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台式X射线系统存在通量低、非相干性等局限, 在显微成像、高精度测量等应用场景中面临巨大挑战. 傅里叶变换关联成像(FGI)对相干性要求较低, 据此原理发展出的空间相关多角度FGI能够有效提高成像效率, 适用于台式X射线系统. 然而该技术仍处于理论阶段, 缺乏调制X射线并形成聚焦多光束的有效器件. 为此, 本文提出一种多光栅调制方法, 将多个子光栅按特定方位排列对X射线进行调制. 单个子光栅出射的X射线为空间相干光, 各子光栅之间的X射线在样品位置非相干叠加, 从而形成聚焦的多角度光束, 有效提高台式X射线系统的通量利用率. 本文对多光栅调制屏的调制原理进行阐述, 通过数值仿真分析光栅尺寸、材质、厚度等参数的影响, 针对液态靶X射线源设计多光栅调制屏, 并完成加工. 本研究能够推动台式X射线系统在高分辨衍射成像中的应用.The desktop X-ray system has limitations such as low flux and poor coherence. It faces great challenges in application scenarios such as microscopic imaging and high-precision measurement. Fourier-transform ghost imaging (FGI) has low requirements for the coherence of the light source. Using this principle, multi-angle FGI based on spatial correlation can effectively improve the imaging efficiency and is suitable for desktop X-ray systems. However, this technology is still in the theoretical stage, and there is a lack of effective devices to modulate X-rays and form focused multiple beams. To this end, a multi-grating modulation method is proposed in this work. The partially coherent radiation of the X-ray source is modulated by arranging multiple sub-gratings in a specific direction. The X-ray emitted by a single sub-grating is spatially coherent light, and the X-rays between the sub-gratings are incoherently superimposed at the sample position to form a focused multi-angle beam. This effectively improves the flux utilization of the desktop system. The modulation principle of multi-grating is described theoretically, and the key design parameters and their selection basis are clarified. Through numerical simulation, the modulation characteristics of partially coherent X-rays in the propagation process behind the modulation screen are systematically analyzed. By optimizing the parameters such as the size, material and thickness of the sub-grating, the influences of the sub-grating on the size, uniformity and diffraction efficiency of the focused spot are investigated. The results show that when the sub-grating size matches the spatial coherence size of the X-ray source, the focusing effect of the beam can be significantly improved, and a smaller and uniform focal spot can be obtained. Based on the theoretical and simulation results, a gold multi-grating modulation screen is designed and fabricated for the liquid target X-ray source. The simulation and theoretical predictions will be validated experimentally, once the experimental conditions are met. The design and implementation of the modulation screen provide effective support and a feasible way for multi-angle diffraction imaging and related applications in miniaturized X-ray systems.
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Keywords:
- tabletop X-ray system /
- multi-grating modulation screen /
- spatial modulation /
- diffraction imaging
[1] Chien C C, Tseng P Y, Chen H H, Hua T E, Chen S T, Chen Y Y, Leng W H, Wang C H, Hwu Y, Yin G C, Liang K S, Chen F R, Chu Y S, Yeh H I, Yang Y C, Yang CS, Zhang G L, Je J H, Margaritondo J 2013 Biotechnol. Adv. 31 375
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图 1 多光栅调制屏调制原理 (a) 多光栅调制的光路示意图; (b) 多光栅调制屏的二维结构
Fig. 1. Modulation principle of multi-grating modulation: (a) Optical schematic diagram of multi-grating modulation; (b) two-dimensional structure of multi-grating modulation screen.
图 2 调制屏后光束传播过程中光斑的强度分布演变的结果 (a) 距离调制屏不同位置$z$处的光斑的强度分布三维图; (b) z = 0.19 m处((a)图)的强度分布二维图; (c) (b)图横截面强度分布曲线
Fig. 2. Simulation results of the evolution of the intensity distribution of the spot in the process of beam propagation behind the modulation screen: (a) Three-dimensional diagram of the intensity distribution of spot at different positions $z$ from the modulation screen; (b) two-dimensional diagram of the intensity distribution of the pattern in Fig.(a) at z = 0.19 m; (c) cross section curve of the intensity distribution of Fig.(b).
