搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

锁相放大器的研究进展

郭忠凯 李永刚 于博丞 周世超 孟庆宇 陆鑫鑫 黄一帆 刘贵鹏 陆俊

引用本文:
Citation:

锁相放大器的研究进展

郭忠凯, 李永刚, 于博丞, 周世超, 孟庆宇, 陆鑫鑫, 黄一帆, 刘贵鹏, 陆俊

Research progress of lock-in amplifiers

Guo Zhong-Kai, Li Yong-Gang, Yu Bo-Cheng, Zhou Shi-Chao, Meng Qing-Yu, Lu Xin-Xin, Huang Yi-Fan, Liu Gui-Peng, Lu Jun
PDF
HTML
导出引用
  • 锁相放大器可同时在时间与幅度两个维度实现高精度信号测量, 是精密系统测控的关键部件. 本文以锁相放大器的概念、技术与应用的概貌作为导引, 先以模拟、数字以及虚拟锁相放大器的主要关系与区分方法说明锁相放大器的发展演变, 继而按照锁相环的阶与型从数学角度对锁相放大器进行分类. 随后介绍锁相放大器的幅度、频率与相位噪声等主要性能的测试流程与计量标定进展, 讨论相位噪声、时域抖动、阿伦方差等关键指标之间的换算关系以及和幅度噪声之间的耦合关联. 最后, 列举锁相放大器在光谱增强、阻抗分析、磁性测量、显微成像、空间探测领域的应用形式与效果, 通过一些新型应用展望它通过智能计算、精准物联等途径从科学仪器走向工业甚至民品的前景.
    The lock-in amplifier can perform high-precision measurement in both time and amplitude dimensions, so that it becomes a key component of instrumental system for precision measurement and control. This article overviews the concept, technology, and application of phase-locked amplifiers as a guide. It first explains the development and evolution of phase-locked amplifiers of analog, digital, and virtual phase-locked amplifiers, demonstrating their relationship and differences. Then, it classifies phase-locked amplifiers from a mathematical perspective based on the order and type of phase-locked loops. Subsequently, the testing process and metrological calibration progress of the main performance of phase-locked amplifiers, such as amplitude, frequency, and phase noise, are introduced. The conversion relationship between key indicators such as phase noise, time-domain jitter, Allan variance, and the coupling relationship with amplitude noise are discussed. Finally, the application forms and effects of phase-locked amplifiers in the fields of spectral enhancement, impedance analysis, magnetic measurement, microscopic imaging, and space exploration are listed. Through some new applications, the prospects of their transition from scientific instruments to industrial and even civilian products through intelligent computing, precise IoT, and other means are briefly given.

    更正: 锁相放大器的研究进展 [物理学报 2023, 72(22): 224206]

    郭忠凯, 李永刚, 于博丞, 周世超, 孟庆宇, 陆鑫鑫, 黄一帆, 刘贵鹏, 陆俊. 锁相放大器的研究进展. 物理学报, 2023, 72(22): 224206. doi: 10.7498/aps.72.249901
      通信作者: 陆俊, lujun@iphy.ac.cn
    • 基金项目: 国家重点研发计划(批准号: 2021YFF0701000)资助的课题.
      Corresponding author: Lu Jun, lujun@iphy.ac.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2021YFF0701000).
    [1]

    陆俊 2020 物理 49 472Google Scholar

    Lu J 2020 Physics 49 472Google Scholar

    [2]

    Best R E 2003 Phase-locked Loops Design, Simulation and Applications (New York: McGraw-Hill) pp151–277

    [3]

    Gardner F M 2005 Phaselock Techniques (Hoboken: Wiley Interscience) pp6–96

    [4]

    Banerjee D 2006 PLL Performance, Simulation, and Design ( Dallas: Texas Instruments) pp9–243

    [5]

    杜勇 2016 锁相环技术原理及FPGA实现 (北京: 电子工业出版社) 第89—262页

    Du Y 2016 Principle and FPGA Implementation of Phase Locked Loop Technology (Beijing: Publishing House of Electronics Industry) pp89–262

    [6]

    远坂俊昭 2006 锁相环(PLL)电路设计与应用 (北京: 科学出版社) 第31—105页

    YuanBan J Z 2006 Design and Application of Phase Locked Loop (PLL) Circuit (Beijing: Science Press) pp31–105

    [7]

    田昭武 1984 电化学研究方法 (北京: 科学出版社) 第395—396页

    Tian Z W 1984 Electrochemical Methods (Beijing: Science Press) pp395–396

    [8]

    高晋占 2004 微弱信号检测 (北京: 清华大学出版社) 第1—36页

    Gao J Z 2004 Weak Signal Detection (Beijing: Tsinghua University Press) pp1–36

    [9]

    Meade M L 1983 Lock-In Amplifiers: Principles and Applications (London: Peter Peregrinus) pp7–147

    [10]

    De Bellescize 1933 U.K. Patent GB19310031 [1933-05-18

    [11]

    王福昌 1996 锁相技术 (武汉: 华中理工大学出版社) 第3—137页

    Wang F C 1996 Phase-locked Technology (Wuhan: Huazhong University of Technology Press) pp3–137

    [12]

    Gaspar J, Chen S F, Gordillo A, Hepp M, Ferreyra P, Marques C 2004 Microprocess. Microsyst. 28 157Google Scholar

    [13]

    Zurich-Instrument https://docs.zhinst.com/overview [2023-8-9

    [14]

    Liquid-Instrument https://www.liquidinstruments.com/products/hardware-platforms/mokupro https://www.thinksrs.com/downloads/man.html [2023-8-9

    [15]

    Stanford-Research-Systems https://www.thinksrs.com/downloads/man.html [2023-8-9

    [16]

    Sine Scientific Instruments https://www.ssi-instrument.com/products/LIA.html [2023-8-9

    [17]

    Huang K, Geng Y Y, Zhang X B, Chen D H, Cai Z G, Wang M, Zhu Z, Wang Z X 2019 Sensors 19 3519Google Scholar

    [18]

    NF株式会社 http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9]

    NF Corporation http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9

    [19]

    国仪量子 https://www.cigtek.com/products. html [2023-8-9]

    CIQTEK https://www.cigtek.com/products.html [2023-8-9

    [20]

    南京鸿宾电子 https://www.ndwshb.com/product/105.html [2023-8-9]

    Nanjing Hongbin https://www.ndwshb.com/product/105.html [2023-8-9

    [21]

