一种调频连续波干涉仪激光波长稳定性测量方法 
下载： 725次
With the rapid development of laser interferometry technologies, the industrial production has put forward higher accuracy requirements for precision machining, optical detection, assembly measurement, etc. For example, the displacement detection of components in computer numerical control machine tools, the deformation detection of bridges and dams, and the internal pressure monitoring of missile guidance all need precise measurements. As the benchmark of interferometry, laser wavelength directly affects measurement accuracy, thus measuring the stability of laser wavelength is of great significance for analyzing the accuracy of interferometry. According to the physical phenomena, the existing laser wavelength stability measurement methods can be divided into optical beating method, interference comparator method, and specific wavelength sensitive material characteristics based method. These methods have a high wavelength measurement resolution, but need a reference laser, which inevitably increases the cost of a measuring equipment. Frequency-modulated continuous wave (FMCW) interferometry technology has the advantages of strong anti-interference ability, high measurement accuracy, and the ability to measure distances, displacements, temperatures and other physical quantities. This paper proposes a frequency-modulated continuous wave interferometric cavity measurement method, which has the advantages of short measurement time, no reference laser, simple optical structure, low cost, and high measurement resolution. This method has high application value in the fields of optical fiber sensing and precision interferometry.
In order to realize the measurement of laser wavelength drifts, a method of frequency-modulated continuous wave laser wavelength stability measurement based on interferometric cavity is proposed. Firstly, the measurement theory of wavelength shifts is deduced. When the cavity length is constant, the shift of the initial phase is caused by the average center wavelength shift, which leads to the "displacement" in the form. Second, the interferometric cavity is insulated and damped to reduce the influence of ambient temperature fluctuation on the Fabry-Perot (F-P) cavity, the F-P cavity length is measured by the frequency discrimination method, and the displacement-wavelength shift coefficient is determined. Third, the inverse cosine look-up table method is used to identify the phase of the fixed point of the beat signal to obtain the displacement variation. According to the linear relationship between the displacement and the laser wavelength shift, the wavelength shift is collected in real time. Finally, the measurement system of FMCW interferometric cavity is built for experimental verification and error analysis.
In order to verify the validity and accuracy of wavelength stability measured by the FMCW interferometric cavity, an experimental device is set up (Fig. 5). The insulation stability of the F-P cavity is tested (Fig. 6). The displacement fluctuation of the F-P cavity is within ±3 nm, which shows that the heat preservation treatment effect of the F-P cavity is good. The laser wavelength drift is collected within the error range (99.942100.058 mm) of the F-P cavity length measured by the frequency discriminator method (Fig. 8). The standard deviations of laser wavelength drifts are 0.05812, 0.05809, and 0.05806 pm, respectively, under different cavity lengths. It can be seen that the measurement error of cavity length has no obvious effect on the measurement of laser wavelength stability and can be ignored. The average center wavelength stability of the laser is measured by the FMCW interferometric cavity (Fig. 10). The results show that the average center wavelength stability of the laser is 0.19×10-6, the measurement standard deviation is 0.049 pm, and the actual measurement resolution of the laser wavelength shift is 0.016 pm. Therefore the relative measurement resolution is 1.02×10-8. The comparison with the existing laser wavelength measurement methods (Table 1) is conducted. The relative measurement resolution of four methods is better than 1×10-7, but the FMCW interferometric cavity measurement method greatly shortens the measurement time. It shows that the proposed method is convenient in real time, high in measurement resolution, and fast in measurement speed. Moreover, the laser under temperature control and current stability has good repeatability and stability.
In this paper, a method for measuring laser wavelength stability with the FMCW interferometric cavity is proposed, which uses the advantages of high precision, high resolution, and real time measurement of FMCW interference to solve the quantification problem of laser wavelength stability. By deducing the theory underlying the interferometric cavity measurement method, the demodulation algorithm of wavelength drifts is designed to realize the real time measurement of laser wavelength drifts and effectively improve the measurement resolution of wavelength drifts. The experimental results show that the measurement resolution of wavelength shift of the proposed method is 0.016 pm, the calculation speed of wavelength shifts is up to 50/s, and the measurement time is 0.02 s. Compared with those of the optical beating method and interference comparator method, the measurement speed is greatly improved. The laser shows an average wavelength stability of 0.19×10-6 within 1 h. This stability is better than that of most dual-frequency lasers on the market . The proposed method is of great significance to the research on improving the accuracy of FMCW interferometry and has good application value in the field of laser wavelength stability measurements.
