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基于衍射光栅的干涉式精密位移测量系统

吕强,李文昊,巴音贺希格,柏杨,刘兆武,王玮

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吕强, 李文昊, 巴音贺希格, 柏杨, 刘兆武, 王玮. 基于衍射光栅的干涉式精密位移测量系统[J]. , 2017, 10(1): 39-50. doi: 10.3788/CO.20171001.0039
引用本文: 吕强, 李文昊, 巴音贺希格, 柏杨, 刘兆武, 王玮. 基于衍射光栅的干涉式精密位移测量系统[J]. , 2017, 10(1): 39-50.doi:10.3788/CO.20171001.0039
LV Qiang, LI Wen-hao, Bayanheshig, BAI Yang, LIU Zhao-wu, WANG Wei. Interferometric precision displacement measurement system based on diffraction grating[J]. Chinese Optics, 2017, 10(1): 39-50. doi: 10.3788/CO.20171001.0039
Citation: LV Qiang, LI Wen-hao, Bayanheshig, BAI Yang, LIU Zhao-wu, WANG Wei. Interferometric precision displacement measurement system based on diffraction grating[J].Chinese Optics, 2017, 10(1): 39-50.doi:10.3788/CO.20171001.0039

基于衍射光栅的干涉式精密位移测量系统

doi:10.3788/CO.20171001.0039
基金项目:

国家重大科研仪器设备研制专项61227901

详细信息
    作者简介:

    吕强(1992-), 男, 山东德州人, 硕士研究生, 2014年于山东师范大学获得学士学位, 主要从事光栅精密位移测量等方面的研究。E-mail:lq_0119@126.com

    通讯作者:

    李文昊, E-mail:leewenho@163.com

  • 中图分类号:TN247;TH744.3

Interferometric precision displacement measurement system based on diffraction grating

Funds:

the National Science and Technology Major Project of the Ministry of Science and Technology of China61227901

More Information
  • 摘要:介绍了基于几何莫尔条纹原理和衍射干涉原理的两种光栅精密位移测量系统及各自的特点。综述了国内外对光栅干涉式精密位移测量系统的研究进展,总结了系统存在的关键问题及发展趋势。光栅干涉式精密位移测量系统的优点是对环境要求小,测量分辨率和精度较高,结构紧凑,成本低。该系统需要解决的问题包括提高光栅以及光学元器件制造和安装精度;寻求一种更高精度的检测手段对光栅位移测量系统进行标定等。光栅干涉式精密位移测量系统的发展方向为更高测量分辨率和精度,大量程、多维度测量以及尺寸小巧。该系统在现代工业加工精密制造领域将具有更广阔的应用前景。

  • 图 1基于几何莫尔条纹原理的光栅位移测量系统结构简图

    Figure 1.Schematic diagram of the grating displacement measurement system based on the principle of geometric Moire fringe

    图 2基于衍射干涉原理的光栅位移测量系统结构简图

    Figure 2.Schematic diagram of the grating displacement measurement system based on the principle of diffraction and interference

    图 3Heidenhain公司衍射光栅干涉式位移测量系统原理图

    Figure 3.Schematic diagram of the diffraction grating interferometer displacement measurement system in Heidenhain

    图 4三光栅系统原理图

    Figure 4.Schematic diagram of three-grating system

    图 5LIP382系统原理图

    Figure 5.Schematic diagram of LIP382

    图 6微型光栅位移测量系统原理图

    Figure 6.Schematic diagram of micro diffraction grating interferometer displacement measurement system

    图 7Bird′s Eye Control系统原理图

    Figure 7.Schematic diagram of Bird′s Eye Control system

    图 86自由度测量系统原理图

    Figure 8.Conceptual design of the six-DOF surface encoder combined with a three-DOF displacement assembly and a three-DOF angle assembly

    图 9光栅干涉位移测量系统光路图

    Figure 9.Schematic diagram of optical setup

    图 10二次衍射系统原理图

    Figure 10.Schematic diagram of double diffraction system

    图 11采用Littrow结构的光栅位移测量系统原理图

    Figure 11.Schematic diagram of diffraction grating interferometer displacement measurement system with Littrow structure