图 3 不同归一化光栅尺寸${R_{\text{l}}}$下的仿真结果 (a) ${R_{\text{l}}}$ = 0.5时的光斑强度分布; (b) ${R_{\text{l}}}$ = 1时的光斑强度分布; (c) ${R_{\text{l}}}$ = 2.4时的光斑强度分布; (d) 光斑的FWHM随归一化光栅尺寸变化的曲线; (e) 光斑均匀性随归一化光栅尺寸变化的曲线
Fig. 3. Simulation results under different normalized grating sizes ${R_{\text{l}}}$: (a) The intensity distribution of the spot when ${R_{\text{l}}}$ = 0.5; (b) the intensity distribution of the spot when ${R_{\text{l}}}$ = 1; (c) the intensity distribution of the spot when ${R_{\text{l}}}$ = 2.4; (d) the curve of the FWHM of the spot changing with the normalized grating size; (e) the curve of the uniformity of the spot with the change of the normalized grating size.
图 4 多光栅调制屏的衍射特性仿真结果 (a) 1 ${\text{nm}}$波长下不同材料的多光栅调制屏衍射效率随厚度变化的曲线; (b) 不同光源波长对应的最大衍射效率及最佳光栅厚度
Fig. 4. Simulation results of diffraction characteristics of multi-grating modulation screen: (a) Diffraction efficiency curves of multi-grating modulation screens made of different materials as a function of thickness at a wavelength of 1${\text{nm}}$; (b) maximum diffraction efficiency and optimal grating thickness for different source wavelengths.
图 5 调制屏尺寸与后焦距对最小光栅周期和系统空间分辨率的影响 (a)—(c) 在调制屏前焦距分别为0.2, 0.36和0.5 m时, 最小光栅周期随调制屏尺寸与后焦距的变化关系; (d)—(f) 在最小光栅周期不小于200 nm的约束条件下, 当调制屏前焦距分别为0.2, 0.36和0.5 m时, 系统空间分辨率随调制屏尺寸与后焦距的变化情况
Fig. 5. Influence of the size of the modulation screen and the back focal length on the minimum grating period and the spatial resolution of the system: (a)–(c) When the focal lengths in front of the modulation screen are 0.2, 0.36 and 0.5 m, respectively, the minimum grating period varies with the size of the modulation screen and the back focal length; (d)–(f) under the constraint that the minimum grating period is not less than 200 nm, when the front focal length of the modulation screen is 0.2, 0.36 and 0.5 m, the spatial resolution of the system varies with the size of the modulation screen and the back focal length.
图 6 多光栅调制屏 (a) 调制屏实物图; (b) 调制屏的整体分布图像; (c) 单个光栅SEM平面图像; (d) 光栅的部分结构SEM图像
Fig. 6. Multi-grating modulation screen: (a) Photograph of the modulation screen; (b) overall distribution image of the modulation screen; (c) SEM image of a single grating plane; (d) SEM image of the partial structure of the grating.
