新型工质堆多相流动形态中子成像表征技术进展及应用

梅中恺; 贺林峰; 文青龙; 邱志方; 陈东风

doi:10.13832/j.jnpe.2025.01.0047

新型工质堆多相流动形态中子成像表征技术进展及应用

doi: 10.13832/j.jnpe.2025.01.0047

梅中恺^{1, 2, 3,},
贺林峰⁴,
文青龙^{1, 2, 3, ,},
邱志方⁵,
陈东风⁴

1.
重庆大学能源与动力工程学院核工程与核技术系，重庆，400044
2.
重庆大学低品位能源利用技术及系统教育部重点实验室，重庆，400044
3.
两江新能源（核能与动力）实验室，重庆，400044
4.
中国原子能科学研究院，北京，102413
5.
中国核动力研究设计院，成都，610213

基金项目: 液态金属流动特性中子示踪研究（U2241282）

详细信息

作者简介:
梅中恺（1994—），男，助理研究员，现主要从事现主要从事反应堆热工水力研究，E-mail: zhongkai.mei@cqu.edu.cn

通讯作者:
文青龙， E-mail: qlwen@cqu.edu.cn

中图分类号: TL99
计量
- 文章访问数: 12
- HTML全文浏览量: 6
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-14
- 修回日期: 2024-09-12
- 刊出日期: 2025-02-15

Progress and Application of Neutron Radiography Characterization Technology for Multiphase Flow Pattern of New Working Medium Reactor

Mei Zhongkai^{1, 2, 3
,},
He Linfeng⁴,
Wen Qinglong^{1, 2, 3
, ,},
Qiu Zhifang⁵,
Chen Dongfeng⁴

1.
Department of Nuclear Engineering and Nuclear Technology, School of Energy & Power Engineering, Chongqing University, Chongqing, 400044, China
2.
Key Laboratory of Low-Grade Energy Utilization Technologies & Systems, Chongqing University, Chongqing, 400044, China
3.
Laboratory of Liangjiang New Energy (Nuclear Energy and Power), Chongqing, 400044, China
4.
China Institute of Atomic Energy, Beijing, 102413, China
5.
Nuclear Power Institute of China, Chengdu, 610213, China

摘要

摘要: 中子成像技术在新型工质堆多相流形态可视化与测量等领域表现出重要的应用潜力。本文阐述了中子成像测量方法的基本原理，全面综述了中子成像技术在传统轻水反应堆及铅铋冷却快堆、热管堆、超临界水堆和钠冷快堆等新型工质堆的研究进展，概述了中子成像技术应用于新型工质堆的未来发展方向，并提供了高保真中子图像获取与流动形态测量的基础方法论。
- 中子成像 /
- 多相流动形态 /
- 新型工质堆 /
- 高保真中子图像 /
- 流动测量方法
Abstract: Neutron radiography shows important application potential in the visualization and measurement of multi-phase flow morphologies in new working medium reactors. This article elaborates on the basic principles of neutron radiography measurement methods, provides a comprehensive review of the research progress of neutron radiography technology in traditional light water reactors, lead-bismuth cooled fast reactors, heat pipe cooled reactors, supercritical water reactors, and sodium-cooled fast reactors. It also outlines the future development directions of neutron radiography technology applied to new working medium reactors and provides the basic methodologies for obtaining high-fidelity neutron images and measuring flow patterns.
- Neutron radiography /
- Multiphase flow pattern /
- New working medium reactor /
- High-fidelity neutron image /
- Flow measurement method

HTML全文

图 1 气液两相流动空泡份额分布^[18]

Figure 1. Void Fraction Distribution of Gas-liquid Two Phase Flow^[18]

下载: 全尺寸图片幻灯片

图 2 中子图像平均灰度值分布^[31]

Figure 2. Average Gray Level Distribution of Neutron Radiography Image^[31]

下载: 全尺寸图片幻灯片

图 3 钠工质热管典型中子成像图像^[44]

Figure 3. Typical Raw Neutron Radiography Image of Sodium-based Heat Pipe^[44]

下载: 全尺寸图片幻灯片

图 4 锂工质热管典型中子成像图像^[45]