    图 12采用单倍望远镜结构的光栅位移测量系统原理图

    Figure 12.Schematic diagram of diffraction grating interferometer displacement measurement system with DiLENS configuration

    图 136-DOF测量系统原理图

    Figure 13.Optical configuration for 6-DOF measurement system

    图 14外差光栅位移测量系统原理图

    Figure 14.Schematic diagram of the novel heterodynegrating interferometer system

  • [1] 陈宝刚, 明名, 吕天宇.大口径球面反射镜曲率半径的精确测量[J].中国光学, 2014, 7(1):163-168.//www.illord.com/CN/abstract/abstract9111.shtml

    CHEN B G, MING M, LV T Y. Precise measurement of curvature radius for spherical mirror with large aperture[J]. Chinese Optics, 2014, 7(1):163-168.(in Chinese)//www.illord.com/CN/abstract/abstract9111.shtml
    [2] 刘淑杰, 张元良, 张洪潮.透明软质薄膜的表面形貌测量[J].中国光学, 2014, 7(2):326-331.//www.illord.com/CN/abstract/abstract9136.shtml

    LIU SH J, ZHANG Y L, ZHANG H CH. Profile measurement of thin transparentsoft film surface[J]. Chinese Optics, 2014, 7(2):326-331.(in Chinese)//www.illord.com/CN/abstract/abstract9136.shtml
    [3] BASILE G, BECKER P, BERGAMIN A, et al.. Combined optical and X-ray interferometry for high-precision dimensional metrology[J]. Proceedings of the Royal Society A, 2000, 456(1995):701-729.doi:10.1098/rspa.2000.0536
    [4] ILEV I, KUMAGAI H, TOYODA K, et al.. An alternative fiber-optic backreflectance method for measurement of distances using a continuous wave laser[J]. Review of Scientific Instruments, 1996, 67(3):662-665.doi:10.1063/1.1146838
    [5] 万德安. 基准高精度测量技术[M].北京:国防工业出版社, 1999.

    WAN D A. Laser Precision Measurement Technology[M]. Beijing:National Defense Industry Press, 1999.(in Chinese)
    [6] 昌学年, 姚毅, 闫玲.位移传感器的发展及研究[J].计量与测试技术, 2009, 36(9):42-44.http://www.cnki.com.cn/Article/CJFDTOTAL-JLYS200909022.htm

    CHANG X N, YAO Y, YAN L. The development and investigation of displacement sensor[J]. Metrology & Measurement Technique, 2009, 36(9):42-44.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-JLYS200909022.htm
    [7] 马爱民, 马忠臣.超精密测量技术的应用进展[J].机械工程, 2013, 6:5.http://www.cnki.com.cn/Article/CJFDTOTAL-JXGU201306002.htm

    MA A M, MA ZH CH. Advances in application of precision measurement technology[J]. Mechanical Engineer, 2013, 6:5.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-JXGU201306002.htm
    [8] 周维来.光栅干涉仪在高精密测量中的技术和应用[J].工具技术, 1994, 1:37-42.http://www.cnki.com.cn/Article/CJFDTOTAL-GJJS199401008.htm

    ZHOU W L. The technology and application of grating interferometer in high precision measurement[J]. Tool Engineering, 1994, 1:37-42.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-GJJS199401008.htm
    [9] TEIMEL A. Technology and Application of Grating Interferometers in High-precision Measurement[M]. Berlin:Springer Berlin Heidelberg, 1991.
    [10] 张善钟.计量光栅技术[M].北京:机械工业出版社, 1985.

    ZHANG SH ZH. Metrology Grating Technology[M].Beijing:China Machine Press, 1985.(in Chinese)
    [11] 曹向群.光栅计量技术[M].杭州:浙江大学出版社, 1992.

    CAO X Q. Grating Measuring Technique[M]. Hangzhou:Zhejiang University Press, 1992.(in Chinese)
    [12] 尚平.高精度衍射光栅干涉位移传感器及关键技术研究[D].合肥:合肥工业大学, 2012.

