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FSI测距是以迈克尔逊干涉仪为基础进行测量的,其依赖于干涉仪两臂的相位差与激光频率扫描之间的线性变化[17-18]。在测量时,通过改变可调谐激光器发射的激光频率达到改变接收光相位的目的,从而引起外差干涉条纹的变化。
FSI测距系统如图1所示。以三角波调制信号为例,信号发生器输出的三角波信号作用到ECLD的压电陶瓷(PZT)上,PZT控制光栅进行线性选频。ECLD发出的激光被第一个分束器(BS1)分离。一部分传入法布里-珀罗干涉仪,用来测量ECLD的扫频范围;另一部分传入迈克尔逊干涉仪。在迈克尔逊干涉仪中,光束被第二偏振器(BS2)分成两部分:一束沿着固定长度的参考臂传输至回射器(RR1);另一束沿着测量臂传输至回射器(RR2)。经两个回射器反射后的光束在探测器(PD2)处形成干涉信号,PD2将记录ECLD光学频率扫描期间干涉信号的相移变化。
绝对距离L可以被表示为:
$$ {L}={N} \cdot \frac{c}{2 \cdot {n} \cdot {r} \cdot {F S R}}+\text{δ}{N} \cdot \frac{c}{2 \cdot {n} \cdot {r} \cdot {F }{S }{R}} $$ (1) 式中:N为测量条纹整数部分;
$ \text{δ}{N}$ 为测量条纹分数部分;FSR为F-P干涉仪的自由光谱区;r为共振态;n为折射率;c为光速。测距系统的不确定度∆L主要受到几个影响因子的约束[19-20]:$$ \Delta {L}=\sqrt{{\left(\frac{c}{2 \cdot n \cdot F S R \cdot r} \cdot \text{δ}{N}\right)}^{2}+{\left(\frac{c \cdot N}{2 \cdot n \cdot {F S R}^{2} \cdot r} \cdot \text{δ}{F} {S} {R}\right)}^{2}+{\left(\frac{c \cdot N}{2 \cdot n \cdot F S R \cdot {r}^{2}} \cdot \text{δ}{r}\right)}^{2}+{\left(\frac{c \cdot N}{2 \cdot {n}^{2} \cdot F S R \cdot r} \cdot \text{δ}{n}\right)}^{2}} $$ (2) 调频非线性,目标微小振动以及色散失配等会将影响因子对系统不确定度的影响放大几十甚至上百倍,因此,分析和补偿这些干扰因素对测量精度至关重要。
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ECLD调频是通过信号发生器控制PZT驱动反射镜转动实现的。虽然信号发生器产生的调制信号是线性的,但PZT具有迟滞性响应的特点,使得光频率呈非线性变化,进而造成干涉信号相位提取误差[21]。图2展示了线性扫频与非线性扫频对相位差的影响,非线性扫频会导致干涉信号在时域中的条纹数发生变化。
图 2 干涉信号相位差计算示意图。(a) 理想线性扫频;(b) 实际非线性扫频
Figure 2. Schematic diagram of calculating the interference signal phase difference. (a) Ideal linear frequency sweeping; (b) Actual nonlinear frequency sweeping
针对非线性扫频造成的不利影响,研究人员提出一系列改进FSI测距系统的方法,例如:搭建重采样系统[22-24]等测量装置,以及最小拟合二乘法[25]、卡尔曼滤波[26]、希尔伯特相位展开[27]等算法。可以将这些方法分成两大类:一类是利用光电晶体[28]、锁相环[29]等技术进行主动稳频,降低非线性扫频;另一类是对干涉信号频率进行追踪,利用算法提取并进行校正相位,被动补偿非线性扫频[30-31]。
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1996年,日本金泽大学的Iiyama等人[29]使用自参考稳频方法。如图3所示,利用参考信号Reference SG与外差干涉信号的频率差值进行锁相放大,与三角波调制信号Triangular SG相叠加,达到非线性校正的目的。经锁相环调制后,在100 GHz扫频范围内,测量20 cm处的目标,分辨率达到1.3 mm,与调制之前的12 mm分辨率相比,测量精度大约提高了10倍。
