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通过统计理论和维纳-辛钦定理推导出激光外差探测系统光电流的功率谱函数，分析了光电流谱线分布与激光光源线宽、中频信号频率以及信号光相对本振光传输延迟时间的关系，修正了相关文献中光电流功率谱的理论公式.根据信号与噪声理论建立了激光线宽引起的相位噪声的一维概率分布模型，并据此得到了基于激光波长、探测距离以及激光线宽的极限位移分辨率的数学模型.对光电流的功率谱和外差光学极限位移分辨率进行了相关的数值仿真，结果表明延迟时间与相干时间的关系决定光电流谱线分布的情况.当激光波长为532 nm，激光线宽在1 kHz，探测距离为100 m时，光学极限位移分辨率为0.266 nm，相关文献中的实验数据与理论推导结果相符合.Photocurrent power spectral density function of laser heterodyne detection is obtained by the statistical theory and Wiener-Khinchin theorem. For a short-range distance heterodyne system without considering atmospheric turbulence, we observe the relations between the photocurrent spectral line distribution and the laser linewidth, the intermediate-frequency signal, and the propagation delay time of signal light relative to local oscillator light. Theoretical formula of photocurrent power spectrum in relevant papers is revised to eliminate the effect of laser linewidth. Onedimensional probability distribution model of phase noise caused by laser linewidth is built based on the signal and noise theory. Accordingly we establish a mathematical model of limit detection accuracy based on laser wavelength, detection distance, and laser linewidth, which indicates the minimum detectable amplitude of heterodyne system. According to the numerical results, we find that the distribution of photocurrent spectral line intensities is greatly dependent on the relation between delay time and coherent time. And the minimum resolvable displacement increases with the detection distance and laser linewidth increasing. When the optical limited displacement resolution is 0.266 nm with a laser wavelength of 532 nm, a laser linewidth is 1 kHz, and a detection distance is 100 m. Experimental data in relevant papers agree well with the theoretical derivations. Our findings show that the research of displacement resolution might provide a quantitative reference for the theoretical research and engineering application of short-range heterodyne resolution.
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Keywords:
- laser Doppler velocimeters /
- laser applications /
- lasers
[1] Kingston R 1977 Opt. News 3 27
[2] Swanson E A, Carter G M 1989 Appl. Opt. 28 3918
[3] Mosley D E, Matson C L, Czyzak S R 1998 Aerospace Defense Sensing and Controls 3380 243
[4] Nan J D, Pi M J, Fan L M 1989 Acta Opt. Sin. 10 714 (in Chinese)[南京达, 皮名嘉, 樊立明, 李洪滨 1989 光学学报 10 714]
[5] Pu L L, Zhou Y, Sun J F, Shen B L, Lu W (in Chinese)[濮莉莉, 周煜, 孙剑锋, 沈宝良, 鲁伟 2011 光学学报 31 260]
[6] Shintaro H, Yuki K, Ryosuke N, Norio H, Tadao N 2015 Opt. Express 23 26689
[7] Luo Y, Feng G Y, Liu J, Zhou C Y, Zhou S H (in Chinese)[罗韵, 冯国英, 刘建, 周晟阳, 周寿桓 2014 中国激光 41 1108001]
[8] Luo H J, Yuan X H (in Chinese)[罗韩君, 元秀华 2013 中国激光 40 173]