    AMETEK https://www.ameteksi.com/products/lock-in-amplifers/7265-dual-phase-lock-in-amplifer [2023-8-9

    [22]

    Chen C 2004 Proc. Natl. Acad. Sci. 101 5303Google Scholar

    [23]

    张勇, 李睿, 刘君华 1998 电测与仪表 35 30

    Zhang Y, Li R, Liu J H 1998 Electr. Meas. Instrum. 35 30

    [24]

    Bobalo Y, Bondariev A, Altunin S, Kiselychnyk M, Maksymiv I 2018 International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering Lviv-Slavske, Ukraine, February 20–24, 2018

    [25]

    Lu J, Pan D A, Bai Y, Qiao L 2008 Meas. Sci. Technol. 19 045702Google Scholar

    [26]

    陆俊 https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9]

    Lu J https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9

    [27]

    Stimpson G A, Skilbeck M S, Patel R L, Green B L, Morley G W 2019 Rev. Sci. Instrum. 90 094701Google Scholar

    [28]

    Wang Z, Shi X, Wang W, Cai W 2023 IEEE Trans. Instrum. Meas. 72 1Google Scholar

    [29]

    Lu J 2020 Rev. Sci. Instrum. 91 075106Google Scholar

    [30]

    《手册》编写组 2017 数学手册 (北京: 高等教育出版社)

    Handbook Writing Group 2017 Mathematical Manual (Beijing: Higher Education Press

    [31]

    Ziemer R, Tranter W 2015 Principles of Communications Systems, Modulation, and Noise (Hoboken: Wiley) pp184– 195

    [32]

    Wullch D, Bar M 1990 Int. J. Circuit Theory Appl. 18 135Google Scholar

    [33]

    Ugarte M, Carlosena A 2015 Circuits Syst. Signal Process. 34 3395Google Scholar

    [34]

    Kudrewicz J, Wasowicz S 2007 Equations of Phase-Locked Loops Dynamics on the Circle, Torus and Cylinder (New Jersey: World Scientific) pp9–123

    [35]

    Kittel P 1977 Rev. Sci. Instrum. 48 1214Google Scholar

    [36]

    原力超导 https://eastfs.com/glpmd [2003-8-9]

    Force superconductivity https://eastfs.com/glpmd [2003-8-9

    [37]

    Rubiola E 2008 Phase Noise and Frequency Stability in Oscillators (London: Cambridge University Press) pp1–135

    [38]

    Schwartz M 1970 Information Transmission Modulation and Noise—A Unified Approach to Communication System (New York: McGRAW-Hill) pp390–570

    [39]

    Bodson M 2005 Int. J. Adapt. Control Signal Process. 19 67Google Scholar

    [40]

    陆俊, 沈保根, 邵晓萍 2018 中国专利 201510182065.7 [2018-01-26]

    Lu J, Shen B G, Shao X P 2018 CHN Patent 201510182065.7 [2018-01-26

    [41]

    张靖悉, 胡勇, 潘柳2020锁相放大器校准规范

    Zhang J X, Hu Y, Pan L 2020 Calibration Specification for Lock-in Amplifiers

    [42]

    大恒新纪元科技股份有限公司 2022 精密大带宽锁相放大器企业标准

    Daheng New Era Technology Co., Ltd 2022 Enterprise Standards for Broadband High Precision Lock-in Amplifiers

    [43]

    王彪, 张江涛, 李艳强, 谷扬, 潘仙林 2012 电测与仪表 49 170

    Wang B, Zhang J T, Li Y Q, Gu Y, Pan X L 2012 Electr. Meas. Instrum. 49 170

    [44]

    Cultrera A, Corminboeuf D, D’Elia V, Tran N T M, Callegaro L, Ortolano M 2021 Metrologia 58 025001Google Scholar

    [45]

    Jia Z S, Liu Z Y, Wang L, He Q, Huang H T, Liu L Y 2018 Measurement 125 606Google Scholar

    [46]

    陆祖良, 杨雁, 黄璐, 王磊 2019 计量学报 40 319

    Lu Z L, Yang Y, Huang L, Wang L 2019 Acta Metrologica Sinica 40 319

    [47]

    陆祖良 2021 计量学报 42 913

    Lu Z L 2021 Acta Metrologica Sinica 42 913

    [48]

    Van B, Herold G 2014 Am. J. Phys. 82 785Google Scholar

    [49]

    Arora H, Klemmer N, Morizio J C, Wolf P D 2005 IEEE Trans. Circuits Syst. Regul. Pap. 52 379Google Scholar

    [50]

    Demir A 2006 IEEE Trans. Circuits Syst. Regul. Pap. 53 1869Google Scholar

    [51]

    Goldman S J 2007 Phase-Locked Loops Engineering Handbook for Integrated Circuits (Norwood: Artech House) pp5–161

    [52]

    Bondariev A P, Altunin S I 2017 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo) Odessa, September 11–15, 2017

    [53]

    Eulalia B, Luca D, Francesco P, Sergio R, Ioan T 2020 Acta Imeko 9 52Google Scholar

    [54]

    刘河山 2015 博士学位论文 (北京: 中国科学院大学)

    Liu H S 2015 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences

    [55]

    Shaddock D, Ware B, Halverson P G, Spero R E, Klipstein B 2006 Laser Interferometer Space Antenna: 6th International LISA Symposium Greenbelt, Maryland, USA, June 19–23, 2006

    [56]

    Cervantes F G, Heinzel G, Marín A F G, Wand V, Steier F, Jennrich O, Danzmann K 2007 Appl. Opt. 46 4541Google Scholar

    [57]

    Gerberding O, Sheard B, Bykov I, Kullmann J, Delgado J J E, Danzmann K, Heinzel G 2013 Classical Quantum Gravity 30 235029Google Scholar

    [58]

    Libbrecht K G, Black E D, Hirata C M 2003 Am. J. Phys. 71 1208Google Scholar

    [59]

    Sterczewski L A, Grzelczak M P, Plinski E F 2016 Rev. Sci. Instrum. 87 014702Google Scholar

    [60]

    Deninger A J, Göbel T, Schönherr D, Kinder T, Roggenbuck A, Köberle M, Lison F, Müller-Wirts T, Meissner P 2008 Rev. Sci. Instrum.79 044702Google Scholar

    [61]

    Zhang Z, Liu Y, Zhu X 2021 J. Phys. Conf. Ser. 1865 022010Google Scholar

    [62]

    Balgos M H, Hayazawa N, Tani M, Tanaka T 2023 Rev. Sci. Instrum. 94 043002Google Scholar