1998年,美国俄勒冈大学的Greiner[28]在谐振腔内加入了抗反射涂层钽酸锂电光晶体EOC,配置为横向相位调制器,可以快速调谐频率。通过锁相环稳频后,将电流调制引入的噪声抑制了两个数量级。
2010年,日本北海道大学的Kakuma等人[32-33]将VCSEL作为光源,克服了ECLD的跳模限制[34],实现太赫兹范围内无跳模频率调谐。2015年,Kakuma用基于锁相环技术的电流控制器稳定VCSEL的扫频速度,同时用铷气体池Rb-cell标记测量频率,通过最小二乘拟合法精确确定干涉条纹的梯度,如图4所示。在14 mm测量范围内,实现亚微米测量精度,测量标准差为0.12 µm,相对误差为0.9×10−5,有较好的重复性。
2015年,西安交通大学的邓忠文等人[35]用子空间识别算法N4SID对非线性扫频建模,构建三角波电压调制信号与F-P干涉仪的干涉信号之间的传递函数G(s)。用校正的G(s)驱动信号替代三角波信号控制PZT,进行反向补偿。在40 mm范围内,用三角波调制信号测量,标准差为16 µm,相对残差为2×10−4。用G(s)校正的驱动信号测量,标准差为7 µm,相对残差为7.5×10−5。该方法有效地抑制了光学扫频的非线性。
2018年,西安交通大学的Zhu等人[36]用频率响应函数(FRF)描述输入信号的每个谐波分量对扫描频率的线性和动态行为的影响。通过三角波的逆FRF处理得到校正的输入信号。在40 mm范围内,用原始三角波调制信号测量,频域峰值的半高宽(FWHM)为4003 Hz,标准差为8 µm,相对误差为2.1×10−4。用校正后的调制信号测量,FWHM为1160 Hz,标准差为2.4 µm,相对误差为9.7×10−5。
主动稳频技术指标如表1所示。
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2005年,韩国光州科技学院的Ahn等人[37]用希尔伯特变换的补偿方法消除非线性扫频,如图5所示,将具有固定延迟时间的辅助干涉仪(Aux. interferometer)添加到常规光频域反射计系统中,利用希尔伯特变换提取干涉信号的相位,并从其导数中得到调谐速率。对速率数据进行插值,补偿调谐频率。补偿后频率的FWHM约为3 cm,原始频率的FWHM约为177.4 cm,精度提高了约60倍。
2009年,比利时蒙斯工程学院的Yuksel等人[38]利用重采样法,降低非线性的影响。借助辅助干涉信号中等频域间隔的位点(峰谷值点),对测量干涉信号进行重采样。重采样后FWHM的分辨率为0.4 cm,相比原始干涉信号的13 cm的FWHM,空间分辨率提高了约30倍。
2015年,天津大学的孟祥松等人[39]用小带宽调制、拼接重采样信号相位的方法,补偿宽带调制中的非线性问题。实验表明,在26 m测量范围内,标准差为50 µm,相对误差为100×10−6。
上述重采样技术[38-39]是基于软件算法实现的,实际信号的位点信息有一定概率不在采样频率点上,会使后续FFT变换出现漏频现象。2016年,天津大学的姚艳南等人[40]用硬件实现等频率间隔的重采样技术,如图6所示,将辅助路正弦干涉信号整形为方波信号,以方波信号的上升沿和下降沿作为数据采集卡DAQ的时钟信号,对通道1的干涉信号进行采集,确保数据点的相位信息真实有效。基于软件的等光频间隔重采样频谱的FWHM为19.68 kHz,基于硬件等光频间隔重采样频谱的FWHM为19.21 kHz。
实验室利用此重采样方法对2 m范围内目标进行测量,对干涉信号直接进行FFT变换,FWHM约为10 mm,无法分辨被测目标的距离,经过重采样后做FFT变换,FWHM为20 µm。
当基于峰谷点等光频间隔重采样时,辅助干涉仪中延迟光纤的光程差(OPD)应至少是测量距离的两倍,这将限制大尺寸测量中辅助光路的光纤长度。2019年,中国科学院大学的Jiang等人[41]用基于希尔伯特相位展开的等光频重采样方法细分等光频间隔,对一个周期内的辅助信号提取多个采样点,在补偿调频非线性的同时有效降低了对辅助路光纤长度的需求。当辅助干涉仪的光纤长度为4.5 m左右时,测量到的目标距离约为5 m,距离测量结果的标准差可达4.64 µm。