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[1] Chien C C, Tseng P Y, Chen H H, Hua T E, Chen S T, Chen Y Y, Leng W H, Wang C H, Hwu Y, Yin G C, Liang K S, Chen F R, Chu Y S, Yeh H I, Yang Y C, Yang CS, Zhang G L, Je J H, Margaritondo J 2013 Biotechnol. Adv. 31 375
Google Scholar
[2] Zhang L, Tao F, Du G, Wang J, Gao R Y, Deng B, Xiao T Q 2023 Nucl. Instrum. Methods Phys. Res. Sect. A 1057 168781
Google Scholar
[3] Yao S, Fan J, Chen Z, Zong Y, Zhang J, Sun Z, Zhang L, Tai R, Liu Z, Chen C, Jiang H D 2018 IUCrJ 5 141
Google Scholar
[4] Foetisch A, Filella M, Watts B, Vinot LH, Bigalke M 2022 J. Hazard. Mater. 426 127804
Google Scholar
[5] Miao J, Sandberg R L, Song C 2011 IEEE J. Sel. Top. 18 399
[6] Prosekov P A, Nosik V L, Blagov A E 2021 Crystallogr. Rep. 66 867
Google Scholar
[7] Pfeiffer F 2018 Nat. Photonics 12 9
Google Scholar
[8] Yuan Q X, Deng B, Guan Y, Zhang K, Liu Y J 2019 Physics 48 205
[9] Withers P J, Bouman C, Carmignato S, Cnudde V, Grimaldi D, Hagen C K, Maire É, Manley M, Plessis A D, Stock S 2021 R Nat. Rev. Methods Primers. 1 18
Google Scholar
[10] Pushie M J, Sylvain N J, Hou H, Hackett M J, Kelly M E, Webb S M 2022 Metallomics 14 mfac032
Google Scholar
[11] Cheng J, Han S S 2004 Phys. Rev. Lett. 92 093903
Google Scholar
[12] Yu H, Lu R H, Han S S, Xie H L, Du G H, Xiao T Q, Zhu D M 2016 Phys. Rev. Lett. 117 113901
Google Scholar
[13] Tan Z J, Yu H, Zhu R G, Lu R H, Han S S, Xue C F, Yang S M, Wu Y Q 2022 Phys. Rev. A. 106 053521
Google Scholar
[14] Zhang A X, He Y H, Wu L A, Chen L M, Wang B B 2018 Optica 5 374
Google Scholar
[15] He Y H, Zhang A X, Li M F, Huang Y Y, Quan B G, Li D Z, Wu L A, Chen L M 2020 APL Photonics 5 056102
Google Scholar
[16] Zhao C Z, Zhang H P, Tang J, Zhao N X, Li Z L, Xiao T Q 2024 J. Synchrotron Radiat. 31 1525
Google Scholar
[17] Li P, Chen X, Qiu X, Chen B L, Chen LX, Sun B Q 2024 Chin. Opt. Lett. 22 112701
Google Scholar
[18] Sun M J, Zhang J M 2019 Sensors 19 732
Google Scholar
[19] Li H Q, Hou W T, Ye Z Y, Yuan T Y, Shao S K, Xiong J, Sun T X, Sun X F 2023 Appl. Phys. Lett. 123 141101
Google Scholar
[20] Wittwer F, Lyubomirskiy M, Koch F, Kahnt M, Seyrich M, Garrevoet J, David C, Schroer C G 2021 Appl. Phys. Lett. 118 171102
Google Scholar
[21] Lyubomirskiy M, Wittwer F, Kahnt M, Koch F, Kubec A, Falch K V, Garrevoet J, Seyrich M, David C, Schroer C G 2022 Sci. Rep. 12 6203
Google Scholar
[22] Li Q Y, Tan Z J, Wang D, Yu H, Han S S 2025 Phys. Rev. A. 111 033531
Google Scholar
[23] Zholudev S I, Terentiev S A, Polyakov S N, Martyushov S Y, Denisov V N, Kornilov N V, Polikarpov M V, Snigirev A A, Snigireva I I, Blank V D 2016 AIP Conf. Proc. 1764 020006
[24] Das A, Heirwegh C M, Gao N, Elam W T, Wade L A, Clark B C, Hurowitz J A, VanBommel S J, Jones M W M, Allwood A C X 2025 X-Ray Spectrom 54 203
Google Scholar
[25] Marshall F J, Bahr R E, Goncharov V N, Glebov V Y, Peng B, Regan S P, Sangster T C, Stoeckl C 2017 Rev. Sci. Instrum. 88 093702
Google Scholar
[26] Ohba A, Nakano T, Onoda S, Mochizuki T, Nakamoto K 2021 Rev. Sci. Instrum. 92 093704
