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相干性作为前沿X射线研究技术的核心要素, 在过去二十年中推动了相干X射线衍射成像、X射线全息术等众多实验的蓬勃发展, 并推动了第四代同步辐射光源与硬X射线自由电子激光的建设. 为了实现对同步辐射光束线相干性及光源尺寸的测量, 本文构建了基于二维单光栅干涉法的X射线测量系统, 深入探讨其测量原理与传播模型. 首先, 依据VanCittert-Zernike定理, 明确干涉点阵可见度与X射线空间相干度的内在联系; 其次, 运用单光栅 Talbot 自成像效应, 精确测量光栅平面处X射线空间相干长度, 并推导光源空间分布. 实验结果表明, 上海光源 X光学测试线弯铁光源相干长度为4.2 μm(H)×13.8 μm(V) @15 keV, 光源尺寸为 124 μm(H)×38 μm(V). 该技术能够同时测量水平和垂直方向的相干长度, 有助于识别X射线源相干区域形状, 也可用于评估X射线光学器件的相干保持能力, 为X射线相干性研究提供了新的有效途径.Coherence, as a core element of cutting-edge X-ray research technology, has driven the vigorous development of many experiments such as coherent X-ray diffraction imaging and X-ray holography in the past two decades, as well as the construction of fourth-generation synchrotron radiation sources and hard X-ray free electron lasers. To measure the size of synchrotron radiation light source and coherence of beamline, an X-ray measurement system based on two-dimensional (2D) single grating interferometry is established in this work, and the measurement principles and propagation models used in the system are also investigated. Firstly, based on the VanCittert-Zernike theorem, the relationship between the visibility of the interference lattice and the spatial coherence of X-rays is established. Secondly, by combining the Talbot self imaging effect of a single grating, the X-ray spatial coherence length of the grating plane is measured, and the spatial distribution of the corresponding light source is obtained through further calculation. The relevant measurement experiments of this study are conducted at the BL09B bending magnet beamline of the Shanghai Synchrotron Radiation Facility (SSRF). A 2D checkerboard π phase-shift grating is used as the core device in the experiment. This setup can not only enable the acquisition of transverse coherence lengths in the vertical and horizontal directions but also further measure the transverse coherence lengths in the directions forming 45° and 135° angles with respect to the horizontal direction. The experimental process strictly follows the technical specifications outlined in this paper: measuring interferograms at different positions downstream of the phase grating along the beam propagation direction. For each interferogram, the corresponding visibility values are extracted by analyzing the harmonic peaks in its Fourier-transformed image. Ultimately, the transverse coherence length in each direction is derived based on the evolution law of visibility as a function of the grating-to-detector distance. The experimental results show that the coherence length of the emitted X-rays on SSRF testline is 4.2 μm(H)×13.8 μm(V) at 15 keV, and the size of the bending magnet source is 124 μm(H)×38 μm(V). The results obtained by this method can provide important references for measuring the electron source size and developing experimental methods with high requirements for uniform illumination.
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Keywords:
- synchrotron radiation /
- X-ray single-grating interferometry /
- coherence /
- source size
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图 1 2D光栅设计图和光栅剖面扫描电子显微镜图像 (a) 设计图; (b) 光栅剖面扫描电子显微镜图像
Fig. 1. The central part of the 2D grating diagram and the SEM image: (a) Design drawing; (b) grating profile SEM image.
图 2 二维单光栅干涉仪检测系统 (a) 示意图; (b) 实物图
Fig. 2. 2D grating interferometry measuring system: (a) Schematic; (b) photographic.
