基于飞秒激光模间拍频法的大尺寸测距方法-张晓声.pdf

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1、物理学报Acta Phys. Sin. Vol. 65, No. 8 (2016) 080602基于飞秒激光模间拍频法的大尺寸测距方法 张晓声1)易旺民2)胡明皓1)杨再华2)吴冠豪1)y1)(清华大学精密仪器系,精密测试技术及仪器国家重点实验室,北京100084)2)(北京卫星环境工程研究所,北京100094)(2015年12月14日收到; 2016年1月7日收到修改稿)本文基于飞秒激光模间拍频法实现多波长相位式绝对距离测量,通过改变光频梳重复频率合成波长扩大测距量程,并采用监测臂和双快门切换系统补偿和消除由电路产生的相位差单向漂移和大幅抖动.实验中以20倍重复频率的拍频进行测量,在30 m

2、in内相位测量的标准偏差为0.022;与双频激光干涉仪比对1125 mm行程内位移测量结果,测距精度优于50 m;实验验证了合成波长方法扩大量程方案的可行性,获得的测距重复性优于3 m,该系统理论上可扩展量程至7.5 km.关键词:模间拍频法,飞秒激光,大尺寸测距PACS: 06.30.Bp, 06.60.Jn, 42.62.Eh DOI: 10.7498/aps.65.0806021引言长度量是科学和工程中最常用的物理量,也是国际单位制的基本物理量之一,目标物与参考点之间的绝对距离即是一种典型的长度量.高精度绝对距离测量在科学研究和工程应用中具有重要意义,随着科学技术的发展,各种场合对测距的

3、量程、精度、速度等指标都出现了更高的要求,在航天器定位、卫星编队、大地测绘、大型土木工程测量、大型机械工件制造等领域,均需要量程大至百米到千米量级,精度达到或优于微米量级的大尺寸高精度绝对距离测量.激光诞生后,基于其高亮度、高相干性和准直特性,产生了干涉法1、飞行时间法2等多种激光测距技术.激光干涉法测量精度可达亚波长数量级,但非模糊范围小,测量过程中需要依赖导轨进行条纹计数实现增量式位移测量;飞行时间法可实现较大量程,但由于光速极快,时间测量精度有限,测距精度较低.这两种方法都不能实现大尺寸下高精度的绝对距离测量.随着飞秒激光频率梳原理和技术的成熟,以飞秒激光器为光源的绝对距离测量技术快速发

4、展,光频梳独特的时域和频域特性使测距系统得以同时实现大量程和高精度3;4.飞秒激光是时域脉宽在飞秒(10 15 s)数量级的周期性超短激光脉冲,其在频域上为一系列频率稳定、等间隔分布且频谱范围极宽的谱线,称为光学频率梳.光频梳脉冲重复频率可由原子钟锁定,具有很高的频率稳定性5;6;各条谱线即各纵模间具有恒定的频率间隔,不同频率间隔的谱线之间会形成模间拍7.飞秒激光技术出现后,发展出了多种测距方法,如2000年日本的Minoshima团队首先提出的基于模间拍频的多波长干涉法8;9,2006年韩国的Joo和Kim10首先提出的光谱干涉法, 2009年美国的Coddington等11提出的双光梳测距

5、方法,以及本课题组在2013年提出的基于光梳的外差干涉测量法12.这些基于光频梳的测距方法较传统激光测距方法在精度或测量范围上有极大提高13;14.大学生创新创业训练计划资助项目(批准号: 201510003B022)、航天器高精度测量实验室基金、国家自然科学基金(批准号:61575105)、瞬态光学与光子技术国家重点实验室开放基金(批准号: SKLST201406)和北京市高等学校青年英才计划(批准号:YETP0085)资助的课题.通信作者. E-mail: 2016中国物理学会Chinese Physical Society http:/080602-1物理学报Acta Phys. Si

6、n. Vol. 65, No. 8 (2016) 080602在上述方法中,基于模间拍频的多波长干涉法使用一套飞秒激光光源,激光器无需锁定载波包络偏移频率(fceo),系统结构简单,且该方法可对测量范围内任意距离进行同等精度的测量,不存在测量盲区,因此有广阔的应用前景.其基本原理是搭建类似迈克尔逊干涉仪的干涉光路,利用光频梳模间差拍信号进行多波长相位式测距,通过电外差方法和低通滤波选择出信号中的某一谐波成分,精确测量参考光信号与测量光信号之间的相位差,解算待测距离.但由于相位差的2 周期性,测量的非模糊范围仅为波长的1/2,因此模间拍频多波长干涉法的测距量程仅为几米,不能满足大尺寸测量的需求.