    SHANG P. Study on the key technology of high-resolution diffraction grating interferometric transducer of linear displacements[D]. Hefei:Hefei University of Technology, 2012.(in Chinese)
    [13] 张金华, 陈良洲, 刘晓军.双光栅干涉位移传感器原理及其误差分析[J].光电技术应用, 2012, 3:41-45.http://www.cnki.com.cn/Article/CJFDTOTAL-GDYG201203013.htm

    ZHANG J H, SUN L ZH, LIU X J. Principle and error analysis of dual-grating interference displacement sensor[J]. Electro-Optic Technology Application, 2012, 3:41-45.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-GDYG201203013.htm
    [14] 森山茂夫, 郑建栋.用衍射光栅进行精密位移检测[J].国外计量, 1984, 6:11-13.http://www.cnki.com.cn/Article/CJFDTOTAL-XDJL198406003.htm

    SENSHAN M F, ZHENG J D. Precision displacement measurement with diffraction grating[J]. Foreign Measurement, 1984, 6:11-13.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-XDJL198406003.htm
    [15] 吕海宝, 曹聚亮, 颜树华, 等.光栅式大量程高分辨率位移测量研究[J].中国机械工程, 2000, 11(8):878-880.http://www.cnki.com.cn/Article/CJFDTOTAL-ZGJX200008013.htm

    LU H B, CAO J L, YAN SH H, et al.. Research for wide range and high resolution displacement measurement with grating[J]. China Mechanical Engineering, 2000, 11(8):878-880.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-ZGJX200008013.htm
    [16] HOLZAPFEL W. Advancements in displacement metrology based on encoder systems[C]. Proceedings of the 23rd Annual ASPE Meeting, Portland, USA, 2008.
    [17] THIEL J, SPANNER E. Interferential linear encoder with 270 mm measurement length for nanometrology[C]. Proceedings of the 1st International Conference and general meeting of the European Society for Precision Engineering and Nanotechnology, Bremen, Germany, 1999:419-422.
    [18] LOF J, DERKSEN A T A M, HOOGENDAM C A, et al.. Lithographic Apparatus and Device Manufacturing Method:US, 6819400B2[P]. 2005-10-21.
    [19] 郑立.三光栅系统[J].光学仪器, 1982, 4(1):35-42

    ZHENG L. Three grating system[J]. Optical Instruments, 1982, 4(1):35-42.(in Chinese)
    [20] 苏绍璟, 刘辉, 吕海宝, 等.纳米级位移分辨率双光栅系统的多普勒分析[J].光学精密工程, 2003, 11(1):17-21.http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200301003.htm

    SU SH J, LIU H, LU H B, et al.. Doppler analysis for double-grating displacement measurement system with nanometer resolution[J]. Opt. Precision Eng., 2003, 11(1):17-21.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200301003.htm
    [21] 卢国刚.SONY跨入皮米级检测和加工时代[J].世界制造技术与装备市场, 2008, 1:92.http://www.cnki.com.cn/Article/CJFDTOTAL-ZBSC200801032.htm

