-
现有的ϕ-OTDR系统,使用声光调制器对光波进行调频,使探测光波的频率
${f_{{c}}}$ 变换为$f = {f_{{c}}} + {f_{{\text{AOM}}}}$ 的光波,同时利用脉冲斩波信号将连续光变为脉冲光。对于大多数声光调制器,频率调制信号的时钟来自驱动器内部,脉冲斩波信号由采集卡TTL触发输入,两种信号的时钟存在非同源问题。而在现有的理论推导过程中,并未考虑声光调制器频率调制信号时钟和脉冲斩波信号时钟的非同源问题。声光调制器内部的频率调制时钟信号
$ {x_m}(t) $ 可以表示为:$$ {x_m}(t) = {A_m}\cos (2\pi {f_{{\text{AOM}}}}t + {\varphi _0}) $$ (1) 式中:
$ {A_m} $ 为频率调制时钟信号的幅值;$ {f_{{\text{AOM}}}} $ 为其调制频率;$ {\varphi _0} $ 为其初始相位;$ t $ 表示时间;$ {x_m}(t) $ 的波形示意如图1所示。图 1 声光调制器驱动器内部的频率调制时钟信号波形示意图
Figure 1. Schematic diagram of frequency modulated clock signal waveform inside acousto-optic modulator driver
输入声光调制器的脉冲斩波信号
$ {x_p}(t) $ 可以表示为:$$ {x_p}(t) = rect\left( {\frac{t}{T}} \right) = \left\{ {\begin{array}{*{20}{c}} {{A_p},kT \leqslant t \leqslant kT + {T_1}} \\ {0,kT + {T_1} \lt t \lt (k + 1)T} \end{array}} \right. $$ (2) 式中:
$ rect( \cdot ) $ 为矩形函数;$ {A_p} $ 为脉冲斩波信号的高电平幅值;$ T $ 为脉冲斩波信号的周期,相应的脉冲斩波信号重复频率为$ {f_{{\text{PULSE}}}} = {1 \mathord{\left/ {\vphantom {1 T}} \right. } T} $ ;$ {T_1} $ 为脉冲斩波信号高电平的持续时间;$ k = 0,1,2,3 \ldots $ 等整数;$ {x_p}(t) $ 的波形示意图如图2所示。图 2 输入声光调制器驱动器的脉冲斩波信号波形示意图
Figure 2. Schematic diagram of pulse chopper signal waveform input to acousto-optic modulator driver
$ {f_{{\text{AOM}}}} $ 为几十MHz量级,常用的规格包括40、80、200 MHz等;$ {f_{{\text{PULSE}}}} $ 取值范围一般为几kHz到几十kHz,检测长度为10 km的传感光纤时,$ {f_{{\text{PULSE}}}} $ 可设定为10 kHz。为了保证脉冲斩波信号和频率调制时钟信号的相位同步,$ {f_{{\text{PULSE}}}} $ 需要为$ {f_{{\text{AOM}}}} $ 的整数倍分频,即$ {f_{{\text{PULSE}}}} = {{{f_{{\text{AOM}}}}} \mathord{\left/ {\vphantom {{{f_{{\text{AOM}}}}} N}} \right. } N} $ ,$ N $ 为正整数。理想情况下,声光调制器驱动器输出的脉冲调制信号波形如图3所示,即每个脉冲周期内的调制波形起始相位、波形和频率相同。图 3 声光调制器驱动器输出的脉冲调制信号波形示意图
Figure 3. Schematic diagram of pulse modulated signal waveform output by acoustooptic modulator driver
但是,现有系统中脉冲斩波信号源与频率调制信号时钟源来自不同时钟,即使
$ {f_{{\text{PULSE}}}} $ 完全等于${f_{{\text{PULSE}}}} = {{{f_{{\text{AOM}}}}} \mathord{\left/ {\vphantom {{{f_{{\text{AOM}}}}} N}} \right. } N}$ ,同样会导致声光调制器输出的频率调制脉冲光信号在每个脉冲周期中的脉冲光初始相位存在随机抖动,存在相位异步现象,如图4所示,斩波信号脉冲宽度90 ns,${f_{{\text{PULSE}}}} = 10 \;{\rm{kHz}}$ ,$ {f_{{\text{AOM}}}} = 80 \;{\rm{MHz}} $ ,即$N = 8\;000$ ,以脉冲斩波信号为参考,由示波器以10 s为间隔采集的经等比例衰减的声光调制器驱动器输出的脉冲调制信号。图 4 传统的声光调制驱动器输出的脉冲调制信号曲线图
Figure 4. Pulse-modulated signal curves output from a conventional acousto-optic modulated driver
图4中,各曲线分别代表不同脉冲周期中,脉冲调制信号频率完全一样,均是
$ {f_{{\text{AOM}}}} $ ,但是由于输入的脉冲斩波信号与声光调制器驱动内部频率调制信号不是同一时钟,使得输出的脉冲调制信号在不同脉冲周期的起始相位不同,且具有随机性,导致波形在时域上存在沿时间轴的轻微抖动。由参考文献[12]可知,两个时钟非同源信号的角频率的误差模型可以表示为:
$$ \Delta {\omega _{asyn}}(t) = \Delta {\omega _n} + \Delta {k_n}t $$ (3) 式中:
$ \Delta {\omega _n} $ 表示两个时钟角频率准确值的差值;$ \Delta {k_n} $ 表示两个时钟稳定度的差值。当存在时钟非同源问题时,ϕ-OTDR系统所检测的后向瑞利散射光[13]应重新表示为:
$$\begin{split} {E_R}\left( t \right) =& \sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \frac{{c{\tau _i}}}{{{n_f}}}} \right)} rect\left( {\frac{{t - {\tau _i}}}{w}} \right)\\ &\cos \left( {({\omega _c} + {\omega _{\rm{{AOM}}}} +\Delta {\omega _{asyn}}(t))\left( {t - {\tau _i}} \right)} \right) \end{split} $$ (4) 式中:
${\omega _c} = 2\pi {f_{{c}}}$ ,${\omega _{\rm{{AOM}}}} = 2\pi {f_{\rm{{AOM}}}}$ ,其他参数定义可参照参考文献[13],当光纤存在扰动时,引入相位变化量$ \varphi (t) $ 时,平衡探测器的输出功率为:$$ {P_{BAPD}} \propto 2{E_S}(t){E_L}(t)\cos ({\omega _{{\text{AOM}}}}t{\text{ + }}\Delta {\omega _{{n}}}t + \Delta {k_n}t + \varphi (t)) $$ (5) 经模数转换,数据采集卡采集到的数字信号为:
$$\begin{split} &S(n) \propto 2{E_S}(n){E_L}(n)\cos ({\omega _{\rm{{AOM}}}}n + \Delta {\omega _n}n + \Delta {k_n}n + \varphi (n)),\\ &n = 1,2,3, \cdots ,N \end{split} $$ (6) 公式(6)中,如果频率调制信号时钟和脉冲斩波信号时钟不同源,仅存在准确值的差值
$ \Delta {\omega _n}n $ ,该差值仅引起后向瑞利相干散射光的相位固定偏移量$ \Delta {\omega _n} $ ,不会对扰动信号的测量结果产生影响。$ \Delta {k_n}n $ 为两个时钟不同源,稳定度差异引起的相位变化量,时钟稳定度$ \Delta {k_n} $ 并非恒定不变的常数,是一个统计数值,相比于$ \Delta {\omega _n}n $ 是一个缓变信号,因此,导致的后向瑞利相干散射信号的变化也是缓慢的、低频的。当测量高频扰动时,可以通过高通滤波器滤除其带来的低频噪声,从而实现对高频扰动的定量检测;但当测量低频扰动时,由于扰动事件也位于低频区间,无法通过滤波器去除其带来的低频噪声,从而导致低频扰动事件无法被区分,对扰动信号引起的相位变化$ \varphi (n) $ 造成干扰,影响扰动信号的相位解调结果准确性和ϕ-OTDR系统低频响应性能。
Optimization of low frequency response performance of phase sensitive optical time-domain reflectometry system
-
摘要: 相位敏感光时域反射系统以其分布式光纤传感技术的优势在分布式水听、压裂微地震检测、自然灾害预警等低频监测领域具有极高的应用前景。文中对系统中脉冲斩波信号与频率调制信号时钟不同源的问题予以验证,并对其产生的影响进行理论分析;设计双路同步时钟源驱动产生脉冲斩波信号和频率调制信号,降低每个脉冲重复周期中频率调制信号的随机低频相位噪声,提高探测脉冲光的相位稳定性;采用时钟同源和时钟非同源两种方式对典型的基于外差相干检测的相位敏感光时域反射系统的声光调制器进行驱动,由信号发生器驱动缠有光纤的压电陶瓷,产生不同频段的扰动信号。实验结果表明:在同一测试条件下,前者在低频段的信噪比、相位解调质量、频率响应方面均优于后者,最小响应频率为0.1 Hz,相对提高两个数量级,降低了系统中低频噪声干扰。该方法易于实现,可与现有的低频性能优化方法或结构兼容,进一步提高系统低频响应性能。Abstract: Phase sensitive optical time-domain reflectometry system due to its advantages of distributed optical fiber sensing technology has a high application prospect in low frequency monitoring fields such as distributed hydrophone, fracture micro-seismic detection and natural disaster warning. The problem of different clock source of pulse chopper signal and frequency modulated signal in the system was verified and the influence was analyzed theoretically in this paper. A dual-channel synchronous clock source was designed to generate pulse chopper signal and frequency modulation signal to reduce the random low-frequency phase noise of frequency modulation signal in each pulse repetition period and improve the phase stability of the detection pulse light. The acousti-optic modulator of typical phase-sensitive optical time-domain reflectometry system based on heterodyne coherent detection was driven by clock homology and clock non-homology, a signal generator drives a piezoelectric ceramic wrapped in optical fibers to generate disturbance signals in different frequency bands. The experimental results show that under the same test conditions, the former is superior to the latter in the aspects of SNR, phase demodulation quality and frequency response in low frequency band. The minimum response frequency is 0.1 Hz, which is 2 orders of magnitude higher than the latter, and reduces the interference of low frequency noise in the system. The method was easy to implement and compatible with the existing low frequency performance optimization methods or structures to further improve the low frequency response performance of the system.