Figure 4. Typical Raw Neutron Radiography Image of Lithium-based Heat Pipe^[45]

下载: 全尺寸图片幻灯片

图 5 液态水形态随温度变化中子图像^[48]

Figure 5. Neutron Radiography Image of Liquid Water with Changing Temperature^[48]

下载: 全尺寸图片幻灯片

图 6 碎片床内两相流动中子图像^[52]

ε—孔隙率；α—空泡份额

Figure 6. Neutron Radiography Image of Two-phase Flow in a Debris Bed^[52]

下载: 全尺寸图片幻灯片

图 7 中子成像系统分辨率模型^[54]

Figure 7. System Resolution Model of Neutron Radiography^[54]

下载: 全尺寸图片幻灯片

图 8 L/D为250与500时各分项MTF曲线^[55]

Figure 8. MTF Curves of Each Component with L/D of 250 and 500^[55]

下载: 全尺寸图片幻灯片

图 9 中子图像中γ白斑噪声像素分布^[57]

Figure 9. γ White Spot Noise Pixel Distribution in Neutron Images^[57]

下载: 全尺寸图片幻灯片

图 10 不同方法中子图像去噪增强结果比较^[57]

Figure 10. Comparison of Denoising and Enhancement Results of Neutron Images by Different Methods^[57]

下载: 全尺寸图片幻灯片

图 11 中子穿透过金属容器观察内部流体原理示意图

Figure 11. Schematic Diagram of the Principle of Observing Internal Fluid by Neutron Penetrating Through a Metal Container

下载: 全尺寸图片幻灯片

图 12 圆柱体沿弦长方向上空泡份额测量^[60]

Figure 12. Chordal Void Fraction Measurement in a Cylinder^[60]

下载: 全尺寸图片幻灯片

图 13 轴对称气泡简图^[37]

a—椭球形气泡长半轴；b—椭球形气泡

Figure 13. Axially Symmetrical Bubble^[37]

下载: 全尺寸图片幻灯片

表 1 传统轻水反应堆中子成像工作汇总

Table 1. Summary of Neutron Radiography for Traditional Light Water Reactors

发表时间	研究者	研究方法	主要研究内容
1988年	Mishima等^[12]	热中子成像	测量狭窄矩形管道中的空气-水流动的空泡份额与界面面积，并且与传统电导探针技术进行对比
1990年	Takenaka等^[13]	热中子成像	证明中子成像对各种多相流可视化的适用性
1996年	Harvel等^[14]	热中子成像	测量截面平均空泡份额与时均空泡份额，并且与X射线成像进行对比
1998年	Takenaka等^[15]	热中子成像	测量一维与三维稳态空泡份额分布
2005年	Cha等^[16]	热中子成像	对两相流流型进行可视化，并且与超声波技术进行对比
2005年	Sarkar等^[17]	热中子成像	研究对流驱动的反应堆流型的稳定性
2005年	Lim等^[18]	热中子成像	测量不同液体与气体组合结果，并且与现有经验关联式进行比较
2009年	Tambouratzis等^[19]	热中子成像	研究流型识别的图像处理算法
2011年	Zboray等^[20]	冷中子成像	研究了沸水堆燃料组件中两个相邻子通道的绝热空气-水环状流以及功能格架性能
2016年	Saxena等^[21]	冷中子成像	测量燃料棒表面液膜厚度分布，并且将实验结果与计算流体力学结果进行比较
2018年	Zboray等^[22]	冷中子成像	获得虚拟燃料棒和格架结构上液膜厚度的分布图
2018年	Zboray等^[23]	冷中子成像	研究了气泡聚并和破碎现象，提取出气泡运动界面
2019年	Zboray等^[24]	冷中子成像	研究了气相分布、气泡大小以及瞬时气相界面速度分布
2021年	Yan等^[25]	热中子成像	提出改进的模拟退火算法，用于两相流界面重构
2021年	Liu等^[26]	冷中子成像	获得两相流动高分辨率速度场
2023年	Ahmed等^[27]	热中子成像	测量碎片床中蒸汽组分