    LU G G. SONY jumping to pico meter world[J]. Key Components for CNC Machine Tool, 2008, 1:92.http://www.cnki.com.cn/Article/CJFDTOTAL-ZBSC200801032.htm
    [22] SAWADA R, HIGURASHI E, OHGUCHI O, et al.. Long-life micro-laser encoder[C]. Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems, 2000:491-495.
    [23] SAWADA R, HIGURASHI E, ITO T, et al.. Monolithic-integrated microlaser encoder[J]. Applied Optics, 1999, 38(33):6866-6873.doi:10.1364/AO.38.006866
    [24] SAWADA R, OHGUCHI O, MISE K, et al.. Fabrication of advanced integrated optical micro-encoder chip[C]. Proceedings of the Micro Electro Mechanical Systems, 1994, MEMS'94, IEEE, 1994:337-342.
    [25] SAWADA R, TANAKA H, OHGUCHI O, et al.. Fabrication of active integrated optical micro-encoder[C]. Proceedings of the Micro Electro Mechanical Systems, 1991, MEMS'91, IEEE, 1991:233-238.
    [26] WAKAMOTO S, KANAYA Y, KOSUGI J, et al.. Actual performance data analysis of overlay, focus, and dose control of an immersion scanner for double patterning[J]. SPIE, 2010, 7640:79-86.https://www.researchgate.net/publication/253303974_Actual_performance_data_analysis_of_overlay_focus_and_dose_control_of_an_immersion_scanner_for_double_patterning
    [27] MAST F V D. Towards ultimate optical lithography with NXT:1950i dual stage immersion platform[J]. SPIE, 2010:7640:511-519.http://adsabs.harvard.edu/abs/2010SPIE.7640E..55C
    [28] SHIBAZAKI Y, KOHNO H, HAMATANI M. An innovative platform for high-throughput high-accuracy lithography using a single wafer stage[J]. SPIE, 2009, 7274:72741-10.https://www.researchgate.net/publication/253014363_An_innovative_platform_for_high-throughput_high-accuracy_lithography_using_a_single_wafer_stage
    [29] PASCH B V D, MAST F V D. Enabling the lithography roadmap:an immersion tool based on a novel stage positioning system[J]. SPIE, 2009, 7274:72741S-8.https://www.researchgate.net/publication/253776706_Enabling_the_lithography_roadmap_an_immersion_tool_based_on_a_novel_stage_positioning_system
    [30] WAKAMOTO S, KIKUCHI T, SHIRATA Y, et al.. Stability and calibration of overlay and focus control for a double patterning immersion scanner[J]. SPIE, 2008, 7973(6):3620-3625.https://www.researchgate.net/publication/253726726_Stability_and_Calibration_of_Overlay_and_Focus_Control_for_a_Double_Patterning_Immersion_Scanner
    [31] LI X, GAO W, MUTO H, et al.. A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage[J]. Precision Engineering Journal of the International Societies for Precision Engineering & Nanotechnology, 2013, 37(3):771-781.https://www.researchgate.net/publication/256969690_A_six-degree-of-freedom_surface_encoder_for_precision_positioning_of_a_planar_motion_stage
    [32] KIMURA A, GAO W, KIM W J, et al.. A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement[J]. Precision Engineering, 2012, 36(4):576-585.doi:10.1016/j.precisioneng.2012.04.005
    [33] GAO W, KIMURA A. A fast evaluation method for pitch deviation and out-of-flatness of a planar scale grating[J]. CIRP Annals-Manufacturing Technology, 2010, 59(1):505-508.doi:10.1016/j.cirp.2010.03.035
    [34] GAO W, KIMURA A. A Three-axis displacement sensor with nanometric resolution[J]. CIRP Annals-Manufacturing Technology, 2007, 56(1):529-532.doi:10.1016/j.cirp.2007.05.126
    [35] GAO W, DEJIMA S, KIYONO S. A dual-mode surface encoder for position measurement[J]. Sensors & Actuators A Physical, 2005, 117(1):95-102.
    [36] DEJIMA S, GAO W, SHIMIZU H, et al.. Precision positioning of a five degree-of-freedom planar motion stage[J]. Mechatronics, 2005, 15(8):969-987.doi:10.1016/j.mechatronics.2005.03.002
    [37] XU D M, WENG C F, LEI M R. Research on the high accuracy displacement measuring and display system[C]. 7th International Symposium on Test and Measurement, Chinese Society of Modern Technology Equipment, Beijing:International Academic Publishers, 2007:3515-3518.(in Chinese)
    [38] CHU X CH, LU H B, ZHAO SH H. Wide rang grating interferometer with nanometer resolution[J]. Optp-electronic Engineering, 2008, 35(1):56-59.(in Chinese)https://www.researchgate.net/publication/296808256_Wide-range_grating_interferometer_with_nanometer_resolution
    [39] CHU X CH, LU H B, CHEN T ZH, et al.. Investigation on long-range nanometer resolution grating moire interferometer[J]. SPIE, 2004, 5635:333-341.
    [40] 杜列波.纳米级光栅位移测量中关键技术的研究[D].长沙:国防科学技术大学, 2004.