    [63]

    Ardekani H, Wilmington R L, Vutukuru M, Chen Z, Brandt R, Swan A, Gundogdu K 2021 Rev. Sci. Instrum. 92 104706Google Scholar

    [64]

    Kierzek M, Deal P E, Miller E W, Mukherjee S, Wachten D, Baumann A, Kaupp U B, Strünker T, Brenker C 2021 eLife 10 63129Google Scholar

    [65]

    陆俊, 杜昱光, 王倬, 张琛, 赵雪, 李国强, 谭广文, 竺晓山, 丁玮 2023 中国专利 202010361964.4 [2023-04-21]

    Lu J, Du Y G, Wang Z, Zhang C, Zhao X, Li G Q, Tan G W, Zhu X S, Ding W 2020 CHN Patent 202010361964.4 [2023-04-21

    [66]

    Sarra A, Stanchieri G D P, De M, Bordi F, Postorino P, Palange E 2021 IEEE Trans. Biomed. Circuits Syst. 15 177Google Scholar

    [67]

    Song X, Jin Y, Zhang X, Yu Y, Zhang D L 2009 Rev. Sci. Instrum. 80 086104Google Scholar

    [68]

    Song D, Yang W, Zhu J, Bai M, Liu Y 2022 J. Supercond. Novel Magn. 35 95Google Scholar

    [69]

    Barnard A W, Mikheev E, Finney J, Hiller H S, Goldhaber-Gordon D 2023 Rev. Sci. Instrum. 94 013902Google Scholar

    [70]

    邓荣, 江国栋 2013 电测与仪表 50 105

    Deng R, Jiang G D 2013 Electr. Meas. Instrum. 50 105

    [71]

    宋改青, 董有尔 2006 中国测试技术 32 78

    Song G Q, Dong Y E 2006 China Meas. Technol. 32 78

    [72]

    Tang T, Liu X, Yuan Y, Kiya R, Zhang T, Yang Y, Suetsugu S, Yamazaki Y, Ota N, Yamamoto K, Kamikubo H, Tanaka Y, Li M, Hosokawa Y, Yalikun Y 2023 Sens. Actuators, B 374 132698Google Scholar

    [73]

    Sandoval B, Janićijević Ž, Palestina R, et al. 2023 ACS Sens. 8 576Google Scholar

    [74]

    Kitta K, Sakamoto M, Hayakawa K, Nukazuka A, Kano K, Yamamoto T 2023 ACS Omega 8 14684Google Scholar

    [75]

    苏少奎 2019 低温物性及测量: 一个实验技术人员的理解合经验总结 (北京: 科学出版社)

    Su S K 2019 Low Temperature Physical Properties and Measurement: An Experimental Technician’s Understanding and Experience Summary (Beijing: Science Press

    [76]

    Carminati M, Ferrari G, Guagliardo F, Sampietro M 2011 Sens. Actuators, A 172 117Google Scholar

    [77]

    陆俊, 沈保根, 邵晓萍 2015 中国专利 201210081375.6 [2015-02-02]

    Lu J, Shen B G, Shao X P 2015 CHN Patent 201210081375.6 [2015-02-02

    [78]

    Heng X, Wei K, Zhao T, Xu Z, Cao Q, Huang X, Zhai Y, Ye M, Quan W 2023 IEEE Trans. Instrum. Meas. 72 1Google Scholar

    [79]

    Li J J, Du P C, Fu J Q, Wang X T, Zhou Q, Wang R Q 2019 Chin. Phys. B 28 040703Google Scholar

    [80]

    詹文山 1982 物理 12 732

    Zhan W S 1982 Physics 12 732

    [81]

    Pu Y, Zhao H, Murayama T, Tonthat L, Okita K, Watanabe Y, Yabukami S 2023 J. Magn. Soc. Jpn. 47 66Google Scholar

    [82]

    Meng Z, He X, Li Y, Huang J, Chen D, Wang Z 2023 IEEE Sens. J. 23 16123Google Scholar

    [83]

    Zhang Z, Xu Z, He J, Lu J 2022 IEEE Trans. Instrum. Meas. 71 1006009Google Scholar

    [84]

    Roos W, Hempel K A, Voigt C, Dederichs H, Schippan R 1980 Rev. Sci. Instrum. 51 612Google Scholar

    [85]

    Chen J, Xi X, Wang S, Lu J, Guo C, Wang W, Liu E, Wang W, Liu L, Wu G 2016 Rev. Sci. Instrum. 87 043902Google Scholar

    [86]

    陆俊, 郗学奎, 王利晨, 蒋建旺 2022 中国专利 202210373018.0 [2022-04-11]

    Lu J, Chi X K, Wang L C, Jiang J W 2022 CHN Patent 202210373018.0 [2022-04-11

    [87]

    Hayek J N, Herreño-Fierro C A, Patiño E J 2016 Rev. Sci. Instrum. 87 103113Google Scholar

    [88]

    Lu J, Pan D A, Bai Y, Su Y J, Qiao L J 2008 IEEE Trans. Magn. 44 2127Google Scholar

    [89]

    Drobac D, Marohnic Z, Zivkovic I, Prester M 2013 Rev. Sci. Instrum.84 054708Google Scholar

    [90]

    Krishnan R V, Banerjee A 1999 Rev. Sci. Instrum. 70 85Google Scholar

    [91]

    Harcombe D M, Ruppert M G, Fleming A J 2020 Beilstein J. Nanotechnol. 11 76Google Scholar

    [92]

    Shi Y, Lu Q 2012 Microsc. Microanal. 18 1016Google Scholar

    [93]

    刘凡微, 陈思丹, 张嘉未, 陈欣中, 毛寒青, 黄思思, 陈曦 2022 电子显微学报 41 627

    Liu F W, Chen S D, Zhang J W, Chen X Z, Mao H Q, Huang S S, Chen X 2022 J. Chin. Electron Microsc. Soc. 41 627

    [94]

    Li X, Sun J, Jin L, Shangguan Y, Chen K, Qin H 2023 Opt. Express 31 19754Google Scholar

    [95]

    Leung M S, Stupian G W 1986 Appl. Surf. Sci. 25 435Google Scholar

    [96]

    徐欣, 谈宜东, 穆衡霖, 李岩, 王加刚, 金景峰 2023 激光与光电子学进展 60 0312006Google Scholar

    Xu X, Tan Y D, Mu H L, Li Y, Wang J G, Jin J F 2023 Laser OptoElectron. Prog. 60 0312006Google Scholar