7、利用飞秒激光器谐振腔长可调谐的特性,通过调整谐振腔长改变重复频率,可以使用两个相近的重复频率进行合成波长测量.合成波长远大于单一重复频率模间差拍信号波长,因此可将量程扩展至千米数量级以上,且保持了单一重复频率模间拍频方法的测距精度,可实现大尺寸高精度的距离测量.本文研究了合成波长法扩大飞秒激光模间拍频法测距量程的方案,分析了影响测距精度的因素和测量误差对量程扩大的限制.在超过模间拍频法量程的5.92 m距离下验证了合成波长测距方案的可行性,测距重复性优于3 m,理论最大扩展量程可达7.5 km;在1125 mm行程内与双频激光干涉仪比对位移测量结果,获得了优于50 m的残差标准差.并且在实验中

8、验证了监测臂光路和双快门系统对于补偿和消除电路漂移和大幅抖动导致的相位差测量误差的作用,获得了30 min内连续测量标准差约0.022的相位差测量精度.2原理和实验系统飞秒激光在频域上为一系列等间隔分布的谱线,各纵模频率为fcomb = nfrep + fceo, n为梳齿序数7.各纵模间形成的拍频均为重复频率的整数倍,即模间差拍信号包含的频率成分可表示为f = mfrep, m为正整数.若使用模间差拍信号中频率为mfrep的成分进行相位法测距,测量出参考信号与测量信号间相位差m,则绝对距离测量结果可表示为Dm = c2nmfrep(m2 +Nm)= 2m(m2 +Nm); (1)其中c为真空

9、光速, n为空气折射率,可根据空气折射率的相关理论由环境参数确定15;16,= c/(nfrep)为光频梳基频波长.由于仪器测得的相位差在02 范围内,测距结果存在模糊范围, (1)式中自然数Nm表示仪器无法决定的相位差2 周期数目.在不能预先给出待测距离估计值的情况下,最大可测距离为Dm;max = /(2m).由原子钟锁定重复频率后,光频梳重复频率抖动 frep 0的情况,令d1 = 1/4 为根据仪器相位差测量值1得出的测量结果.改变重复频率至frep = frep +frep,此时d1 = 1/4 为根据仪器相位差测量值1得出的测量结果,则待测距离D1 = d1 + 2N1 = d1

10、+ 2 N1; (3)式中 = c/nfrep,为改变重复频率后的基频波长.容易推知,当D1 0时无法确定其具体值的问题.根据(2)(4)式,合成波长模间拍频法测距结果可表示为(式中方括号均表示向下取整运算)D = Dm= 2m(m2 +2m(d1 + 22(d1 d1) +12)m2 + 12): (5)为正确解算出N1, (d1 d1)的测量偏差应不使取整运算结果发生变化.根据(4)式,测量误差必须满足j N1j = 2j (d1 d1)j 1o 1oQGg图3 (网刊彩色)相位差测量结果(为了显示清晰,图中的差值曲线做了平移)Fig. 3. (color online) Phase me

11、asurement results (thevertical origin of the black curve was shifted to zerofor clarity).以上实验中 = cfrepnf2rep= 18:93 mm,根据实验结果, j N1j SS1 2 3 4 5 6 7 8 9 105918.7685918.7705918.7725918.7745918.7765918.778p/mm图4合成波长重复测量结果(a) N1计算结果(取整前); (b)绝对距离测量结果Fig. 4. Repeated measurement results: (a) Calcula-tio

12、n results of N1 with decimals; (b) absolute distancemeasurement results.Ggu0 225 450 675 900 11254795.005020.005245.005470.005695.005920.00XAo(Gg/mmLGpGg/mm-0.10-0.08-0.06-0.04-0.0200.020.040.060.080.10u/mm图5 (网刊彩色)干涉仪比对测量结果Fig. 5. (color online) Distance measurement resultscompared to an interferom

13、eter.以5.92 m绝对距离为起点,反射目标沿光路方向平移,在1125 mm行程内以步长56.25 mm测量21处位置的绝对距离,并与双频激光干涉仪的位移测量值比对,测量结果和残差如图5所示,所得残差标准差42.2 m.实验结果说明在较大的移动范围下,合成波长测距系统可以保持较好的线性程度和较高的测量精度.如前文所述,本实验中光频梳频率抖动frep 1 mHz,它的相对误差小于1 mHz/56:27 MHz = 1:8 10 11,因此对测距结果的精度影响可以忽略,相位差测量误差是主要误差来源.引起相位差测量误差的因素包括: 1)测量相位差的仪器(锁相放大器)本身的测量不确定度,以及测量电

14、路中未被监测臂和快门切换系统完全消除的抖动,由于这些因素引入的是随机误差,可以通过适当增加测量点数目取平均值的方式减小误差,因此不会对测量的准确性造成较大影响; 2)由于相位差测量结果直接与待测距离相关,因此空气抖动引起的光路变化和折射率改变、反射目标的微小机械振动等导致的待测距离(光程)变化也将反映到相位差测量上,引起相位差测量误差; 3)在位移测量中,反射目标的前后移动、导轨机械公差引起的反射目标横向微小偏移或空气扰动导致的光路偏折均会导致返回光束的位置变化,将使探测器接收到光信号的强度发生改变,也将导致相位差测量偏差18,这一偏差为系统误差,需要监测探测器接收到光信号强度,对相位差测量结