    DU L B. Research on key technology of nano scale grating displacement[D]. Changsha:National University of Defense Technology, 2004.(in Chinese)
    [41] SU SH J, LU H B. High-speed great-capacity storing and processing technique of video sensor signal[J]. SPIE, 2000, 4077:396-399.
    [42] PU J, ZHANG H, NEMOTO S. Spectral shifts and spectral switches of partially coherent light passing through an aperture[J]. Optics Communications, 1999, 162(1-3):57-63.doi:10.1016/S0030-4018(99)00051-6
    [43] POST D. Moire fringe multiplication with a nonsymmetrical doubly blazed reference grating[J]. Applied Optics, 1971, 10(4):901-907.doi:10.1364/AO.10.000901
    [44] FAN K C, ZHANG Y L, MIAO J W, et al.. Error compensation of grating interferometer due to angular error of linear stage[C]. Proceedings of the Advanced Intelligent Mechatronics (AIM), IEEE, 2012:428-431.
    [45] FAN K C, LIU Y S, CHEN Y J, et al.. A linear diffraction grating interferometer with high accuracy[J]. SPIE, 2006, 6280:628008-6.
    [46] KAO C F, LU S H, SHEN H M, et al.. Diffractive laser encoder with a grating in littrow configuration[J]. Japanese J. Applied Physics, 2008, 47(3):1833-1837.doi:10.1143/JJAP.47.1833
    [47] CHUNG Y C, FAN K C, LEE B C. Development of a novel planar encoder for 2D displacement measurement in nanometer resolution and accuracy[C]. Proceedings of the 9th World Congress on Intelligent Control and Automation (WCICA), Taiwan, China, 2011:PID1723643.
    [48] WU C C, WU W J, PAN Z S, et al.. Laser linear encoder with both high fabrication and head-to-scale tolerances[J]. Applied Optics, 2007, 46(16):3169-3176.doi:10.1364/AO.46.003169
    [49] LEE C K, WU C C, CHEN S J, et al.. Design and construction of linear laser encoders that possess high tolerance of mechanical runout[J]. Applied Optics, 2004, 43(31):5754-5762.doi:10.1364/AO.43.005754
    [50] HSIEH H L, PAN S W. Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements[J]. Optics Express, 2015, 23(3):2451-2465.doi:10.1364/OE.23.002451
    [51] HSIEH H L, PAN S W. Three-degree-of-freedom displacement measurement using grating-based heterodyne interferometry[J]. Applied Optics, 2013, 52(27):6840-6848.doi:10.1364/AO.52.006840
    [52] HSIEH H L, CHEN J C, LERONDEL G, et al.. Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer[J]. Optics Express, 2011, 19(10):9770-9782.doi:10.1364/OE.19.009770
    [53] HSIEH H L, LEE J Y, WU W T, et al.. Quasi-common-optical-path heterodyne grating interferometer for displacement measurement[J]. Measurement Science & Technology, 2010, 21(11):280-284.
    [54] WANG L J, ZHANG M, ZHU Y, et al.. American society for precision engineering a novel heterodyne grating interferometer system for in-plane and out-of-plane displacement measurement with nanometer resolution[C]. Proceedings of the Meeting of the American Society for Precision Engineering, ASPE, 2014.
    [55] LIN D, JIANG H, YIN C. Analysis of nonlinearity in a high-resolution grating interferometer[J]. Optics & Laser Technology, 2000, 32(2):95-99.
    [56] WANG L J, ZHANG M, ZHU Y, et al.. Construction and accuracy test of a novel heterodyne grating interferomter system for two-dimensional displacement measurement[J]. Laser, 2013, 89(3):69.
    [57] 朱煜, 张鸣, 王磊杰, 等.一种双频光栅干涉仪位移测量系统:中国,

    WO2014/071816A1[P]. 2013-02-20. ZHU Y, ZHANG M, WANG L J, et al.. Dual-frequency grating interferometer displacement measurement system:China, WO2014/071816A1[P]. 2013-02-20.(in Chinese)
    [58] 张鸣, 朱煜, 王磊杰, 等.一种二自由度外差光栅干涉仪位移测量系统:中国,