    [97]

    Finneran I A, Welsch R, Allodi M A, Miller I I I, Blake G A 2017 J. Phys. Chem. Lett. 8 4640Google Scholar

    [98]

    Li H, Li Z, Wan W, Zhou K, Liao X, Yang S, Wang C, Cao J C, Zeng H 2020 ACS Photonics 7 49Google Scholar

    [99]

    Jain P, Priya P, Ram T V S, Parikh K S, Bandi T N 2021 Rev. Sci. Instrum. 92 124705Google Scholar

    [100]

    Slim J, Nikolaev N, Rathmann F, Wirzba A, Zurek M 2021 Phys. Rev. Accel. Beams 2 4Google Scholar

    [101]

    Boss J, Cujia K, Zopes J, Degen C 2017 Science 356 837Google Scholar

    [102]

    Lu J 2021 A Reconfigurable Electrical Circuit Auto-Processing Method for Direct Electromagnetic Inversion, As a Chapter in Intelligent Computing and Block Chain (Singapore: Springer Nature) pp190–203

    [103]

    Jung S M 2016 Ph. D. Dissertation (Tucson: The University of Arizona

    [104]

    Kaptein M, Van E, Iannuzzi D, Braunstein L A 2017 Plos One 12 e0174182Google Scholar

    [105]

    Golestan S, Guerrero J M, Vasquez J C 2017 IEEE Trans. Power Electron. 32 9013Google Scholar

    [106]

    Uzzaman T, Kim U, Choi W 2022 IEEE Access 10 32870Google Scholar

    [107]

    Neunteufel D, Grebien S, Arthaber H 2022 Sensors 22 2663Google Scholar

    [108]

    Aguirre J, Medrano N, Calvo B, Celma S 2011 IEEE Sensors Conference Limerick, Ireland, October 28–31, 2011 6127317

  • 图 1  典型锁相放大器原理图

    Fig. 1.  Schematic diagram of a typical lock-in amplifier.

    图 2  锁相环、信号幅度与锁相放大器作为关键词的文献关键词聚类分析图

    Fig. 2.  Literature keyword clustering plot with phase-locked loop, signal amplitude and lock-in amplifier as keywords.

    图 3  锁相环与锁相放大器结构关联与差异示意图

    Fig. 3.  Schematic diagram of structural correlation and difference between phase-locked loop and lock-in amplifier.

    图 4  数字锁相环中的核心器件用数字电路实现

    Fig. 4.  Primary components in a digital lock-in amplifier are realized using digital circuits.

    图 5  虚拟锁相放大器中由CPU等指令工作流完成所有运算

    Fig. 5.  In the virtual lock-in amplifier, all computations are accomplished by the CPU instruction workflow.

    图 6  模拟、数字与虚拟锁相放大器的分类标准图示及说明

    Fig. 6.  Schematic description of classification criteria for analog, digital and virtual lock-in amplifiers.

    图 7  锁相环的型与阶分类以及典型结构功能与表达式列举示意图

    Fig. 7.  Schematic diagram of the type and order classification of phase-locked loops and the enumeration of typical structural functions and expressions.

    图 8  锁相放大器的典型测试系统各部分连接关系图

    Fig. 8.  Illustration of a typical test system for lock-in amplifiers.

    图 9  锁相放大器的幅度、频率与相位测量不确定度性能测试流程图

    Fig. 9.  Flow chart of evaluation process for lock-in amplifiers, to obtain performance on measuring amplitude, frequency and phase.

    图 10  锁相放大器的诸多噪声抑制性能及其相互转换关系示意图

    Fig. 10.  Various indicators of noise suppression properties and their relationship for evaluating lock-in amplifiers.

    图 11  锁相放大器用于光谱信噪比增强的两种光路图 (a)斩波器调制; (b)高速电控开关

    Fig. 11.  Lock-in amplifier is used to enhance the spectral signal-to-noise ratio in optical measurement via two kind of modulations: (a) Chopper modulation; (b) high speed electronic control switch.

    图 12  运用锁相放大器进行阻抗测量的几种典型场景电路 (a)电池内阻测量[70]; (b)生物电阻抗在微流控中监测运动[72]; (c)超导电阻测量[68]; (d)精密电容监控[76]

    Fig. 12.  Several typical application scenes with circuits for impedance measurement using Lock-in amplifier: (a) Battery internal resistance measurement[70]; (b) bioimpedance for movement monitoring in microfluidic channels[72]; (c) superconducting resistance measurement[68]; (d) precision capacitor monitoring[76].

    图 13  几种典型应用锁相放大器开展的磁测量场景示意图 (a)基于原子磁共振的磁强计[79]; (b)振动样品磁强计测量直流磁矩[83]; (c)交流磁化率仪; (d)动态磁致伸缩测量[85]

    Fig. 13.  Schematic diagrams of typical magnetic measurements carried out by lock-in amplifier: (a) Magnetometer based on atomic magnetic resonance[79]; (b) the vibrating sample magnetometer measures the DC magnetic moment[83]; (c) AC magnetic susceptibility measurement; (d) dynamic magnetostriction measurement[85].

    图 14  几种用到锁相放大器的显微成像系统 (a)原子力显微镜[92]; (b)近场光谱显微镜[94]; (c)扫描俄歇电子显微镜[95]

    Fig. 14.  Several microscopic imaging systems using lock-in amplifier: (a) Atomic force microscopy[92]; (b) near field spectroscopic microscope[94]; (c) scanning Auger electron microscope[95].

    图 15  激光外差干涉采取的两种运用锁相反馈的光路 (a)单激光源输出相位可控的一对激光束; (b)主从双激光源输出一对激光束

    Fig. 15.  Laser heterodyne interference two optical paths using phase-locked feedback: (a) A pair of laser beams with controllable phase coherence from a single Laser; (b) the master-slave dual light source outputs a pair of laser beams.

    表 1  国内外目前锁相放大器产品性能指标的对比

    Table 1.  Comparison of performance for current available lock-in amplifier products around the world.