2016年,西安交通大学的Liu等人[42]采用扩展卡尔曼滤波(EKF)技术跟踪干涉信号频率,补偿非线性光频输出,提高相位提取精度。在3 m测量范围内,绝对距离测量的标准偏差小于2.4 µm,相对误差为1.1×10−4。2018年,西安交通大学的Wang等人[43]在Liu等人[42]的研究基础上利用复数移位小波提取相位的方法,跟踪干涉信号的瞬时频率,同样估计分数相位。3 m范围内,绝对距离测量的标准偏差小于1.69 µm。
2020年,西安交通大学的邓忠文等人[44]用干涉信号的峰值反向截断检测到的光频率曲线补偿频率调谐的非线性。如图7所示,对任意两个相邻F-P峰之间的M-Z干涉信号的采样点进行拟合,降低了F-P腔的FSR (1.5 GHz)对频率分辨率的限制[45],得到精确的频率变化曲线。测量约为2.6 mm的台阶,与X光测量相比,残余误差为3.1~8.3 µm。
被动补偿式方法技术指标如表2所示。
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在实际测量中,待测目标会受到振动等外界环境的影响,产生多普勒频移现象[46-47]。此时,很难区分以下两个因素对干涉条纹造成的影响:(1)扫描频率形成的合成波长
${\Lambda }$ 条纹,(2)微小振动造成距离变化从而引起的光学波长$ \mathrm{\lambda } $ 条纹变化。这将使微小振动引起的位移误差成系数放大,放大系数为$ \mathrm{\Lambda }/\mathrm{\lambda } $ 。因此,实际绝对距离如公式(3)所示[48-49]。对于中心波长为1550 nm,扫描带宽为20 nm的激光器,位移误差将被放大77.49倍。近20年,如何解决多普勒频移造成的影响成为FSI测距研究的热点之一。$${L}={N} \cdot \frac{\varLambda }{2{n}}-{{\Delta }{L}}_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{f}\mathrm{t}} \cdot \frac{\varLambda }{{\lambda }} $$ (3) 2001年,西门子公司的Schneider等人[50]用双向扫频方法,如图8所示,用两台可调谐激光器,同时向上和向下调谐频率,调频范围相同。因为是同步扫频,目标振动对两个外差信号产生的影响是相同的,可以通过两干涉信号彼此相乘,经过滤波处理,抵消掉多普勒频移的影响。
2004年,牛津大学的Coe等人[51]将Schneider等人提出的双扫方法[50]应用在对ATLAS粒子对撞机内部的半导体跟踪器SCT的形状变化上,使用两个扫频方向相反的激光器完成测距,大大降低干涉仪长度漂移引起的误差,可以测量大于10 µm的形变。
2005年,美国密歇根大学的Yang等人[52]用滑动测量窗口法提取目标的振动频率与振动幅度。在两者为常数的情况下,距离测量仅取决于时间窗口的大小,如公式(4)所示:
$$ \Delta {L}=4{{a}}_{\mathrm{v}\mathrm{i}\mathrm{b}}\frac{\varLambda }{{\lambda }}\mathrm{s}\mathrm{i}\mathrm{n}\left[{\pi }{{f}}_{\mathrm{v}\mathrm{i}\mathrm{b}}\right({t}-{{t}}_{0}\left)\right] $$ (4) 式中:
${{a}}_{\mathrm{v}\mathrm{i}\mathrm{b}}$ 为振动幅度;${{f}}_{\mathrm{v}\mathrm{i}\mathrm{b}}$ 为振动频率。每将固定长度的测量窗口向前移动一个F-P峰,把一个扫频周期内所有测量的实际距离的算术平均值视为扫频测量距离,多次测量取平均值,可以极大地抑制振动效应。在实验室环境下,10~70 cm范围内的测量精度为50 nm。同年,荷兰代尔夫特理工大学的Swinkels等人[53]利用扫频干涉与定频干涉相结合的方法测量目标的漂移信息。将固定频率干涉信号偏振复用,在正交中测量四个点的瞬时相位,补偿目标漂移。在15 m范围内,测量的相对误差为130 µm。2005年,葡萄牙国家工程技术创新研究所的Cabral等人[54]用一台可调谐激光器以不同的扫描持续时间进行两次连续测量,借助两个FSI连续条纹数确定目标移动速度以及偏移距离,进而补偿漂移,获得实际的绝对距离。
2008年,瑞士巴汝拉地区工程师学院的Le Floch等人[55-56]利用射频发生器控制做双边带调制扫频,产生大约45 GHz的可调频率差。在光电探测器上会探测到两个距离相关的干涉信号,经带通滤波后解调频率信息。在15 m范围内,测量精度达到50 µm。