-
图 7 0.1 Hz扰动信号。(a)时钟同源系统的位置-时间-强度响应图;(b)时钟非同源系统的位置-时间-强度响应图;(c)两者的相位解调曲线;(d)两者的频谱图
Figure 7. 0.1 Hz disturbance signal. (a) Position-time-intensity response diagram of clock homologous system; (b) Position-time-intensity response diagram of clock non-homologous system; (c) Phase demodulation curve of both; (d) Spectrum diagram of both
8 10 Hz扰动信号。(a)时钟同源系统的位置-时间-强度响应图;(b)时钟非同源系统的位置-时间-强度响应图;(c)两者的相位解调曲线;(d)两者的频谱图
8. 10 Hz disturbance signal. (a) Position-time-intensity response diagram of clock homologous system; (b) Position-time-intensity response diagram of clock non-homologous system; (c) Phase demodulation curve of both; (d) Spectrum diagram of both
图 9 500 Hz扰动信号。(a)时钟同源系统的位置-时间-强度响应图;(b)时钟非同源系统的位置-时间-强度响应图;(c)两者的相位解调曲线;(d)两者的频谱图
Figure 9. 500 Hz disturbance signal. (a) Position-time-intensity response diagram of clock homologous system; (b) Position-time-intensity response diagram of clock non-homologous system; (c) Phase demodulation curve of both; (d) Spectrum diagram of both
图 10 1 kHz扰动信号。(a)时钟同源系统的位置-时间-强度响应图;(b)时钟非同源系统的位置-时间-强度响应图;(c)两者的相位解调曲线;(d)两者的频谱图
Figure 10. 1 kHz disturbance signal. (a) Position-time-intensity response diagram of clock homologous system; (b) Position-time-intensity response diagram of clock non-homologous system; (c) Phase demodulation curve of both; (d) Spectrum diagram of both
-
[1] Lu Y, Zhu T, Chen L, et al. Distributed vibration sensor based on coherent detection of Phase-OTDR [J]. Journal of Lightwave Technology, 2010, 28(22): 3243-3249. [2] Ye Qing, Pan Zhengqing, Wang Zhaoayong, et al. Progress of research and applications of phase-sensitive optical time domain reflectometry [J]. Chinese Journal of Lasers, 2017, 44(6): 060001. (in Chinese) [3] Cai Haiwen, Ye Qing, Wang Zhaoyong, et al. Distributed optical fiber acoustic sensing technology based on coherent rayleigh scattering [J]. Laser & Optoelectronics Progress, 2020, 57(5): 050001. (in Chinese) [4] Zhang Xuping, Ding Zhewen, Hong Rui, et al. Phase sensitive optical time-domain reflective distributed optical fiber sensing technology [J]. Acta Optica Sinica, 2021, 41(1): 0106004. (in Chinese) [5] Meng Zhou, Chen Wei, Wang Jianfei, et al. Research progress of fiber optic hydrophone technology [J]. Laser & Optoelectronics Progress, 2021, 58(13): 1306009. (in Chinese) [6] Dong Xiaowei, Xie Bin, Pan Yong, et al. Development and application of distributed optical fiber acoustic vibration sensor system [J]. Journal of Applied Optics, 2020, 41(6): 1298-1304. doi: 10.5768/JAO202041.0608002 [7] Wang Shun. Research and application of fiber-optic low-frequency acoustic sensing technology[D]. Wuhan: Huazhong University of Science & Technology, 2016. (in Chinese) [8] Fu Siyi. Research on the fading-suppression broadband φ-OTDR[D]. Nanjing: Nanjing University, 2019. (in Chinese) [9] Liu Huawei. Research on influence and suppression algorithm of polarization dependence in distributed optical fiber vibration sensing system[D]. Nanjing: Southeast University, 2020. (in Chinese) [10] Qin Z, Liang C, Bao X. Wavelet denoising method for improving detection performance of distributed vibration sensor [J]. IEEE Photonics Technology Letters, 2012, 24(7): 542-544. doi: 10.1109/LPT.2011.2182643 [11] Zhang X, Sun Z, Shan Y, et al. A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement [J]. Photonics Journal IEEE, 2017, 9(3): 1-12. [12] Zeng Tao, Yin Pilei, Yang Xiaopeng, et al. Time and phase synchronization for distributed aperture coherent radar [J]. Journal of Radars, 2013(1): 105-110. [13] Yu Miao, Sun Mingyang, Zhang Yaolu, et al. Phase ambiguity and unwrapping of phase-sensitive optical time-domain reflectometer [J]. Infrared and Laser Engineering, 2021, 50(5): 20200437. (in Chinese) doi: 10.3788/IRLA20200437