    地区 品牌 型号 工作频率范围 最大输出数据率 相位噪声 电压噪声/
    (nV·Hz–1/2)
    动态储备
    /dB
    推出年份
    国外 Standford SR830 $1\ {\rm{mHz}} — 102\ {\rm{kHz}}$ 256 kSa/s 87 μrad 6 100 1980
    Research (美国) SR865A $1\ {\rm{mHz}} — 4\ {\rm{MHz}}$ 1.25 MSa/s 1.7 μrad 2.5 120 2015
    Zurich HF2LI $\rm{DC} — 50\ {\rm{MHz}}$ 0.5 MSa/s >17 nrad 5 120 2008
    Instrument UHFLI $\rm{DC} — 600\ {\rm{MHz}}$ 1.6 MSa/s (LAN) >17 nrad 4 100 2013
    (瑞士) SHFLI $\rm{DC} — 8.5\ {\rm{GHz}}$ 1.6 MSa/s (LAN) >17 nrad 4 100 2022
    Liquid Moku:Lab $1\ {\rm{kHz}} — 200\ {\rm{MHz}}$ 1 MSa/s 1 nrad·Hz–1/2 30 120 2017
    Instrument (澳洲) Moku:Pro $1\ {\rm{kHz}} — 300\ {\rm{MHz}}$ 10 MSa/s 1 nrad·Hz–1/2 20 120 2021
    AMETEK
    (美国)
    Signal $1\ {\rm{mHz}} —250\ {\rm{kHz}}$ 1 MSa/s (典型) 1.7 μrad 5 100—120 1999
    Recovery 7265
    NF(日本) LI5660 $0.5\ \rm{\; Hz} — 11\ {\rm{MHz}}$ 1.5 MSa/s 17 μrad 4.5 100 2018
    国内 赛恩科仪 OE1022 $10\ \text{μ} {\rm{Hz}} — 250\ {\rm{kHz}}$ 1 MSa/s > 17 nrad 2.5 120 2012
    OE2041 $10\ \text{μ} {\rm{Hz}} — 60\ {\rm{MHz}}$ 1 MSa/s > 17 nrad 2.5 120 2020
    国仪量子 LIA001M ${\mathrm{DC}} — 1\ {\rm{MHz}}$ N.A. > 170 nrad 2.5 120 2021
    南京鸿宾 HB293(JD-1) $1\ \rm{\; Hz} — 100\ {\rm{kHz}}$ N.A. N.A. 3 140 ~1980
    下载: 导出CSV
  • [1]

    陆俊 2020 物理 49 472Google Scholar

    Lu J 2020 Physics 49 472Google Scholar

    [2]

    Best R E 2003 Phase-locked Loops Design, Simulation and Applications (New York: McGraw-Hill) pp151–277

    [3]

    Gardner F M 2005 Phaselock Techniques (Hoboken: Wiley Interscience) pp6–96

    [4]

    Banerjee D 2006 PLL Performance, Simulation, and Design ( Dallas: Texas Instruments) pp9–243

    [5]

    杜勇 2016 锁相环技术原理及FPGA实现 (北京: 电子工业出版社) 第89—262页

    Du Y 2016 Principle and FPGA Implementation of Phase Locked Loop Technology (Beijing: Publishing House of Electronics Industry) pp89–262

    [6]

    远坂俊昭 2006 锁相环(PLL)电路设计与应用 (北京: 科学出版社) 第31—105页

    YuanBan J Z 2006 Design and Application of Phase Locked Loop (PLL) Circuit (Beijing: Science Press) pp31–105

    [7]

    田昭武 1984 电化学研究方法 (北京: 科学出版社) 第395—396页

    Tian Z W 1984 Electrochemical Methods (Beijing: Science Press) pp395–396

    [8]

    高晋占 2004 微弱信号检测 (北京: 清华大学出版社) 第1—36页

    Gao J Z 2004 Weak Signal Detection (Beijing: Tsinghua University Press) pp1–36

    [9]

    Meade M L 1983 Lock-In Amplifiers: Principles and Applications (London: Peter Peregrinus) pp7–147

    [10]

    De Bellescize 1933 U.K. Patent GB19310031 [1933-05-18

    [11]

    王福昌 1996 锁相技术 (武汉: 华中理工大学出版社) 第3—137页

    Wang F C 1996 Phase-locked Technology (Wuhan: Huazhong University of Technology Press) pp3–137

    [12]

    Gaspar J, Chen S F, Gordillo A, Hepp M, Ferreyra P, Marques C 2004 Microprocess. Microsyst. 28 157Google Scholar

    [13]

    Zurich-Instrument https://docs.zhinst.com/overview [2023-8-9

    [14]

    Liquid-Instrument https://www.liquidinstruments.com/products/hardware-platforms/mokupro https://www.thinksrs.com/downloads/man.html [2023-8-9

    [15]

    Stanford-Research-Systems https://www.thinksrs.com/downloads/man.html [2023-8-9

    [16]

    Sine Scientific Instruments https://www.ssi-instrument.com/products/LIA.html [2023-8-9

    [17]

    Huang K, Geng Y Y, Zhang X B, Chen D H, Cai Z G, Wang M, Zhu Z, Wang Z X 2019 Sensors 19 3519Google Scholar

    [18]

    NF株式会社 http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9]

    NF Corporation http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9

    [19]

    国仪量子 https://www.cigtek.com/products. html [2023-8-9]

    CIQTEK https://www.cigtek.com/products.html [2023-8-9

    [20]

    南京鸿宾电子 https://www.ndwshb.com/product/105.html [2023-8-9]

    Nanjing Hongbin https://www.ndwshb.com/product/105.html [2023-8-9

    [21]

    AMETEK https://www.ameteksi.com/products/lock-in-amplifers/7265-dual-phase-lock-in-amplifer [2023-8-9

    [22]

    Chen C 2004 Proc. Natl. Acad. Sci. 101 5303Google Scholar

    [23]

    张勇, 李睿, 刘君华 1998 电测与仪表 35 30

    Zhang Y, Li R, Liu J H 1998 Electr. Meas. Instrum. 35 30

    [24]

    Bobalo Y, Bondariev A, Altunin S, Kiselychnyk M, Maksymiv I 2018 International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering Lviv-Slavske, Ukraine, February 20–24, 2018

    [25]

    Lu J, Pan D A, Bai Y, Qiao L 2008 Meas. Sci. Technol. 19 045702Google Scholar

    [26]

    陆俊 https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9]

    Lu J https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9

    [27]

    Stimpson G A, Skilbeck M S, Patel R L, Green B L, Morley G W 2019 Rev. Sci. Instrum. 90 094701Google Scholar

    [28]

    Wang Z, Shi X, Wang W, Cai W 2023 IEEE Trans. Instrum. Meas. 72 1Google Scholar

    [29]

    Lu J 2020 Rev. Sci. Instrum. 91 075106Google Scholar

    [30]

