实验散斑涨落特性, 并通过Siegert关系拟合、散射矢量区域选择及粒子运动步长与温度关系验证了模拟程序的可行性. 关键参数灵敏度分析表明: 光阑孔径与光束束腰存在最优匹配条件$r/\sigma=1$, 此时相干性与光子通量达到平衡; 机械振动振幅达到运动步长1500倍时, 关联函数出现周期性振荡, 导致动力学参数提取失真; 低光强条件下泊松噪声与光强波动显著降低信噪比. 研究建立的全光路模拟框架, 揭示了光源特性、光学元件参数及噪声因素对实验结果的影响机制, 为XPCS实验参数优化提供了理论依据, 明确了噪声抑制与动力学解析的协同机制, 为该技术在更多实验场景的应用奠定了模拟基础.
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 ($\beta, \gamma$), $\varGamma{\text{-}}q^2$ 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 在不同散射矢量q处的空间相干因子β和拉伸指数γ模拟数据
Fig. 1. Simulated spatial coherence factor β and stretching exponent γ at different scattering vectors q
图 2 在不同步长s时的空间相干因子β和拉伸指数γ模拟数据
Fig. 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 q^2 $, 其中$ D= $$ 3.63\times10^{-4} $ nm2/s
Fig. 3. Fitting of relaxation rate to scattering vector: $ \varGamma=D q^2 $, where $ D=3.63\times 10^{-4} $ nm2/s
图 5 弛豫率与步长平方的拟合: $ \varGamma=k s^2 $, 其中$ k= $ $5.93\times 10^4\;{\mathrm{s}^{-1}} $
Fig. 5. Fitting of relaxation rate versus the square of step length: $ \varGamma=k s^2 $, where $ k=5.93\times 10^4 \;{\mathrm{s}^{-1}}$.
图 7 光子计数噪声(泊松噪声)对实验散斑衬度的影响
Fig. 7. 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
Fig. 8. Effect of light intensity fluctuation 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 amplitude/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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[1] Martinelli A, Baldi G, Dallari F, Rufflé B, Zontone F, Monaco G 2020 Philos. Mag. 100 2636
Google Scholar
[2] Zhong W, Liu F, Wang C 2021 J. Phys. Condens. Matter 33 313001
Google Scholar
[3] Jo W, Stern S, Westermeier F, Rysov R, Riepp M, Schmehr J, Lange J, Becker J, Sprung M, Laurus T, Graafsma H, Lokteva I, Gruebel G, Roseker W 2023 Opt. Express 31 3315
Google Scholar
[4] Sandy A R, Zhang Q, Lurio L B 2018 Annu. Rev. Mater. Res. 48 167
Google Scholar
[5] Sutton M, Lhermitte J R, Ehrburger-Dolle F, Livet F 2021 Phys. Rev. Res. 3 013119
Google Scholar
[6] Mohanty S, Cooper C B, Wang H, Liang M, Cai W 2022 Modell. Simul. Mater. Sci. Eng. 30 075004
Google Scholar
[7] Rudd R E, Briggs G, Sutton A, Medeiros-Ribeiro G, Williams R S 2003 Phys. Rev. Lett. 90 146101
Google Scholar
[8] Miao J, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
Google Scholar
[9] Tessarini S 2022 Ph. D. Dissertation (Zurich: ETH Zurich
[10] Sheyfer D, Zhang Q, Lal J, Loeffler T, Dufresne E M, Sandy A R, Narayanan S, Sankaranarayanan S K R S, Szczygiel R, Maj P, Soderholm L, Antonio M R, Stephenson G B 2020 Phys. Rev. Lett. 125 125504
Google Scholar
[11] Sheyfer D, Zheng H, Krogstad M, Thompson C, You H, Eastman J A, Liu Y, Wang B X, Ye Z G, Rosenkranz S, Phelan D, Dufresne E M, Stephenson G B, Cao Y 2024 J. Synchrotron Radiat. 31 55
Google Scholar
[12] Chen Y, Han W, Bin G, Wu S, Morgan S P, Sun S 2024 Sci. Rep. 14 27665
Google Scholar
[13] Hu Z, Donatelli J J 2024 Phys. Rev. B 110 214305
Google Scholar
[14] Semeraro E F, Möller J, Narayanan T 2018 J. Appl. Crystallogr. 51 706
Google Scholar
[15] Narayanan T, Sztucki M, Van Vaerenbergh P, Léonardon J, Gorini J, Claustre L, Sever F, Morse J, Boesecke P 2018 J. Appl. Crystallogr. 51 1511
Google Scholar
[16] Andrews R N, Narayanan S, Zhang F, Kuzmenko I, Ilavsky J 2018 J. Appl. Crystallogr. 51 35
Google Scholar
[17] Lehmkühler F, Dallari F, Jain A, Sikorski M, Moller J, Frenzel L, Lokteva I, Mills G, Walther M, Sinn H, Schulz F, Dartsch M, Markmann V, Bean R, Kim Y, Vagovic P, Madsen A, Mancuso A P, Grubel G 2020 Proc. Natl. Acad. Sci. U.S.A. 117 24110
Google Scholar
[18] Berne B J, Pecora R 2000 Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Chelmsford: Courier Corporation) pp40, 41
[19] Patterson G D, Lindsey C P 1981 Macromolecules 14 83
Google Scholar
[20] Khan F, Narayanan S, Sersted R, Schwarz N, Sandy A 2018 J. Synchrotron Radiat. 25 1135
Google Scholar
[21] Arango M T, Zhang Y, Zhao C, Li R, Doerk G, Nykypanchuk D, Chen-Wiegart Y C K, Fluerasu A, Wiegart L 2020 Mater. Today Phys. 14 100220
Google Scholar
[22] Ruta B, Evenson Z, Hechler S, Stolpe M, Pineda E, Gallino I, Busch R 2015 Phys. Rev. Lett. 115 175701
Google Scholar
[23] Katzav E, Schwartz M 2004 Phys. Rev. E 69 052603
Google Scholar
[24] Einstein A 1905 Ann. Phys. 322 549
Google Scholar
[25] Pérez-Madrid A, Rubí J M, Mazur P 1994 Physica A 212 231 (in Chinese)
Google Scholar
[26] Duhr S, Braun D 2006 Phys. Rev. Lett. 96 168301
Google Scholar
[27] Zhou Z, Zhang M, Cui C, Wei L, Li S, Guo Z, Xu Y, Tian F, Li X, Jiang H, Tai R 2025 Phys. Scr. 100 075115
Google Scholar
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