15、果进行补偿校正以减小测量误差.除相位差测量误差外,由于本实验系统的测量臂较长,大气参数只是在单点测量,无法反映整个测量路径的空气折射率分布,折射率的计算和取值误差也将导致测距误差.尽管存在上述各项误差,本实验系统依然实现了0.022的相位测量精度.受探测器带宽限制,实验中用于精确测量的20次谐波成分的频率仍不够高,如果能选择更高带宽的探测器获取更高频率的谐波信号,采用更短的波长进行测量,则可大大提高本实验系统的精度.4结论本文研究了飞秒激光模间拍频法大尺寸测距方法,分析了测距量程、测距精度及测量误差对量程扩大的限制.通过原理验证性实验,验证了监测臂和双快门切换系统对于补偿和消除由电路产生的相位

16、差单向漂移和大幅度抖动的作用, 30 min内相位差测量结果标准差0.022;在超过单一重复频率模间拍频法量程的5.92 m距离处验证了合成波长扩大测距量程方案的可行性,测距结果重复性优于3 m,理论最大可扩展量程可达7.5 km;与干涉仪比对结果显示反射目标在1125 mm移动行程内,距离测量精度优于50 m.实验的测距精度还可通过选择更高带宽的探测器进一步提高.080602-5物理学报Acta Phys. Sin. Vol. 65, No. 8 (2016) 080602参考文献1 Bobro N 1993 Meas. Sci. Technol. 4 9072 Smullin L D, F

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22、 beat of a femtosecond laser Zhang Xiao-Sheng1) Yi Wang-Min2) Hu Ming-Hao1) Yang Zai-Hua2) Wu Guan-Hao1)y1)(State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, TsinghuaUniversity, Beijing 100084, China)2)(Beijing Institute of Spacecraft Envir

23、onment Engineering, Beijing 100094, China)( Received 14 December 2015; revised manuscript received 7 January 2016 )AbstractLarge-scale absolute distance measurement system with high accuracy plays a signicant role in science and en-gineering applications. In many elds such as aerospace technology, l

24、arge-scale manufacture, geodetic survey and civilengineering, absolute distance measurement systems with a range of up to kilometers and accuracy of better than sev-eral micrometers are generally required. Traditional laser ranging methods such as the time-of-ight method and theinterferometry method

25、 are dicult to achieve both large scale and high accuracy. With the development of femtosecondoptical frequency comb technology, several ranging methods with larger range and higher accuracy are developed. In thefrequency domain, the optical frequency comb has a large number of stable mode lines, or

26、 the longitudinal modes, at reg-ular intervals, which generates the inter-mode beat signal. In this study, based on the inter-mode beat of a femtosecondlaser, an absolute distance measurement system using multi-wavelength interferometric method is demonstrated. It hasa simple experimental setup with

27、 high accuracy but in a limited range of 2.5 m due to the 2 -period of phase detection.To achieve a large-scale measurement system, the measurement range of the experimental system is extended by usingthe synthetic wavelength generated by tuning the repetition frequency of the laser. With a repetiti

28、on frequency change of0.2 MHz, a synthetic wavelength of up to 1.5 km is realized, thus the measurement range of the experimental setup canbe extended to 0.75 km. Besides the reference and measurement path beams, a monitor path beam and two alternatelyopened mechanical shutters are used to measure a

29、nd compensate for the phase drift due to the unbalanced drift of theelectronic circuit. By using this method, the standard deviation of the phase measurement results in 30 min is 0.022 inthe experiment, and the phase drift can be compensated for very well. The measurement results from the experiment

30、alsystem are compared with the results from a commercial heterodyne interferometer, and the comparison between resultsshows a precision of better than 50 m in a displacement of 1125 mm. In the experiment, the repeatability of absolutedistance measurement using the range extending method is better th

31、an 3 m, thus the range of the distance measurementsystem can be theoretically extended up to 7.5 km. In conclusion, we demonstrate that a large-scale absolute distancemeasurement system using inter-mode beat of a femtosecond laser, has a range of up to 7.5 km, an accuracy of betterthan 50 m and a re

32、peatability of better than 3 m. The accuracy of the experimental system can be further improvedby using photodetectors with higher bandwidth so that a higher inter-mode beat and a shorter wavelength can be used.Keywords: inter-mode beat, femtosecond laser, large-scale distance measurementPACS: 06.30

33、.Bp, 06.60.Jn, 42.62.Eh DOI: 10.7498/aps.65.080602* Project supported by the Training Program of Innovation and Entrepreneurship for Undergraduates, China (Grant No.201510003B022), the Foundation of the Laboratory of High-accuracy Measurement of Spacecraft, China, the NationalNatural Science Foundation of China (Grant NO. 61575105), the Funding of State Key Laboratory of Transient Optics andPhotonics, China (Grant NO. SKLST201406), and the Young Elite Teacher Project of Beijing Higher Education, China(Grant No. YETP0085). Corresponding author. E-mail: 080602-7