1 引言
在激光干涉测量技术飞速发展的今天，工业生产对精密加工、光学检测、装配测量等提出了越来越高的精度要求[1]。如数控机床中部件位移的检测、桥梁大坝的形变检测和导弹制导系统内部的压力监测等都需要进行精密的测量。调频连续波(Frequency-Modulated Continuous Wave，FMCW)干涉测量技术[2-4]具有抗干扰能力强、测量精度高和能够实现距离、位移、温度等多物理量的测量等优点，而激光波长作为干涉测量的基准直接影响测量精度[5]，所以测量激光波长稳定性对于分析干涉测量精度具有重要的作用。
在激光干涉测量系统中，分布反馈(Distributed Feedback，DFB)激光器温控系统的波动、驱动电流的漂移、激光器自身的不完全耦合以及光路或电路器件老化等问题造成激光器波长漂移[6]，大多学者从优化激光器内部结构和电路设计两方面来减小激光波长漂移。为了明确波长漂移量，学者们研究了激光漂移量的测量。辛国锋等[7]以透镜、半导体激光器与体布拉格光栅构成外腔激光器，使激光器工作波长稳定在体布拉格光栅的布拉格波长处。唐七星等[8]基于改进的时域相关光谱修正算法，将系统稳定性评估中的波长漂移标准偏差修正为0.1443 nm。Kim等[9]利用光纤中受激布里渊散射引起的斯托克斯波随波长变化的频移，测量了半导体激光器的中心波长漂移，长期波长稳定性(>4 h)为10 pm。
目前，激光波长稳定性测量方法按物理现象可分为光学拍频法、干涉比较法和使用特定波长敏感材料特性的方法等[10]。光学拍频法是利用快速光电探测器测量参考激光器和测试激光器之间的频率差，从而得出波长，该方法的相对测量分辨率达1×10-14～1×10-9，测量时间为0.1～1 s；干涉比较法通过改变干涉仪中的光程差，观察参考激光和测试激光干涉条纹的相位变化以测量波长，该方法的相对测量分辨率可达1×10-8，测量时间为1 s～15 min；使用特定波长敏感材料特性的方法的相对测量分辨率达1×10-7，测量时间为0.1～1 s。上述方法均有较高的波长测量分辨率，但需要参考激光器，增加了测量设备的成本。而FMCW干涉腔测量法具有测量时间短、不需要参考激光器、光学结构简单、成本低、测量分辨率较高的优势。
为了实现激光波长漂移量的测量，本文提出了一种利用FMCW干涉腔测量激光波长稳定性的新方法。首先，基于调频连续波干涉测量原理，推导了激光波长稳定性测量理论；再对干涉腔作保温和减振处理，确保了位移-波长漂移量变化系数的准确性；然后，设计了拍频信号波长漂移解调算法，搭建了FMCW干涉腔测量系统，验证了该测量方法的有效性，并结合实验结果分析了测量误差；最终，确定了FMCW干涉测量系统光源的稳定性，达到了提高激光波长漂移测量分辨率和响应速度的目的。
2 基本原理
光学调频连续波即频率(或角频率)受到连续调制的光波，调制波波形是周期函数。本文选择锯齿波调制波形。调频连续波激光干涉技术的原理是通过向待测目标发射频率连续调制的激光，光束经过光纤环行器出射到法布里-珀罗(Fabry-Perot，F-P)腔的前端面(即半反半透参考镜)上，其中一部分经参考镜反射作为参考光，另一部分透射至干涉腔后端面，经目标全反镜反射后作为信号光，与参考光相遇产生干涉拍频信号，通过对拍频信号进行解调，可实现目标位移、距离、压力、液位、速度、振动等物理量的测量。FMCW干涉光路图如
激光器驱动电路产生的锯齿波调制信号与经信号采集电路转化后的拍频信号的波形如
图 2. FMCW干涉仪的锯齿波调制信号与拍频信号的波形
Fig. 2. Waveforms of sawtooth modulated signal and beat signal of FMCW interferometer
每个调制周期内的拍频信号为
拍频信号的频率vb为
拍频信号的初相位φb0为
由(3)式可知，当OP改变一个波长时，拍频信号会移动一个周期。初相位φb0的变化反映了波形动态的移动情况，初相位的变化主要用于相对物理量的测量，且初相位与中心波长有关，波长的漂移直接影响测量的精度。
根据微分定理对拍频信号初相位公式进行推导，发现在OP恒定下，平均中心波长漂移引起初相位的移动，进而导致形式上的“位移”。
联立(5)、(6)式，有
3 FMCW干涉腔测量法
在调频连续波激光干涉测量系统中，DFB激光器以其调制速率高、直接电流调制、调制范围大、尺寸小以及成本低的优点成为FMCW干涉系统的最佳光源，根据激光波长稳定性测量理论，本文提出了FMCW干涉腔测量法，方案框图如