图 3 (a) d2,0° = 157 mm和(b) d6,45° = 947 mm处获得的干涉图案的中心部分; (c), (d) 对应的傅里叶变换图像, 黄色虚线区域表示不同的方向; (e)—(h) 2D光栅不同方向能见度随d的变化, 黑线是实验数据, 红线是峰值处的高斯拟合数据
Fig. 3. Interferograms recorded at d2,0° = 157 mm (a) and d6,45° = 947 mm (b); (c), (d) their Fourier transform images, with the yellow dashed regions indicating the different directions; (e)–(h) the visibility evolution as a function of the grating-to-detector distance, d, the black lines are the experimental data, while the red lines are data selected around each Talbot distances for the Gaussian envelope fitting.
图 4 光子能量为15 keV时, BL09B弯铁光源尺寸的模拟结果
Fig. 4. Simulation results of BL09B bending magnet source size at a photon energy of 15 keV.
表 1 2D单光栅干涉测量中提取的光源相干长度和尺寸
Table 1. Extracted source coherence length and beam sizes from 2D single grating interferometry measurements.
θ/(°) 相干长度/μm 光源尺寸/μm 0 4.2±0.1 124±2 45 7.2±0.1 72±1 90 13.8±0.8 38±2 135 6.9±0.1 75±1 
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[1] 周光照, 佟亚军, 陈灿, 任玉琦, 王玉丹, 肖体乔 2011 物理学报 60 028701
Google Scholar
Zhou G Z, Tong Y J, Chen C, Ren Y Y, Wang Y D, Xiao T Q 2011 Acta Phys. Sin. 60 028701
Google Scholar
[2] Mcnulty I, Kirz J, Jacobsen C, Anderson E H, Howells M R, Kern D P 1992 Science 256 1009
Google Scholar
[3] Grubel G, Zontone F 2004 Alloys. Compd. 362 3
Google Scholar
[4] Wilkins S W, Nesterets Y I, Gureyev T E 2014 Phil. Trans. R. Soc. A 372 0021
[5] Yoshio S 2004 Rev. Sci. Instrum. 75 1026
Google Scholar
[6] Guigay J P, Zabler S, Cloetens P, David C, Mokso R, Schlenker M 2004 J. Synchrotron Rad. 11 476
Google Scholar
[7] Rutishauser S, Samoylova L, Krzywinski J, Bunk O, Grünert J, Sinn H, Cammarata M, Fritz D M, David C 2012 Nat. Commun. 3 947
Google Scholar
[8] Wang H, Sawhney K, Berujon S 2014 Opt. Lett. 39 2518
Google Scholar
[9] 戚俊成, 叶琳琳, 陈荣昌, 谢红兰, 任玉琦, 杜国浩, 邓彪, 肖体乔 2014 物理学报 63 104202
Google Scholar
Qi J C, Ye L L, Chen R C, Xie H L, Ren Y Q, Du G H, Deng B, Xiao T Q 2014 Acta Phys. Sin. 63 104202
Google Scholar
[10] Matsuyama S, Yokoyama H, Fukui R, Kohmura Y, Tamasaku K, Yabashi M, Yashiro W, Momose A, Ishikawa T, Yamauchi K 2012 Opt. Express 20 24977
Google Scholar
[11] Liu Y, Seaberg M, Zhu D, Krzywinski J, Seiboth F, Hardin C, Cocco D, Aquila A, Nagler B, Lee H J, Boutet S, Feng Y, Ding Y, Marcus G, Sakdinawat A 2018 Optica 5 967
Google Scholar
[12] Inoue T, Matsuyama S, Kawai S, Yumoto H, Inubushi Y, Osaka T, Inoue I, Koyama T, Tono K, Ohashi H, Yabashi M, Ishikawa T, Yamauchi K 2018 Rev. Sci. Instrum. 89 043106
Google Scholar
[13] Born M, Wolf, E 1999 Principles of Optics (7th Ed.) (Cambridgeshire: Cambridge University Press) pp554–632
[14] Li Z, Fan Y, Xue L, Zhang Z, Wang J 2019 Proceedings Of The 13th International Conference On Synchrotron Radiation Instrumentation—Sri 2018 Taipei, Taiwan, China, June 11–15, 2018 p060040
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