    WO2014/201950A1[P]. 2013-09-18. ZHANG M, ZHU Y, WANG L J, et al.. Displacement measurement system for two-degree-of-freedom heterodyne grating interferometer:China, WO2014/201950A1[P]. 2013-09-18.(in Chinese)
    [59] 张鸣, 朱煜, 王磊杰, 等.一种外差光栅干涉仪位移测量系统:中国,

    WO2014/071807A1[P]. 2013-02-27. ZHANG M, ZHU Y, WANG L J, et al.. Heterodyne grating interferometer displacement measurement system:China, WO2014/201950A1[P]. 2013-02-27.(in Chinese)
    [60] WEI P, LU Z, LIU L. Double-grating diffraction interferometric stylus probing system for surface profiling and roughness measurement[C]. International Symposium on Precision Engineering Measurement and Instrumentation. International Society for Optics and Photonics, 2015:94461N.
    [61] 王雪英.基于衍射干涉原理的高精度光栅位移测量系统研究[D].哈尔滨:哈尔滨工业大学, 2014.http://cn.bing.com/academic/profile?id=85ea26740fef3b7fa6ab892e28475896&encoded=0&v=paper_preview&mkt=zh-cn

    WANG X Y. Research of high-precision displacement measurement system based on the principle of diffraction and interference[D]. Harbin:Harbin Institute of Technology, 2014.(in Chinese)http://cn.bing.com/academic/profile?id=85ea26740fef3b7fa6ab892e28475896&encoded=0&v=paper_preview&mkt=zh-cn
    [62] LIN J, GUAN J, MA L, et al.. Effects of parameters of Bessel-Gaussian on the achievement of optical needle with longitudinal polarization[J]. SPIE, 2013, 8759:875937.
    [63] 徐敏儿.基于衍射光栅的高分辨力位移测量系统研究[D].哈尔滨:哈尔滨工业大学, 2013.

    XU M E. Research on and high-resolution displacement measurement system based on diffractive grating[D]. Harbin:Harbin Institute of Technology, 2013.(in Chinese)
    [64] 邸晶晶.基于衍射光栅的高精度位移测量系统的设计[D].哈尔滨:哈尔滨工业大学, 2012.

    DI J J. Design of high-precision displacement measurement system based on diffractive grating[D]. Harbin:Harbin Institute of Technology, 2012.(in Chinese)
    [65] CHENG F, FAN K C. An improved design of the linear diffraction grating interferometer[C]. Proceedings of ASPEN20009, Kitakyushu, Japan, 2009.
    [66] XIA H J, FEI Y T, WANG Z Y. Basic theoretical research about the 2-D diffraction grating in nano-scale measurement[R], ISIST2004, 1226-1231.
    [67] 刘玉圣, 范光照, 陈叶金.高精度线性衍射光栅干涉仪的研制[J].工业计量, 2006, 16(2):1-3.http://www.cnki.com.cn/Article/CJFDTOTAL-GYJL200602000.htm

    LIU Y SH, FAN G ZH, CHEN Y J. A research on diffraction grating interferometer with high accuracy[J]. Industrial Measurement, 2006, 16(2):1-3.(in Chinese)http://www.cnki.com.cn/Article/CJFDTOTAL-GYJL200602000.htm
    [68] AKIHIRO K. Optical displacement measurement system:US, 6407815B2[P].2002-06-18.
    [69] KURODA A. Optical displacement measurement system for detecting the relative movement of a machine part:US, 6166817[P].2000-12-26.
    [70] TANIGUCHI K, TSUCHIYA H, TOYAMA M. Optical instrument for measuring displacement:US, 4676645[P].1987-06-30.
    [71] SCHATTENBURG M L, SMITH H I. The critical role of metrology in nanotechnology[J]. SPIE, 2002, 4608:116-124.http://d.wanfangdata.com.cn/NSTLQK_10.1117-12.437273.aspx
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  • 收稿日期:2016-08-22
  • 修回日期:2016-09-16
  • 刊出日期:2017-02-01

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