下载: 导出CSV

表 2 铅铋冷却快堆中子成像工作汇总

Table 2. Summary of Neutron Radiography for Lead-Bismuth Cooled Fast Reactors

发表时间	研究者	研究方法	主要研究内容
1996年	Takenaka等^[30]	热中子成像	测量铅铋熔融合金中速度场分布
1998年	Uchimura等^[31]	热中子成像	提出包括降噪、管道-流体界面识别和图像平滑处理步骤的图像处理方法
1999年	Mishima等^[32]	热中子成像	观察熔融金属在预混过程中滴入水中的行为
1999年	Mishima等^[33]	热中子成像	对铅铋金属两相流进行可视化并测量空泡份额
2000年	Hibiki等^[34]	热中子成像	对熔融铅铋中单个孤立氮气气泡的形状、大小和上升速度进行测量
2004年	Saito等^[35]	热中子成像	研究再循环流量对气泡行为的影响
2005年	Saito等^[36]	热中子成像	比较中子成像与电导率探针两种方法
2009年	Saito等^[37]	热中子成像	对铅铋熔融合金中含有液滴的蒸汽气泡的动态行为及特征参数进行可视化测量

下载: 导出CSV

表 3 高温碱金属热管中子成像工作汇总

Table 3. Summary of Neutron Radiography for High-Temperature Alkali Metal Heat Pipes

发表时间	研究者	工质	研究内容
2011年	Kihm等^[44]	钠	对金属钠在热管内进行了多尺度输运可视化表征，并且验证方法的可行性
2013年	Kihm等^[45]	锂	研究高温钼-锂热管中锂工质的蒸发行为
2013年	Kirchoff等^[46]	锂	对锂工质的热物性变化进行可视化研究
2014年	Hight等^[47]	锂	研究不凝气体对热管传热的影响

下载: 导出CSV

表 4 超临界水中子成像工作汇总

Table 4. Summary of Neutron Radiography for Supercritical Water

发表时间	研究者	研究方法	研究内容
2009年	Balaskó等^[48]	热中子成像	研究超临界水在容器中的行为
2013年	Balaskó等^[49]	热中子成像	研究封闭回路中超临界水流动特性
2013年	Takenaka等^[50]	热中子成像	对超临界水和亚临界水的混合过程进行了可视化分析
2017年	Kiss等^[51]	热中子成像	研究自然循环下超临界水的温度、绝对压力、压差和质量流量

下载: 导出CSV

参考文献(66)