    《手册》编写组 2017 数学手册 (北京: 高等教育出版社)

    Handbook Writing Group 2017 Mathematical Manual (Beijing: Higher Education Press

    [31]

    Ziemer R, Tranter W 2015 Principles of Communications Systems, Modulation, and Noise (Hoboken: Wiley) pp184– 195

    [32]

    Wullch D, Bar M 1990 Int. J. Circuit Theory Appl. 18 135Google Scholar

    [33]

    Ugarte M, Carlosena A 2015 Circuits Syst. Signal Process. 34 3395Google Scholar

    [34]

    Kudrewicz J, Wasowicz S 2007 Equations of Phase-Locked Loops Dynamics on the Circle, Torus and Cylinder (New Jersey: World Scientific) pp9–123

    [35]

    Kittel P 1977 Rev. Sci. Instrum. 48 1214Google Scholar

    [36]

    原力超导 https://eastfs.com/glpmd [2003-8-9]

    Force superconductivity https://eastfs.com/glpmd [2003-8-9

    [37]

    Rubiola E 2008 Phase Noise and Frequency Stability in Oscillators (London: Cambridge University Press) pp1–135

    [38]

    Schwartz M 1970 Information Transmission Modulation and Noise—A Unified Approach to Communication System (New York: McGRAW-Hill) pp390–570

    [39]

    Bodson M 2005 Int. J. Adapt. Control Signal Process. 19 67Google Scholar

    [40]

    陆俊, 沈保根, 邵晓萍 2018 中国专利 201510182065.7 [2018-01-26]

    Lu J, Shen B G, Shao X P 2018 CHN Patent 201510182065.7 [2018-01-26

    [41]

    张靖悉, 胡勇, 潘柳2020锁相放大器校准规范

    Zhang J X, Hu Y, Pan L 2020 Calibration Specification for Lock-in Amplifiers

    [42]

    大恒新纪元科技股份有限公司 2022 精密大带宽锁相放大器企业标准

    Daheng New Era Technology Co., Ltd 2022 Enterprise Standards for Broadband High Precision Lock-in Amplifiers

    [43]

    王彪, 张江涛, 李艳强, 谷扬, 潘仙林 2012 电测与仪表 49 170

    Wang B, Zhang J T, Li Y Q, Gu Y, Pan X L 2012 Electr. Meas. Instrum. 49 170

    [44]

    Cultrera A, Corminboeuf D, D’Elia V, Tran N T M, Callegaro L, Ortolano M 2021 Metrologia 58 025001Google Scholar

    [45]

    Jia Z S, Liu Z Y, Wang L, He Q, Huang H T, Liu L Y 2018 Measurement 125 606Google Scholar

    [46]

    陆祖良, 杨雁, 黄璐, 王磊 2019 计量学报 40 319

    Lu Z L, Yang Y, Huang L, Wang L 2019 Acta Metrologica Sinica 40 319

    [47]

    陆祖良 2021 计量学报 42 913

    Lu Z L 2021 Acta Metrologica Sinica 42 913

    [48]

    Van B, Herold G 2014 Am. J. Phys. 82 785Google Scholar

    [49]

    Arora H, Klemmer N, Morizio J C, Wolf P D 2005 IEEE Trans. Circuits Syst. Regul. Pap. 52 379Google Scholar

    [50]

    Demir A 2006 IEEE Trans. Circuits Syst. Regul. Pap. 53 1869Google Scholar

    [51]

    Goldman S J 2007 Phase-Locked Loops Engineering Handbook for Integrated Circuits (Norwood: Artech House) pp5–161

    [52]

    Bondariev A P, Altunin S I 2017 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo) Odessa, September 11–15, 2017

    [53]

    Eulalia B, Luca D, Francesco P, Sergio R, Ioan T 2020 Acta Imeko 9 52Google Scholar

    [54]

    刘河山 2015 博士学位论文 (北京: 中国科学院大学)

    Liu H S 2015 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences

    [55]

    Shaddock D, Ware B, Halverson P G, Spero R E, Klipstein B 2006 Laser Interferometer Space Antenna: 6th International LISA Symposium Greenbelt, Maryland, USA, June 19–23, 2006

    [56]

    Cervantes F G, Heinzel G, Marín A F G, Wand V, Steier F, Jennrich O, Danzmann K 2007 Appl. Opt. 46 4541Google Scholar

    [57]

    Gerberding O, Sheard B, Bykov I, Kullmann J, Delgado J J E, Danzmann K, Heinzel G 2013 Classical Quantum Gravity 30 235029Google Scholar

    [58]

    Libbrecht K G, Black E D, Hirata C M 2003 Am. J. Phys. 71 1208Google Scholar

    [59]

    Sterczewski L A, Grzelczak M P, Plinski E F 2016 Rev. Sci. Instrum. 87 014702Google Scholar

    [60]

    Deninger A J, Göbel T, Schönherr D, Kinder T, Roggenbuck A, Köberle M, Lison F, Müller-Wirts T, Meissner P 2008 Rev. Sci. Instrum.79 044702Google Scholar

    [61]

    Zhang Z, Liu Y, Zhu X 2021 J. Phys. Conf. Ser. 1865 022010Google Scholar

    [62]

    Balgos M H, Hayazawa N, Tani M, Tanaka T 2023 Rev. Sci. Instrum. 94 043002Google Scholar

    [63]

    Ardekani H, Wilmington R L, Vutukuru M, Chen Z, Brandt R, Swan A, Gundogdu K 2021 Rev. Sci. Instrum. 92 104706Google Scholar

    [64]

    Kierzek M, Deal P E, Miller E W, Mukherjee S, Wachten D, Baumann A, Kaupp U B, Strünker T, Brenker C 2021 eLife 10 63129Google Scholar

    [65]

    陆俊, 杜昱光, 王倬, 张琛, 赵雪, 李国强, 谭广文, 竺晓山, 丁玮 2023 中国专利 202010361964.4 [2023-04-21]

    Lu J, Du Y G, Wang Z, Zhang C, Zhao X, Li G Q, Tan G W, Zhu X S, Ding W 2020 CHN Patent 202010361964.4 [2023-04-21

    [66]

    Sarra A, Stanchieri G D P, De M, Bordi F, Postorino P, Palange E 2021 IEEE Trans. Biomed. Circuits Syst. 15 177Google Scholar

    [67]

    Song X, Jin Y, Zhang X, Yu Y, Zhang D L 2009 Rev. Sci. Instrum. 80 086104Google Scholar