2009年,德国不伦瑞克联邦物理技术研究院的Pollinger等人[57]采用扫频干涉测量与双波长干涉测量相结合的方法,细化干涉条纹的精细度,补偿多普勒频移引起的放大位移量。在20 m测量范围内,测量精度达到12 µm,相对不确定度为5.1×10−7。
2011年,北京航空航天大学的李志栋等人[58]利用外差干涉和频分复用实现绝对距离和光程差位移量的同时测量。用高精度波长计对扫频终点频率进行测量,剔除与扫频终点频率和光程差位移量有关的误差相位偏移量,实现频移补偿。在50 m测量范围内,测量残差为5~55 µm。
2012年,日本北海道大学的Kakuma等人[59]使用两台VCSEL在相反方向上同步扫频,通过解调两个干涉信号中的反向相移,得到两个距离信息,取其平均值抵消目标振动的影响。在11 mm测量范围内,测量标准差为4 µm,相对误差为3.6×10−4。
2014年,牛津大学的Dale等人[60]用双扫干涉测量与气体吸收池组合的测量系统实现动态目标追踪。如图9所示,在每个扫频周期内用气体吸收池的跃迁谱线做为频率标准标记。结合双扫干涉,补偿目标振动的影响。在20 m范围内,测量的相对不确定度为0.4×10−6,FWHM为40 nm。同年,西安交通大学的陶龙等人[61-62]利用卡尔曼滤波技术进行动态距离测量。通过卡尔曼滤波计算干涉信号的状态,估计目标的绝对距离和移动速度可以。在0.66 m范围内,目标振动幅度为1 µm,振动频率为4.7 Hz时,测量标准差为0.48 µm。
2015年,英国南威尔士大学的Martinez等人[63]用基于四波混频(FWM)的双扫测距系统降低目标振动的影响,如图10所示,利用SOA的三阶非线性效应,产生四波混频。经滤波后,用两个镜像对称的扫频信号测距。相比于Schneider等人[50]提出的双可调谐激光器扫频测距,此方法仅用到一台可调谐激光器,降低了系统成本和两个扫频信号的同步性伺服控制难度。当测量范围为0.4 m,目标以9 µm振幅,2 Hz频率振动时,测量标准差为21 µm。
2016年,德国不伦瑞克联邦物理技术学院的Prellinger等人[64-65],将637 nm处碘跃迁的饱和光谱用于频率参考标记,结合双扫测距,补偿环境振动的影响。与牛津大学Dale等人[60]提出的用气室标定参考光路频率相似,但碘分子跃迁的光谱特性相对稳定,不受环境影响。在4 m测量范围内,测量标准差为11 µm,相对误差为6.0×10−7。同年,哈尔滨工业大学的Lu等人[66]建立了绝对距离测量中多普勒效应的理论模型。结构如图11所示,用多普勒测速仪校正干涉信号中的频移放大。对16 m处的目标进行测量,测量分辨率为65.5 µm,标准差为3.15 µm。
2016年,哈尔滨工业大学的刘国栋等人[67]建立了振动对宽带激光扫频干涉测距系统的影响模型,结合卡尔曼滤波方法对目标距离信息进行状态估计。测量9.6 m处的目标,标准差由185.4 µm降低到9.0 µm,有效降低了环境振动对测量结果的影响。
2017年,南京航空航天大学的陈希伦等人[68-69]采用基于电光调制器的双边带调制,做双扫测距。在3.48 m测量范围内,当光路中存在7.7 mm扰动时,测量标准差为60 µm。同年,中国科学院电子学研究所的Mo等人[70]将马赫-曾德尔调制器作用于固定频率的激光器上,产生双边带扫频信号,同样做双扫测距。在千米量级的绝对距离,测距精度可达3 µm。
2018年,西安交通大学的Jia等人[71-72]利用时变卡尔曼滤波器的时间更新方程和测量更新方程迭代地估计目标的绝对长度和速度,描述目标的瞬时运动,实现动态测量。当目标的振幅为1 µm,振动频率为1 Hz时,在0.3 m测量范围内,测量精度为2.5 µm。同年,浙江科技大学的Zhang等人[73]设计了一种结合扫频干涉(FSI)和多波长干涉(MWI)[74]的正弦相位调制型绝对距离干涉仪。在4.25 m的距离内重复进行20次实验,结果表明标准差为0.18 µm,最大测量残差为0.36 µm。
2019年,天津大学的张福民等人[75]将三角波调制的一个周期内上下扫频干涉信号相乘,做Chirp-Z变换,建立了振动效应模型,对干涉信号进行补偿,抵消振动偏移量。当目标做振幅为10 µm,频率为1 Hz的正弦振动时,在3 m测量范围内,标准偏差从775 µm减小到12 µm。在自然环境中,通过使用振动补偿,标准偏差从289 µm减小到11 µm。