[1]	KALLMANN H, KUHN E. Photographic detection of slowly moving neutrons: US, 2186757A[P]. 1940-01-09.
[2]	THEWLIS J. Neutron radiography[J]. British Journal of Applied Physics, 1956, 7(10): 345-350. doi: 10.1088/0508-3443/7/10/301
[3]	LOHVITHEE M, RASSAME S, HIBIKI T. Applications of neutron computed tomography to thermal-hydraulics research[J]. Progress in Nuclear Energy, 2022, 149: 104262. doi: 10.1016/j.pnucene.2022.104262
[4]	TAMBOURATZIS T, PÀZSIT I. A general regression artificial neural network for two-phase flow regime identification[J]. Annals of Nuclear Energy, 2010, 37(5): 672-680. doi: 10.1016/j.anucene.2010.02.004
[5]	杨安波,弋然. 中子照相技术及其发展和应用[J]. 科学技术创新,2023(12): 22-25. doi: 10.3969/j.issn.1673-1328.2023.12.007
[6]	李环宇. 小型热中子照相系统关键部件的仿真与设计[D]. 长春: 东北师范大学,2022.
[7]	张俊哲. 中子照相技术及其在核工程中的应用[J]. 核动力工程,1991,12(2): 92-96.
[8]	陈东风,刘蕴韬,韩松柏. 中国先进研究堆中子散射谱仪建设现状和展望[J]. 中国材料进展,2009, 28(12): 1-5.
[9]	GARRETT D A, BERGER H. The technological development of neutron radiography[J]. Atomic Energy Review, 1977, 15(2): 125-142.
[10]	乔浩. 高分辨冷中子成像探测器的研究进展[D]. 兰州: 兰州大学,2017.
[11]	赵世平. 基于蒙特卡洛方法模拟中子照相[D]. 长春: 东北师范大学,2008.
[12]	MISHIMA K, FUJINE S, YONEDA K, et al. A study of air-water flow in a narrow rectangular duct using an image processing technique[M]//JONES O C, MICHIYOSHI I. Dynamics of Two-Phase Flows. Boca Raton: Begell House, 2023: 141-160.
[13]	TAKENAKA N, FUJII T, AKAGAWA K, et al. Application of neutron radiography to visualization of multiphase flows[J]. Flow Measurement and Instrumentation, 1990, 1(3): 149-156. doi: 10.1016/0955-5986(90)90004-Q
[14]	HARVEL G D, HORI K, KAWANISHI K, et al. Real-time cross-sectional averaged void fraction measurements in vertical annulus gas-liquid two-phase flow by neutron radiography and X-ray tomography techniques[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1996, 371(3): 544-552.
[15]	TAKENAKA N, ASANO H, FUJII T, et al. Three-dimensional visualization of void fraction distribution in steady two-phase flow by thermal neutron radiography[J]. Nuclear Engineering and Design, 1998, 184(2-3): 203-212. doi: 10.1016/S0029-5493(98)00197-6
[16]	CHA J E, LIM I C, SIM C M, et al. Observation of the two-phase flow patterns for a finned assembly using neutron radiography[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2005, 542(1-3): 175-180.
[17]	SARKAR P S, KASHYAP Y, SINHA A, et al. Applications for real-time neutron radiography for convection driven flow pattern transition studies[J]. IEEE Transactions on Nuclear Science, 2005, 52(1): 290-294. doi: 10.1109/TNS.2005.843653
[18]	LIM I C, SIM C M, CHA J E, et al. Measurement of the void fraction in a channel simulating the HANARO fuel assembly using neutron radiography[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2005, 542(1-3): 181-186.
[19]	TAMBOURATZIS T, PÁZSIT I. Fuzzy inference systems for efficient non-invasive on-line two-phase flow regime identification[C]//Proceedings of the 9th International Conference on Adaptive and Natural Computing Algorithms. Kuopio: Springer, 2009: 423-429.
[20]	ZBORAY R, KICKHOFEL J, DAMSOHN M, et al. Cold-neutron tomography of annular flow and functional spacer performance in a model of a boiling water reactor fuel rod bundle[J]. Nuclear Engineering and Design, 2011, 241(8): 3201-3215.
[21]	SAXENA A, ZBORAY R, PRASSER H M. Simulations and measurements of adiabatic annular flows in triangular, tight lattice nuclear fuel bundle model[J]. Nuclear Engineering and Design, 2016, 299: 163-173. doi: 10.1016/j.nucengdes.2015.07.063
[22]	ZBORAY R, BOLESCH C, PRASSER H M. Development of neutron and X-ray imaging techniques for nuclear fuel bundle optimization[J]. Nuclear Engineering and Design, 2018, 336: 24-33. doi: 10.1016/j.nucengdes.2017.04.035