[9] Li C Q, Wang T F, Zhang H Y, Xie J J, Liu L S, Guo J 2016 Acta Phys. Sin. 65 084206 (in Chinese)[李成强, 王挺峰, 张合勇, 谢京江, 刘立生, 郭劲 2016 65 084206]
[10] Shang J H, Zhao S G, He Y, Chen W B, Jia N 2011 Chin. Opt. Lett. 9 081201
[11] An Y Y, Liu J F, Li Q H 2007 Optoelectronic Technology (2nd Ed.) (Beijing:Publishing House of Electronics Inducstry) p167 (in Chinese)[安毓英, 刘继芳, 李庆辉 2007 光电子技术 (第二版) (北京:电子工业出版社) 第167页]
[12] Wang Y D, Wang J 2011 Fundamentals of Random Signal Analysis (3rd Ed.) (Beijing:Publishing House of Electronics Inducstry) (in Chinese)[王永德, 王军 2011 随机信号分析基础 (第三版) (北京:电子工业出版社)]
[13] Rowe H E 1965 Signal and Noise in Communication Systems (Princeton, NJ:van Nostrand)
[14] Gallion P B, Debarge G 1984 IEEE J. Quantum Electron. 20 343
[15] Yves P, Michel P, Michel M, Michel T 2009 Opt. Express 17 3659
[16] Siegman A E, Benedetto D, Manes K R 1967 IEEE J. Quantum Electron. 3 180
[17] Wolfgang Osten 2007 Optical Inspection of Microsystems (1st Ed.) (New York:CRC Press) p246
[18] Dandridge A, Tveten A B 1982 Opt. Lett. 7 279
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[1] Kingston R 1977 Opt. News 3 27
[2] Swanson E A, Carter G M 1989 Appl. Opt. 28 3918
[3] Mosley D E, Matson C L, Czyzak S R 1998 Aerospace Defense Sensing and Controls 3380 243
[4] Nan J D, Pi M J, Fan L M 1989 Acta Opt. Sin. 10 714 (in Chinese)[南京达, 皮名嘉, 樊立明, 李洪滨 1989 光学学报 10 714]
[5] Pu L L, Zhou Y, Sun J F, Shen B L, Lu W (in Chinese)[濮莉莉, 周煜, 孙剑锋, 沈宝良, 鲁伟 2011 光学学报 31 260]
[6] Shintaro H, Yuki K, Ryosuke N, Norio H, Tadao N 2015 Opt. Express 23 26689
[7] Luo Y, Feng G Y, Liu J, Zhou C Y, Zhou S H (in Chinese)[罗韵, 冯国英, 刘建, 周晟阳, 周寿桓 2014 中国激光 41 1108001]
[8] Luo H J, Yuan X H (in Chinese)[罗韩君, 元秀华 2013 中国激光 40 173]
[9] Li C Q, Wang T F, Zhang H Y, Xie J J, Liu L S, Guo J 2016 Acta Phys. Sin. 65 084206 (in Chinese)[李成强, 王挺峰, 张合勇, 谢京江, 刘立生, 郭劲 2016 65 084206]
[10] Shang J H, Zhao S G, He Y, Chen W B, Jia N 2011 Chin. Opt. Lett. 9 081201
[11] An Y Y, Liu J F, Li Q H 2007 Optoelectronic Technology (2nd Ed.) (Beijing:Publishing House of Electronics Inducstry) p167 (in Chinese)[安毓英, 刘继芳, 李庆辉 2007 光电子技术 (第二版) (北京:电子工业出版社) 第167页]
[12] Wang Y D, Wang J 2011 Fundamentals of Random Signal Analysis (3rd Ed.) (Beijing:Publishing House of Electronics Inducstry) (in Chinese)[王永德, 王军 2011 随机信号分析基础 (第三版) (北京:电子工业出版社)]
[13] Rowe H E 1965 Signal and Noise in Communication Systems (Princeton, NJ:van Nostrand)
[14] Gallion P B, Debarge G 1984 IEEE J. Quantum Electron. 20 343
[15] Yves P, Michel P, Michel M, Michel T 2009 Opt. Express 17 3659
[16] Siegman A E, Benedetto D, Manes K R 1967 IEEE J. Quantum Electron. 3 180
[17] Wolfgang Osten 2007 Optical Inspection of Microsystems (1st Ed.) (New York:CRC Press) p246
[18] Dandridge A, Tveten A B 1982 Opt. Lett. 7 279
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