2020年,重庆大学的Shao等人[76]结合扫频和定频干涉测量的相位信息,组成了一种动态位移测量法。从扫频干涉信号SFSI(t)中重新构造一个类似定频干涉SFFI(t)的信号,展开FFI信号相位并计算相位增量,得到每个时刻点的动态距离值。在1 cm测量范围内,测量不确定度为2 µm。
天津大学的Shang等人[77]用连续波单频激光器及波分复用器建立了一种外差干涉仪,检测距离的变化。如图12所示,利用AOM对于扫频和固定频率做频移,当固定信号的频率等于扫频信号的截止频率时,将固定频率的干涉信号与扫频干涉信号相乘,做低通滤波,消除由目标振动引起的频偏。在10 m范围内实现了4.26 µm的测量精度。
目标振动补偿的技术指标如表3所示。
表 3 补偿振动漂移的FSI系统测距精度比较
Table 3. Comparison of FSI system ranging accuracy for compensating vibration drift
Author Distance/m Standard deviation/µm Relative error FWHM Ref. Yang 0.7 - - 50 nm [52] Martinez 0.4 21 - - [63] Tao 0.66 0.48 - - [61-62] Zhang 3 11 - - [75] Prellinger 4 11 6.0×10−7 - [64-65] Kakuma 11 4 3.6×10−4 - [59] Swinkels 15 - 1.3×10−4 - [53] Le Floch 15 - - 50 µm [55-56] Lu 16 3.15 - 65.5 µm [66] Dale 20 - 0.4×10−6 40 nm [60] Pollinger 20 - 5.1×10−7 12 µm [57] -
对于高分辨率扫频干涉测距系统,光纤光路的色散失配也是限制提高测量分辨率的重要因素。色散效应将导致测量信号频域峰值FWHM展宽[78-79],从而导致测量分辨率下降,因此,需要对色散失配进行补偿。
2010年,美国蒙塔纳州立大学的Barber等人[80-81]提出了一种基于H13C14N气室吸收线的分辨率增强和色散误差校正的方法。对H13C14N气室吸收的离散激光频率和交叉时间进行最小二乘拟合,得到ECLD扫描速率曲线和频率啁啾曲线,通过相邻点替换和样条插值消除色散失配引起的采样误差。在100 m测量范围内,测量不确定度为1×10−7。
2015年,哈尔滨工业大学的许新科等人[82-83]设计了一种啁啾斜率校准和相位补偿相结合的方法,将测量的信号被分成M个部分,并进行Chirp Z变换,获得频率分布的斜率Dsi。选择合适的M值,平衡线性调频Chirp Z变换的频率分辨率和拟合点。在2.53 m范围内进行测量,FWHM为64.5 µm,标准差为4.5 µm。
2018年,天津大学的潘浩等人[84]利用H13C14N分子频率参考线的光谱学进行测量,结合相邻点替换和样条插值技术,消除采样误差。与相关的HCN气室校准工作[80-81]有所不同,此处线性调频曲线用于计算与线性扫描曲线的偏差,残差反馈到频率控制器中以校准激光扫频。在8 m范围内,绝对距离测量精度为45 µm。
2019年,杭州电子科技大学的时光等人[85]用抽真空的P-F干涉仪作为辅助路,有效避免了基于M-Z干涉仪光纤回路带来的色散失配问题。将扫频信号在F-P腔中产生的周期性最大值作为采样信号,对测量路干涉信号进行重采样。测量6.7 m处的目标,标准差为34 µm。
色散失配补偿技术指标如表4所示。
Research progress of absolute distance measurement methods based on tunable laser frequency sweeping interference