[23]	ZBORAY R, TRTIK P. 800 fps neutron radiography of air-water two-phase flow[J]. MethodsX, 2018, 5: 96-102. doi: 10.1016/j.mex.2018.01.008
[24]	ZBORAY R, TRTIK P. In-depth analysis of high-speed, cold neutron imaging of air-water two-phase flows[J]. Flow Measurement and Instrumentation, 2019, 66: 182-189.
[25]	YAN M F, HU H S, HU G, et al. Development of a novel reconstruction method for two-phase flow CT with improved simulated annealing algorithm[J]. Nuclear Engineering and Technology, 2021, 53(4): 1304-1310.
[26]	LIU T S, ZBORAY R, TRTIK P, et al. Optical flow method for neutron radiography flow diagnostics[J]. Physics of Fluids, 2021, 33(10): 101702. doi: 10.1063/5.0063836
[27]	AHMED Z, ROSS M, CEBULA A, et al. Neutron imaging based vapor fraction measurements in an inductively heated boiling packed bed[J]. International Journal of Heat and Mass Transfer, 2023, 216: 124527. doi: 10.1016/j.ijheatmasstransfer.2023.124527
[28]	MISHIMA K, HIBIKI T. Development of high-frame-rate neutron radiography and quantitative measurement method for multiphase flow research[J]. Nuclear Engineering and Design, 1998, 184(2-3): 183-201. doi: 10.1016/S0029-5493(98)00196-4
[29]	HIBIKI T, MISHIMA K, YONEDA K, et al. Visualization of fluid phenomena using a high frame-rate neutron radiography with a steady thermal neutron beam[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1994, 351(2-3): 423-436.
[30]	TAKENAKA N, ASANO H, FUJII T, et al. Liquid metal flow measurement by neutron radiography[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1996, 377(1): 156-160.
[31]	UCHIMURA K, HARVEL G D, MATSUMOTO T, et al. An image processing approach for two-phase interfaces visualized by a real time neutron radiography technique[J]. Flow Measurement and Instrumentation, 1998, 9(4): 203-210.
[32]	MISHIMA K, HIBIKI T, SAITO Y, et al. Visualization study of molten metal–water interaction by using neutron radiography[J]. Nuclear Engineering and Design, 1999, 189(1-3): 391-403. doi: 10.1016/S0029-5493(98)00263-5
[33]	MISHIMA K, HIBIKI T, SAITO Y, et al. Visualization and measurement of gas–liquid metal two-phase flow with large density difference using thermal neutrons as microscopic probes[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1999, 424(1): 229-234.
[34]	HIBIKI T, SAITO Y, MISHIMA K, et al. Study on flow characteristics in gas-molten metal mixture pool[J]. Nuclear Engineering and Design, 2000, 196(2): 233-245. doi: 10.1016/S0029-5493(99)00293-9
[35]	SAITO Y, MISHIMA K, TOBITA Y, et al. Velocity field measurement in gas–liquid metal two-phase flow with use of PIV and neutron radiography techniques[J]. Applied Radiation and Isotopes, 2004, 61(4): 683-691.
[36]	SAITO Y, MISHIMA K, TOBITA Y, et al. Application of high frame-rate neutron radiography to liquid-metal two-phase flow research[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2005, 542(1-3): 168-174.
[37]	SAITO Y, SHEN X, MISHIMA K, et al. Shape measurement of bubble in a liquid metal[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2009, 605(1-2): 192-196.
[38]	KURETA M. Development of a neutron radiography three-dimensional computed tomography system for void fraction measurement of boiling flow in tight lattice rod bundles[J]. Journal of Power and Energy Systems, 2007, 1(3): 211-224. doi: 10.1299/jpes.1.211
[39]	SHEN X Z, YAMAMOTO T, HAN X, et al. Interfacial area concentration in gas-liquid metal two-phase flow[J]. Experimental and Computational Multiphase Flow, 2023, 5(1): 84-98. doi: 10.1007/s42757-021-0110-x
[40]	SIBAMOTO Y, NAKAMURA H, ANODA Y. Neutron radiography flow visualization of liquid metal injected into an empty vessel and a vessel containing saturated water[J]. Nuclear Technology, 2001, 133(1): 119-132.
[41]	李文军,肖星宇,周圣辉,等. 高温热管的研究进展及应用[J]. 现代化工,2020, 40(6): 15-18,23.