    [68]

    Song D, Yang W, Zhu J, Bai M, Liu Y 2022 J. Supercond. Novel Magn. 35 95Google Scholar

    [69]

    Barnard A W, Mikheev E, Finney J, Hiller H S, Goldhaber-Gordon D 2023 Rev. Sci. Instrum. 94 013902Google Scholar

    [70]

    邓荣, 江国栋 2013 电测与仪表 50 105

    Deng R, Jiang G D 2013 Electr. Meas. Instrum. 50 105

    [71]

    宋改青, 董有尔 2006 中国测试技术 32 78

    Song G Q, Dong Y E 2006 China Meas. Technol. 32 78

    [72]

    Tang T, Liu X, Yuan Y, Kiya R, Zhang T, Yang Y, Suetsugu S, Yamazaki Y, Ota N, Yamamoto K, Kamikubo H, Tanaka Y, Li M, Hosokawa Y, Yalikun Y 2023 Sens. Actuators, B 374 132698Google Scholar

    [73]

    Sandoval B, Janićijević Ž, Palestina R, et al. 2023 ACS Sens. 8 576Google Scholar

    [74]

    Kitta K, Sakamoto M, Hayakawa K, Nukazuka A, Kano K, Yamamoto T 2023 ACS Omega 8 14684Google Scholar

    [75]

    苏少奎 2019 低温物性及测量: 一个实验技术人员的理解合经验总结 (北京: 科学出版社)

    Su S K 2019 Low Temperature Physical Properties and Measurement: An Experimental Technician’s Understanding and Experience Summary (Beijing: Science Press

    [76]

    Carminati M, Ferrari G, Guagliardo F, Sampietro M 2011 Sens. Actuators, A 172 117Google Scholar

    [77]

    陆俊, 沈保根, 邵晓萍 2015 中国专利 201210081375.6 [2015-02-02]

    Lu J, Shen B G, Shao X P 2015 CHN Patent 201210081375.6 [2015-02-02

    [78]

    Heng X, Wei K, Zhao T, Xu Z, Cao Q, Huang X, Zhai Y, Ye M, Quan W 2023 IEEE Trans. Instrum. Meas. 72 1Google Scholar

    [79]

    Li J J, Du P C, Fu J Q, Wang X T, Zhou Q, Wang R Q 2019 Chin. Phys. B 28 040703Google Scholar

    [80]

    詹文山 1982 物理 12 732

    Zhan W S 1982 Physics 12 732

    [81]

    Pu Y, Zhao H, Murayama T, Tonthat L, Okita K, Watanabe Y, Yabukami S 2023 J. Magn. Soc. Jpn. 47 66Google Scholar

    [82]

    Meng Z, He X, Li Y, Huang J, Chen D, Wang Z 2023 IEEE Sens. J. 23 16123Google Scholar

    [83]

    Zhang Z, Xu Z, He J, Lu J 2022 IEEE Trans. Instrum. Meas. 71 1006009Google Scholar

    [84]

    Roos W, Hempel K A, Voigt C, Dederichs H, Schippan R 1980 Rev. Sci. Instrum. 51 612Google Scholar

    [85]

    Chen J, Xi X, Wang S, Lu J, Guo C, Wang W, Liu E, Wang W, Liu L, Wu G 2016 Rev. Sci. Instrum. 87 043902Google Scholar

    [86]

    陆俊, 郗学奎, 王利晨, 蒋建旺 2022 中国专利 202210373018.0 [2022-04-11]

    Lu J, Chi X K, Wang L C, Jiang J W 2022 CHN Patent 202210373018.0 [2022-04-11

    [87]

    Hayek J N, Herreño-Fierro C A, Patiño E J 2016 Rev. Sci. Instrum. 87 103113Google Scholar

    [88]

    Lu J, Pan D A, Bai Y, Su Y J, Qiao L J 2008 IEEE Trans. Magn. 44 2127Google Scholar

    [89]

    Drobac D, Marohnic Z, Zivkovic I, Prester M 2013 Rev. Sci. Instrum.84 054708Google Scholar

    [90]

    Krishnan R V, Banerjee A 1999 Rev. Sci. Instrum. 70 85Google Scholar

    [91]

    Harcombe D M, Ruppert M G, Fleming A J 2020 Beilstein J. Nanotechnol. 11 76Google Scholar

    [92]

    Shi Y, Lu Q 2012 Microsc. Microanal. 18 1016Google Scholar

    [93]

    刘凡微, 陈思丹, 张嘉未, 陈欣中, 毛寒青, 黄思思, 陈曦 2022 电子显微学报 41 627

    Liu F W, Chen S D, Zhang J W, Chen X Z, Mao H Q, Huang S S, Chen X 2022 J. Chin. Electron Microsc. Soc. 41 627

    [94]

    Li X, Sun J, Jin L, Shangguan Y, Chen K, Qin H 2023 Opt. Express 31 19754Google Scholar

    [95]

    Leung M S, Stupian G W 1986 Appl. Surf. Sci. 25 435Google Scholar

    [96]

    徐欣, 谈宜东, 穆衡霖, 李岩, 王加刚, 金景峰 2023 激光与光电子学进展 60 0312006Google Scholar

    Xu X, Tan Y D, Mu H L, Li Y, Wang J G, Jin J F 2023 Laser OptoElectron. Prog. 60 0312006Google Scholar

    [97]

    Finneran I A, Welsch R, Allodi M A, Miller I I I, Blake G A 2017 J. Phys. Chem. Lett. 8 4640Google Scholar

    [98]

    Li H, Li Z, Wan W, Zhou K, Liao X, Yang S, Wang C, Cao J C, Zeng H 2020 ACS Photonics 7 49Google Scholar

    [99]

    Jain P, Priya P, Ram T V S, Parikh K S, Bandi T N 2021 Rev. Sci. Instrum. 92 124705Google Scholar

    [100]

    Slim J, Nikolaev N, Rathmann F, Wirzba A, Zurek M 2021 Phys. Rev. Accel. Beams 2 4Google Scholar

    [101]

    Boss J, Cujia K, Zopes J, Degen C 2017 Science 356 837Google Scholar

    [102]

    Lu J 2021 A Reconfigurable Electrical Circuit Auto-Processing Method for Direct Electromagnetic Inversion, As a Chapter in Intelligent Computing and Block Chain (Singapore: Springer Nature) pp190–203

    [103]

    Jung S M 2016 Ph. D. Dissertation (Tucson: The University of Arizona

    [104]