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摘要: 绝对距离测量的精度对于航空航天科技、精密装备加工、卫星编队、行星空间定位等领域具有重要意义。近年来,基于可调谐激光器的扫频干涉(FSI)测距技术以其突破2π模糊度、无测量死区、不接触且不依赖导轨等优点成为国际研究热点。文中在阐述FSI测距原理的基础上,简要分析了测距系统中部分器件的类型与性能,如可调谐激光器、探测器等,以及影响测距系统不确定度的因素,包括非线性扫频、多普勒频移、色散失配等方面,着重介绍了国内外对影响不确定度因素的相应补偿方法,并对补偿后的测量结果进行对比与总结。Abstract: The accuracy of absolute distance measurement is of great significance to the fields of aerospace technology, precision equipment processing, satellite formation, and planetary space positioning. The frequency sweeping interferometry (FSI) ranging technology based on tunable lasers has become an international research hotspot in recent year. It has the advantages of breaking 2π ambiguity, no dead zone of measurement, non-touch and independent of guide rail. The principle of FSI ranging, types and performance of some devices in the ranging system were briefly introduced, such as tunable lasers, detectors, etc. The factors that affect the uncertainty of the ranging system, including non-linear frequency sweep, Doppler frequency shift, dispersion mismatch, etc. were analyzed. Corresponding compensation methods for influencing uncertainty factors were discussed, and measurement results after compensation were compared and summarized.
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Key words:
- FSI /
- non-linear frequency sweep /
- Doppler frequency shift /
- dispersion mismatch /
- uncertainty
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表 1 主动稳频式FSI系统测距精度比较
Table 1. Comparison of ranging accuracy of active frequency stabilized FSI system
表 2 被动补偿式FSI系统测距精度比较
Table 2. Comparison of ranging accuracy of passive compensation FSI system
表 3 补偿振动漂移的FSI系统测距精度比较
Table 3. Comparison of FSI system ranging accuracy for compensating vibration drift
Author Distance/m Standard deviation/µm Relative error FWHM Ref. Yang 0.7 - - 50 nm [52] Martinez 0.4 21 - - [63] Tao 0.66 0.48 - - [61-62] Zhang 3 11 - - [75] Prellinger 4 11 6.0×10−7 - [64-65] Kakuma 11 4 3.6×10−4 - [59] Swinkels 15 - 1.3×10−4 - [53] Le Floch 15 - - 50 µm [55-56] Lu 16 3.15 - 65.5 µm [66] Dale 20 - 0.4×10−6 40 nm [60] Pollinger 20 - 5.1×10−7 12 µm [57] -
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