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TGD-OFDR系统中,光电探测器(photodetector, PD)接收端接收到的信号可以表示为[8]:
$ \begin{array}{l} i\left( t \right) \propto \left\{ {{\mathop{\rm Re}\nolimits} \left[ {{E_{\rm{s}}}\left( t \right)E_{{\rm{LO}}}^*\left( t \right)} \right]} \right\} = \sum\limits_{i = 1}^N {{a_i}{r_i}{\rm{rect}}} \left( {\frac{{t - \tau i}}{{{\tau _{\rm p}}}}} \right) \times \\ \;\;\;\;\;\;\cos \left[ { - {\omega _{\rm c}}{\tau _i} + 2{\rm{ \mathit{ π} }}{f_{\rm{0}}}\left( {t - {\tau _i}} \right) + {\rm{ \mathit{ π} }}k{{\left( {t - {\tau _i}} \right)}^2}} \right] \end{array} $
(1) 式中, Es(t)表示散射光信号,ELO(t)表示本振信号,t是时间变量, 上标*表示复共轭, ai为衰减系数,ri为瑞利散射系数,N表示散射点个数,τi表示第i个散射点对应的时间, τp为脉冲宽度,ωc为光载频,f0为起始频率,k为啁啾率。由于散射点尺寸特别小(小于0.1λ),所以在脉冲宽度范围内的散射点数目很多, 故而(1)式可以转化为:
$ \begin{array}{*{20}{l}} {i\left( t \right) = \int_{\rm{0}}^{\tau {\rm{p}}} {a\left( \tau \right)r\left( \tau \right){\rm{rect}}\left( {\frac{{t - \tau }}{{{\tau _{\rm p}}}}} \right)} \exp \{ {\rm{j}}[2{\rm{ \mathsf{ π} }}{f_0}\left( {t - \tau } \right) + }\\ {\;\;\;\;\;\;\;\;{\rm{ \mathsf{ π} }}k{{\left( {t - \tau } \right)}^2} - {\omega _{\rm{c}}}\tau ]\} {\rm{d}}\tau = h\left( t \right) \otimes s\left( t \right)} \end{array} $
(2) 式中,τ表示散射点之间的时间差,a和r表示衰减系数和瑞利散射系数, h(t)表示光纤中脉冲响应函数:
$ h\left( t \right) = a\left( t \right)r\left( t \right)\exp \left[ {{\rm{j}}\left( { - {\omega _{\rm{c}}}t} \right)} \right] $
(3) s(t)为任意函数发生器(arbitrary function generator, AFG)产生的线性扫频信号:
$ s\left( t \right) = {\rm{rect}}\left( {\frac{t}{{{\tau _{\rm{p}}}}}} \right)\exp \left[ {{\rm{j}}\left( {2{\rm{ \mathit{ π} }}{f_{\rm{0}}}t + {\rm{ \mathit{ π} }}k{t^2}} \right)} \right] $
(4) 通过匹配滤波器之后信号转化为:
$ \begin{array}{l} y\left( t \right) = i\left( t \right) \otimes {s^*}\left( { - t} \right) = h\left( t \right) \otimes \\ \;\;{\rm{rect}}\left( {\frac{t}{{2{\tau _{\rm{p}}}}}} \right)\frac{{{\tau _{\rm{p}}}\sin \left[ {{\rm{ \mathit{ π} }}k\left( {{\tau _{\rm{p}}} - \left| t \right|} \right)t} \right]}}{{{\rm{ \mathit{ π} }}k{\tau _{\rm{p}}}t}} \end{array} $
(5) 此时,主瓣的3dB带宽表示空间分辨率大小[5],即:
$ R = \frac{c}{{2nk{\tau _{\rm{p}}}}} = \frac{c}{{2nB}} $
(6) 式中, c表示真空中的光速,n表示光纤折射率。从(6)式可知,在TGD-OFDR系统中,空间分辨率只与扫频范围B(探测脉冲的带宽)相关,且与扫频范围B成反比,而扫频范围取决于啁啾率和脉冲宽度,可以通过增大啁啾率或者脉宽的方法提高扫频范围,实现高空间分辨率。
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在TGD-OFDR系统中,为了量化光纤感知到的外界参量的变化,必须要解调光相位,目前TGD-OFDR系统几乎都采用相干探测[13-15]方式接收光信号,并将其转换为电信号。在相干探测方法中,探测到的电信号噪声主要来自光电转换过程,主要包含:热噪声σt和散粒噪声σs两个部分。其中热噪声σt2=(4kBT/Rl)σfΔf(kB为玻尔兹曼常数,T表示绝对温度,Rl表示负载电阻,σf表示前置放大器的噪声, Δf表激光器线宽),散粒噪声σs2=2q(I+Id)ΔB(q表示电子数目,ΔB表示带宽,Id表示暗电流,I表示电流,且Id≪I)。假设脉冲的峰值功率为Pp,则扫频脉冲信号的总能量可以表示为[5]:Ps=τpPp,信噪比(signal-to-noise ratio, SNR)可以表示为[13]:
$ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;{R_{{\rm{SNR}}}} = \frac{{{P_{\rm{s}}}}}{{\left( {\sigma _{\rm{s}}^2 + \sigma _{\rm{t}}^2} \right)}} \propto \\ \frac{{{\tau _{\rm{p}}}{P_{\rm{p}}}}}{{2q\left( {{R_1}{P_{{\rm{LO}}}} + {I_{\rm{d}}}} \right)\Delta B + \left( {4{k_{\rm{B}}}T/{R_{\rm{1}}}} \right){\sigma _{\rm{f}}}\Delta f}} \end{array} $