由于激光器波长受电流和温度的影响，对DFB激光器驱动电流[11]和工作温度[12]进行控制，以提高激光器波长稳定性和光信号质量。测量方案的原理为激光器发射锯齿波调制信号，从光纤环行器出射至被黄铜管保护的准直器中，再经准直器出射至F-P腔中，然后对整个不锈钢管作保温处理，光信号在F-P腔的前端面发生干涉，干涉产生的拍频信号携带有激光波长漂移信息，通过光电探测器将光信号转换成电信号，电信号经放大滤波电路、芯片的模拟数字转换(ADC)和算法处理后，解调得到波长漂移量。
激光波长漂移量的解调算法流程如
具体步骤如下。
1)算法以边调制边采集的方式进行处理。采集到一个调制周期内的拍频信号后，先选取拍频信号中间信噪比较高的有效拍频波形，30% ～80%点数区间内的波形为有效处理对象，利用冒泡法找出拍频信号有效区间中的极值点大小和位置。
2)激光器的电流调制使拍频信号伴随有强度调制，且参考光与信号光之间的对比度使拍频信号的极小值不为零，所以将拍频信号归一化为标准余弦信号，便于鉴别相位，即
3)为了提高相位鉴别精度，在有效区间内均匀选取多个固定点进行鉴相，以解算平均相位，从而减小鉴相算法的随机误差。
4)为了提高算法速度，将180°相位细分为2048份以形成反余弦表，每份的最小相位分辨率为
5)根据相位变化量-位移-波长漂移量之间的线性关系，实现波长漂移量的测量。算法位移测量分辨率为1 nm[15]，由(7)式可知波长漂移量的测量分辨率为0.016 pm。
4 实验验证与误差分析
为了验证FMCW干涉腔测量波长稳定性的有效性和准确性，搭建了实验装置，如
在实验中，激光器电流调制频率设置为20 kHz，平均驱动电流为60 mA，调制率为400 mA/ms，每个周期的采样点数为140，采样率为2.8 MHz，激光器设定温度为24.8 ℃。调制频率为解算波长漂移量的速度，即1 s输出20000个波长漂移量数据。在实际测量中，为了降低数据波动以及方便观察，人为分频降低速度，算法累计计算400次输出一次数据，测量速度为1 s输出50个波长漂移量数据，即测量时间为0.02 s。同时，对F-P腔进行保温和减振处理，以减小环境温度变化和振动对F-P腔的影响，测试F-P腔的保温稳定性，1 s采集1个位移数据，测试30 min，如
由
4.6 干涉测量法的验证分析
通过计算可知，当平均中心波长λ＝1579.152 nm，腔长L＝100 mm，位移从-20 nm累计变化到20 nm时，理论波长漂移量如
利用鉴频法测量F-P腔长，在测量F-P腔长的误差范围(99.942～100.058 mm)内采集激光波长漂移量。测量时，三个腔长分别为99.942，100.000，100.058 mm，每秒输出50个数据，测量结果如
结果表明，在不同腔长下，波长漂移量的标准差分别为0.05812，0.05809，0.05806 pm，可见腔长的测量误差对激光波长稳定性测量的影响很小，可忽略不计。将
4.7 激光器中心波长的稳定性测试
使用光谱仪(波长范围为0.6～1.7 μm，分辨率为20 pm)测量激光器平均中心波长，10 min记录一次数据，测量时间为1 h，如
图 10. FMCW干涉腔测试波长稳定性
Fig. 10. Test of wavelength stability by FMCW interferometric cavity
结果表明，激光器平均中心波长稳定性为0.19×10-6，测量标准差为0.049 pm，激光波长漂移量的实际测量分辨率为0.016 pm，则相对测量分辨率为1.02×10-8。与现有的激光波长测量方法进行对比，结果如
表 1. FMCW干涉腔测量法与现有测量法的性能对比
Table 1. Performance comparison among FMCW interferometric cavity measurement method and existing measurement methods
|
5 结论
提出了一种新的FMCW干涉腔测量激光波长稳定性的方法，利用FMCW干涉高精度、高分辨率、测量实时快速的优势，解决了激光波长稳定性的量化问题。通过推导干涉腔测量法理论，设计了波长漂移量解调算法，实现了激光波长漂移量的实时测量，有效提高了波长漂移量的测量分辨率。实验结果表明，该方法测量分辨率为0.016 pm，测量时间为0.02 s，相比光学拍频法和干涉比较法，缩短了测量时间。激光器在1 h内表现出0.19×10-6的平均波长稳定性。此稳定性优于市场上大部分双频激光器，这对提高FMCW干涉测量的精度具有重要意义，在激光波长稳定性测量领域中有较好的应用价值。
[1] 张健. 线性调频DFB半导体激光器的非线性矫正技术研究[D]. 西安：中国科学院西安光学精密机械研究所，2019.