[42]	刘豪杰,秦凯文,魏强林,等. 不同热管工质对热管冷却反应堆堆芯物理参数的影响与分析[J]. 科学技术与工程,2023, 23(8): 3289-3294. doi: 10.12404/j.issn.1671-1815.2023.23.08.03289
[43]	李衍智,都家宇,吴莘馨,等. 先进核能技术中的热管应用[J]. 清华大学学报: 自然科学版,2023, 63(8): 1173-1183.
[44]	KIHM K D, HUSSEY D, PRATT D M, et al. Neutron imaging feasibility of liquid metal coolant behaviors inside a high-temperature alloy heat pipe[C]//Proceedings of the ASME/JSME 8th Thermal Engineering Joint Conference. Honolulu: ASME, 2011: T10185.
[45]	KIHM K, KIRCHOFF E, GOLDEN M, et al. Neutron imaging of alkali metal heat pipes[J]. Physics Procedia, 2013, 43: 323-330. doi: 10.1016/j.phpro.2013.03.038
[46]	KIRCHOFF E H. Neutron imaging of lithium inside a high-temperature heat pipe[D]. Knoxville: The University of Tennessee, 2013.
[47]	HIGHT B H. Neutron imaging of lithium (Li) coolants inside high temperature Niobium (Nb) heat pipes[D]. Knoxville: The University of Tennessee, 2014.
[48]	BALASKÓ M, HORVÁTH L, HORVÁTH Á, et al. Study of the behavior of supercritical water by dynamic neutron radiography[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2009, 605(1-2): 138-141.
[49]	BALASKÓ M, HORVÁTH L, HORVÁTH Á, et al. Study on the properties of supercritical water flowing in a closed loop using dynamic neutron radiography[J]. Physics Procedia, 2013, 43: 254-263. doi: 10.1016/j.phpro.2013.03.029
[50]	TAKENAKA N, SUGIMOTO K, TAKAMI S, et al. Application of neutron radiography to flow visualization in supercritical water[J]. Physics Procedia, 2013, 43: 264-268.
[51]	KISS A, BALASKÓ M, HORVÁTH L, et al. Experimental investigation of the thermal hydraulics of supercritical water under natural circulation in a closed loop[J]. Annals of Nuclear Energy, 2017, 100: 178-203. doi: 10.1016/j.anucene.2016.09.020
[52]	ITO D, SAITO Y. Visualization of bubble behavior in a packed bed of spheres using neutron radiography[J]. Physics Procedia, 2015, 69: 593-598. doi: 10.1016/j.phpro.2015.07.084
[53]	MISHIMA K, HIBIKI T. Quantitative limits of thermal and fluid phenomena measurements using the neutron attenuation characteristics of materials[J]. Experimental Thermal and Fluid Science, 1996, 12(4): 461-472. doi: 10.1016/0894-1777(95)00181-6
[54]	ANDERSON I S, MCGREEVY R L, BILHEUX H Z. Neutron imaging and applications[M]. New York: Springer, 2009: 987.
[55]	贺林峰. 快速中子照相技术及其在两相流研究中的应用[D]. 北京: 中国原子能科学研究院,2014.
[56]	叶晗. 基于Perona-Malik的中子图像去噪研究[D]. 长春: 东北师范大学,2020.
[57]	赵辰一. 低对比度核成像增强方法研究[D]. 长春: 东北师范大学,2018.
[58]	BUADES A, COLL B, MOREL J M. A review of image denoising algorithms, with a new one[J]. Multiscale Modeling & Simulation, 2005, 4(2): 490-530.
[59]	DABOV K, FOI A, KATKOVNIK V, et al. Image denoising with block-matching and 3D filtering[C]//Proceedings of SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning. San Jose: SPIE, 2006: 606414.
[60]	ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Transactions on Image Processing, 2006, 15(12): 3736-3745.
[61]	吴晓阳. 噪声强度估计及其在中子图像去噪中的应用研究[D]. 长春: 东北师范大学,2019.
[62]	CIMBALA J M, SATHIANATHAN D. Streakline flow visualization with neutron radiography[J]. Experiments in Fluids, 1988, 6(8): 547-552. doi: 10.1007/BF00196601
[63]	OGINO F. Application of neutron radiography to study of liquid-solid two phase flow[J]. Proceedings of WCNR-4, 1994: 339-346.
[64]	TAKENAKA N, FUJII T, ONO A, et al. Visualization of streak lines in liquid metal by neutron radiography[J]. Nondestructive Testing and Evaluation, 1994, 11(2-3): 107-113. doi: 10.1080/10589759408952823
[65]	MA X F, TAKEDA T. Asymmetric Abel inversion by neural network for reconstruction of plasma density distribution[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2002, 492(1-2): 178-189.
[66]	DUPONT J, MIGNOT G, ZBORAY R, et al. Infrared film thickness measurement: comparison with cold neutron imaging[J]. Journal of Nuclear Science and Technology, 2016, 53(5): 673-681.