(7) 式中,PLO表示本振信号光功率。在相干探测中,系统的散粒噪声远大于热噪声,因此热噪声可以忽略。当本振信号保持不变的情况下,信噪比主要取决于信号带宽和脉冲宽度。而ΔB=kτp,所以(7)式可以表示为:
$ {R_{{\rm{SNR}}}} \propto \frac{{{P_{\rm{s}}}}}{{\left( {\sigma _{\rm{s}}^2 + \sigma _{\rm{t}}^2} \right)}} = \frac{{{P_{\rm{p}}}}}{{2q\left( {{R_1}{P_{{\rm{LO}}}} + {I_{\rm{d}}}} \right)k}} $
(8) 由(8)式可知,扫频脉冲信号峰值功率与本振信号不变的情况下,系统信噪比只与啁啾率相关,且与啁啾率成反比。
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系统相位噪声由系统信噪比和激光器相位噪声两个部分决定,相互之间的关系如图 1所示。在相干探测系统中,随着SNR的增加,系统相位噪声先减小后保持不变[16]。而激光器相位噪声对系统相位噪声的影响相对复杂一些,散射光信号通过相干探测之后,(5)式将转化为[7]:
$ \begin{array}{*{20}{l}} {{y_{\rm{n}}}\left( t \right) = i\left( t \right) \otimes {s^*}\left( { - t} \right) = h\left( t \right) \otimes {\rm{rect}}\left( {\frac{t}{{2{\tau _{\rm{p}}}}}} \right) \times }\\ {\frac{{{\tau _{\rm{p}}}\sin \left[ {{\rm{ \mathsf{ π} }}k {\left({\tau _{\rm{p}}} - \left| t \right|\right)t} } \right]}}{{{\rm{ \mathsf{ π} }}k{\tau _{\rm{p}}}t}}\exp \left\{ {{\rm{j}}\left[ {\Delta \varphi \left( {{\tau _{\rm{d}}}} \right)} \right]} \right\}} \end{array} $
(9) 式中, Δφ(τd)=φ(t)-φ(t-τd)。其中,τd表示延迟时间,φ表示对应的相位。根据激光器相位噪声的特性可知,激光器引起的相位噪声与激光器的线宽大小相关[17-18],通常采用标准差(standard deviation, SD)来衡量一段时间内相位噪声σφ2(t)的累积量,即:
$ \sigma _\varphi ^2\left( t \right) = 2{\rm{ \mathit{ π} }}\Delta ft $
(10) 由此可知,激光器相位噪声正比于激光器线宽,当激光器线宽一定时,相位噪声与t成正相关,如图 1c所示。其中, Δf1, Δf2表示不同的线宽。
通过理论分析可知,当输入脉冲信号峰值功率与本振信号功率不变时,系统信噪比仅与啁啾率k相关,且与啁啾率k成反比。系统相位噪声受系统信噪比和激光器相位噪声影响。相位噪声与系统信噪比成反比,但是当信噪比达到一定阈值之后,系统相位噪声不变;当激光器线宽不变时,相位噪声与延时成正比;当扫频范围B一定时,系统相位噪声由系统信噪比和激光器相位噪声共同决定。为了验证啁啾率、信号脉宽对系统信噪比和相位噪声的影响,下面利用MATLAB对TGD-OFDR系统进行仿真。
脉冲参量对时间门控光频域反射仪性能的影响
The influence of pulse parameters on the performance of time-gated digital optical frequency domain reflectometer
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摘要: 为了对时间门控光频域反射仪系统参量设置进行优化,采用光脉冲压缩原理搭建了时间门控光频域反射仪试验系统,进行了理论分析与实验验证,取得了仿真与实验数据。结果表明,当探测光脉冲信号的峰值功率和本振光信号功率不变时,系统信噪比只与啁啾率相关,且与其成反比;当扫频范围保持80MHz不变时,系统相位噪声随脉宽增加呈现先减小后增大的趋势,且最小值处于2.5μs附近;在实际应用中,满足系统最大扫频范围的条件下,通过调节扫频信号的脉宽,可以获得最优系统相位噪声(最小值)。这一结论对时间门控光频域反射仪系统参量设置与优化是有帮助的。Abstract: In order to optimize the parameter settings of the time-gated digital optical frequency domain reflectometer (TGD-OFDR) system, an experimental system was built based on the optical pulse compression reflectometry. Theoretical analysis and experimental verification were carried out, and simulation and experimental data were obtained. Both of the results show that the system signal-to-noise ratio (SNR) is only related to the chirp rate. When the pulse power of the probe light and the signal power of the local oscillator light have been set, the chirp rate increases with the SNR decreasing. And the phase noise decreases firstly and then increases with the increase of the pulse width with the minimum value of about 2.5μs when the sweep range keeps 80MHz. Hence, the optimal phase noise (minimum value) can be obtained by adjusting the pulse width with the maximum sweep frequency range of the system remains unchanged. The results have certain reference significance to the parameter optimization of the TGD-OFDR system design.