ZhangJ. Study on nonlinear rectification technology of LFM DFB semiconductor laser[D]. Xi’an: University of Chinese Academy of Sciences, 2019.
[2] ZhengJ. Optical frequency-modulated continuous-wave (FMCW) interferometry[M]. New York: Springer-Verlag, 2005.
[3] Zheng J. Analysis of optical frequency-modulated continuous-wave interference[J]. Applied Optics, 2004, 43(21): 4189-4198.
[4] Zheng J. Single-mode birefringent fiber frequency-modulated continuous- wave interferometric strain sensor[J]. IEEE Sensors Journal, 2010, 10(2): 281-285.
[5] Cai Y D, Feng B K, Sang Q, et al. Real-time correction and stabilization of laser diode wavelength in miniature homodyne interferometer for long-stroke micro/nano positioning stage metrology[J]. Sensors, 2019, 19(20): 4587.
[6] de Marcellis A, Ferri G, D’Amico A, et al. A fully-analog lock-in amplifier with automatic phase alignment for accurate measurements of ppb gas concentrations[J]. IEEE Sensors Journal, 2012, 12(5): 1377-1383.
[7] 辛国锋, 程灿, 瞿荣辉, 等. 体布拉格光栅外腔半导体激光器光谱特性研究[J]. 光学学报, 2007, 27(10): 1821-1826.
[8] 唐七星, 张玉钧, 陈东, 等. 调谐激光吸收光谱波长偏移修正算法研究[J]. 光谱学与光谱分析, 2018, 38(11): 3328-3333.
[9] Kim J, Park S, Choi Y K, et al. Wavelength stabilization of a semiconductor laser using wavelength-dependent frequency shift by stimulated Brillouin scattering[J]. Optical Engineering, 2016, 55(12): 120501.
[10] Dobosz M, KoAZ′Guchowski M. Overview of the laser-wavelength measurement methods[J]. Optics and Lasers in Engineering, 2017, 98: 107-117.
[11] 吴涛, 庞涛, 汤玉泉, 等. 基于频率补偿的高稳定抽运激光器驱动电路[J]. 中国激光, 2019, 46(8): 0801010.
[12] 何启欣, 刘慧芳, 李彬, 等. 多通道半导体激光器温控系统[J]. 光学学报, 2017, 37(11): 1114002.
[13] 张雄星，郑刚，井李强，等. 一种调频连续波干涉信号幅度归一化方法：CN109870677A[P]. 2019-06-11.
ZhangX X, ZhengG, JingL Q, et al. A method for amplitude normalization of frequency modulated continuous wave interference signal: CN109870677A[P]. 2019-06-11.
[14] 井李强, 郑刚, 孙彬, 等. 基于调频连续波干涉技术的运动目标距离测量[J]. 中国激光, 2019, 46(12): 1204001.
[15] 张雄星，郑刚，高明，等. 一种调频连续波干涉信号的快速鉴相方法：CN110646789A[P]. 2020-01-03.
ZhangX X, ZhengG, GaoM, et al. A fast phase discrimination method for FMCW interference signal: CN110646789A[P]. 2020-01-03.
郭媛, 郑刚, 盛启明, 聂梦笛, 白浪, 韩园. 一种调频连续波干涉仪激光波长稳定性测量方法[J]. 中国激光, 2022, 49(4): 0404002. Yuan Guo, Gang Zheng, Qiming Sheng, Mengdi Nie, Lang Bai, Yuan Han. New Method for Measuring Laser Wavelength Stability by Using Frequency-Modulated Continuous Wave Interferometer[J]. Chinese Journal of Lasers, 2022, 49(4): 0404002.
PDF全文