Google Scholar
[27] Chen B Y, Yin G C, Lee C Y, Hsu M Y, Lin B H, Tseng S C, Li X Y, Chen H Y, Wu J X, Chang S H, Tang M T 2018 Synchrotron Radiat. News 31 27
Google Scholar
[28] Mohacsi I, Vartiainen I, Rösner B, Guizar-Sicairos M, Guzenko V A, McNulty I, Winarski R, Holt M V, David C 2017 Sci. Rep. 7 43624
Google Scholar
[29] Li T, Senesi A J, Lee B 2016 Chem. Rev. 116 11128
Google Scholar
[30] Hirose M, Higashino T, Ishiguro N, Takahashi Y 2020 Opt. Express 28 1216
Google Scholar
[31] Zhu Z, Ellis R A, Pang S 2018 Optica 5 733
Google Scholar
[32] Born M, Wolf E 2013 Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Elsevier) pp572–577
[33] Moreau P A, Toninelli E, Morris P A, Aspden R S, Gregory T, Spalding G, Boyd R W, Padgett M J 2018 Opt. Express 26 7528
Google Scholar
[34] Goodman J W 2005 Introduction to Fourier Optics (Roberts and Company publishers) pp80–82
[35] Palmer C, Loewen E G 2005 Diffraction grating handbook (Newport Corporation) pp21–22
[36] Harvey J E, Pfisterer R N 2019 Opt. Eng. 58 087105
[37] Pascarelli S, Mathon O, Munoz M, Mairs T, Susini J 2006 J. Synchrotron Radiat. 13 351
Google Scholar
[38] 许成文, 钟理京, 秦应雄, 郭海平, 唐霞辉 2016 中国激光 43 102001
Google Scholar
Xu C W, Zhong L J, Qin Y X, Guo H P, Tang X H 2016 Chin. J. Lasers. 43 102001
Google Scholar
[39] 谢常青 2022 光学精密工程 30 1815
Google Scholar
Xie C Q 2022 Opt. Precis. Eng. 30 1815
Google Scholar
[40] 邱克强, 徐向东, 刘颖, 洪义麟, 付绍军 2008 物理学报 57 6329
Google Scholar
Qiu K Q, Xu X D, Liu Y, Hong Y L, Fu S J 2008 Acta Phys. Sin. 57 6329
Google Scholar
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Google Scholar
Gao Y Z, Wu L J, Lu W E, Liu H Y, Xia Y, Zhao L L, Li Y L, Kong X D, Han L 2021 Acta Opt. Sin. 41 1111002
Google Scholar
[42] 杨家敏, 丁耀南, 崔明启, 曹磊峰, 丁永坤, 朱佩平, 赵屹东, 杨国洪, 郑志坚, 王耀梅, 张文海, 黎刚 2000 强激光与粒子束 12 723
Yang J M, Ding Y N, Cui Q M, Cao L F, Ding Y K, Zhu P P, Zhao Y D, Yang G H, Zheng Y J, Wang Y N, Zhang W H, Ni G 2000 High Power Laser Part. Beams 12 723
[43] Pinzek S J 2023 Ph. D. Dissertation (Munich: Technische Universität München
[44] Burwitz V, Reinsch K, Greiner J, Rauch T, Suleimanov V, Walter F W, Mennickent R E, Predehl P 2007 Adv. Space Res. 40 1294
Google Scholar
[45] Morimoto N, Fujino S, Ohshima K, Harada J, Hosoi T, Watanabe H, Shimura T 2014 Opt. Lett. 39 4297
Google Scholar
[46] Moore A S, Guymer T M, Kline J L, Morton J, Taccetti M, Lanier N E, Bentley C, Workman J, Peterson B, Mussack K, Cowan J, Prasad R, Richardson M, Burns S, Kalantar D H, Benedetti L R, Bell P, Bradley D, Hsing W, Stevenson M 2012 Rev. Sci. Instrum. 83 10E132
[47] Gross H, Henn M, Heidenreich S, Rathsfeld A, Bär M 2012 Appl. Opt. 51 7384
Google Scholar
[48] Wansleben M, Zech C, Streeck C, Weser J, Genzel C, Beckhoff B, Mainz R 2019 J. Anal. At. Spectrom. 34 1497
Google Scholar
[49] Tong X, Chen Y F, Mu C Y, Chen Q C, Zhang X Z, Zeng G, Li Y C, Xu Z J, Zhao J, Zhen X J, Mao C W, Lu H L, Tai R Z 2023 Nanotechnology 34 215301
Google Scholar
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