    Kaptein M, Van E, Iannuzzi D, Braunstein L A 2017 Plos One 12 e0174182Google Scholar

    [105]

    Golestan S, Guerrero J M, Vasquez J C 2017 IEEE Trans. Power Electron. 32 9013Google Scholar

    [106]

    Uzzaman T, Kim U, Choi W 2022 IEEE Access 10 32870Google Scholar

    [107]

    Neunteufel D, Grebien S, Arthaber H 2022 Sensors 22 2663Google Scholar

    [108]

    Aguirre J, Medrano N, Calvo B, Celma S 2011 IEEE Sensors Conference Limerick, Ireland, October 28–31, 2011 6127317

  • [1] 刘鑫, 周晓鹏, 汶伟强, 陆祺峰, 严成龙, 许帼芹, 肖君, 黄忠魁, 汪寒冰, 陈冬阳, 邵林, 袁洋, 汪书兴, 马万路, 马新文. 电子束离子阱光谱标定和Ar13+离子M1跃迁波长精密测量. 物理学报, 2022, 71(3): 033201. doi: 10.7498/aps.71.20211663
    [2] 赵天择, 杨苏辉, 李坤, 高彦泽, 王欣, 张金英, 李卓, 赵一鸣, 刘宇哲. 频域反射法光纤延时精密测量. 物理学报, 2021, 70(8): 084204. doi: 10.7498/aps.70.20201075
    [3] 刘鑫, 周晓鹏, 汶伟强, 陆祺峰, 严成龙, 许帼芹, 肖君, 黄忠魁, 汪寒冰, 陈冬阳, 邵林, 袁洋, 汪书兴, 马万路(Wan-Lu MA), 马新文. 电子束离子阱光谱标定和Ar13+离子M1跃迁波长精密测量. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211663
    [4] 刘建平, 邬俊飞, 黎卿, 薛超, 毛德凯, 杨山清, 邵成刚, 涂良成, 胡忠坤, 罗俊. 万有引力常数G精确测量实验进展. 物理学报, 2018, 67(16): 160603. doi: 10.7498/aps.67.20181381
    [5] 王磊, 郭浩, 陈宇雷, 伍大锦, 赵锐, 刘文耀, 李春明, 夏美晶, 赵彬彬, 朱强, 唐军, 刘俊. 基于金刚石色心自旋磁共振效应的微位移测量方法. 物理学报, 2018, 67(4): 047601. doi: 10.7498/aps.67.20171914
    [6] 彭世杰, 刘颖, 马文超, 石发展, 杜江峰. 基于金刚石氮-空位色心的精密磁测量. 物理学报, 2018, 67(16): 167601. doi: 10.7498/aps.67.20181084
    [7] 穆秀丽, 李传亮, 邓伦华, 汪海玲. 用于α和μ常数变化测量的碘离子光谱研究. 物理学报, 2017, 66(23): 233301. doi: 10.7498/aps.66.233301
    [8] 史平, 马健, 钱轩, 姬扬, 李伟. 铷原子气体自旋噪声谱测量的信噪比分析. 物理学报, 2017, 66(1): 017201. doi: 10.7498/aps.66.017201
    [9] 刘鸿吉, 刘双龙, 牛憨笨, 陈丹妮, 刘伟. 基于环形抽运光的红外超分辨显微成像方法. 物理学报, 2016, 65(23): 233601. doi: 10.7498/aps.65.233601
    [10] 贾果, 黄秀光, 谢志勇, 叶君建, 方智恒, 舒桦, 孟祥富, 周华珍, 傅思祖. 液氘状态方程实验数据测量. 物理学报, 2015, 64(16): 166401. doi: 10.7498/aps.64.166401
    [11] 张宣妮, 张淳民, 艾晶晶. 四分束风成像偏振干涉仪信噪比的研究. 物理学报, 2013, 62(3): 030701. doi: 10.7498/aps.62.030701
    [12] 王金涛, 刘子勇. 基于静力悬浮原理的单晶硅球间微量密度差异精密测量方法研究. 物理学报, 2013, 62(3): 037702. doi: 10.7498/aps.62.037702
    [13] 马再如, 隋展, 冯国英, 孙年春, 王屹山, 张彬, 陈建国. 光谱扫描滤波法提升飞秒激光信噪比的理论分析. 物理学报, 2012, 61(7): 074206. doi: 10.7498/aps.61.074206
    [14] 曾冰, 曾曙光, 张彬, 孙年春, 隋展. 提升啁啾脉冲激光信噪比的扫描滤波方法. 物理学报, 2012, 61(15): 154209. doi: 10.7498/aps.61.154209
    [15] 王德江, 匡海鹏. 模拟增益对电荷耦合器件信噪比与动态范围影响的实验研究. 物理学报, 2011, 60(7): 077208. doi: 10.7498/aps.60.077208
    [16] 李伟昌, 王兆华, 刘成, 滕浩, 魏志义. 飞秒超强激光多通预放大过程中的脉冲信噪比研究. 物理学报, 2011, 60(12): 124210. doi: 10.7498/aps.60.124210
    [17] 张一驰, 武寄洲, 马杰, 赵延霆, 汪丽蓉, 肖连团, 贾锁堂. 最优化参数控制提高超冷铯分子振转光谱的信噪比. 物理学报, 2010, 59(8): 5418-5423. doi: 10.7498/aps.59.5418
    [18] 袁志林, 张淳民, 赵葆常. 新型偏振干涉成像光谱仪信噪比研究. 物理学报, 2007, 56(11): 6413-6419. doi: 10.7498/aps.56.6413
    [19] 韩海年, 张 炜, 王 鹏, 李德华, 魏志义, 沈乃澂, 聂玉昕, 高玉平, 张首刚, 李师群. 飞秒钛宝石光学频率梳的精密锁定. 物理学报, 2007, 56(5): 2760-2764. doi: 10.7498/aps.56.2760
    [20] 韩海年, 张 炜, 佟娟娟, 王延辉, 王 鹏, 魏志义, 李德华, 沈乃澂, 聂玉昕, 董太乾. 利用锁相环和TV-Rb钟控制飞秒激光脉冲的载波包络相移. 物理学报, 2007, 56(1): 291-295. doi: 10.7498/aps.56.291
计量
  • 文章访问数:  5020
  • PDF下载量:  474
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-04-11
  • 修回日期:  2023-07-14
  • 上网日期:  2023-09-05
  • 刊出日期:  2023-11-20

/

返回文章
返回