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[1] TAYLOR H F, LEE C E. Apparatus and method for fiber optic intrusion sensing: US5194847[P].1993-03-21. [2] SHIMIZU K, HORIGUCHI T, KOYAMADA Y, et al. Characteristics and reduction of coherent fading noise in rayleigh backscattering mea-surement for optical fibers and components[J]. Journal of Lightwave Technology, 1992, 10(7): 982-987. doi: 10.1109/50.144923 [3] WANG M Y, SHENG L, TAO Y, et al. Effect of laser linewidth on characteristics of φ-OTDR system[J]. Laser Technology, 2016, 40(4): 615-618(in Chinese). [4] FROGGATT M, MOORE J. High-spatial-resolution distributed strain measurement in optical fiber with rayleigh scatter[J]. Applied Optics, 1998, 37(10): 1735-1740. doi: 10.1364/AO.37.001735 [5] ZOU W W, YANG S, LONG X, et al. Optical pulse compression re-flectometry: Proposal and proof-of-concept experiment[J]. Optics Express, 2015, 23(1): 25988-25995. [6] LIU Q W, FAN X, HE Z Y, et al. Time-gated digital optical frequency domain reflectometry with 1.6m spatial resolution over entire 110km range[J]. Optics Express, 2015, 23(20): 25988-25995. doi: 10.1364/OE.23.025988 [7] WANG S, FAN X Y, LIU Q W, et al. Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR[J]. Optics Express, 2015, 23(26): 33301-33309. doi: 10.1364/OE.23.033301 [8] CHEN D, LIU Q W, HE Z Y, et al. Phase-detection distributed fiber-optic vibration sensor without fading-noise based on time-gated digital OFDR[J]. Optics Express, 2017, 25(7): 8315-8325. doi: 10.1364/OE.25.008315 [9] CHEN D, LIU Q W, HE Z Y, et al. High-fidelity distributed fiber-optic acoustic sensor with fading noise suppressed and sub-meter spatial resolution [J]. Optics Express, 2018, 23(16): 16138-16146. [10] JUAN P G, LUIS R C. SNR enhancement in high-resolution phase-sensitive OTDR systems using chirped pulse amplification concepts[J]. Optics Letters, 2017, 42(9): 1728-1731. doi: 10.1364/OL.42.001728 [11] MARÍA R, FERNÁNDEZ R, JUAN P G, et al. Laser phase-noise cancellation in chirped-pulse distributed acoustic sensors[J]. Journal of Lightwave Technology, 2018, 36(4): 979-985. doi: 10.1109/JLT.2017.2766688 [12] CHEN D, LIU Q W, HE Z Y. 108km distributed acoustic sensor with 220p epsilon/root Hz strain resolution and 5m spatial resolution[J]. Journal of Lightwave Technology, 2019, 37(18): 4462-4468. doi: 10.1109/JLT.2019.2901276 [13] LU Y, ZHU T, BAO X Y, et al. Distributed vibration sensor based on coherent detection of phase-OTDR[J]. Journal of Lightwave Technology, 2010, 28(2): 3243-3249. [14] WANG Z, ZHANG L, RAO Y J, et al. Coherent Φ-OTDR based on I/Q demodulation and homodyne detection[J]. Optics Express, 2016, 24(2): 853-858. doi: 10.1364/OE.24.000853 [15] LI T J. Research on TGD-OFDR technology based on internally mo-dulated DFB laser[D]. Shanghai: Shanghai Jiaotong University, 2017: 1-66(in Chinese). [16] ALEKSEEV A E, TEZADOV Y A, POTAPOV V T, et al. Intensity noise limit in a phase-sensitive optical time-domain reflectometer with a semiconductor laser source[J]. Laser Physics, 2017, 27(5): 055101. doi: 10.1088/1555-6611/aa6378 [17] TKACH R, CHRAPLYVY A R. Phase noise and linewidth in an InGaAsP DFB laser [J]. Journal of Lightwave Technology, 1986, 4(11): 1711-1716. doi: 10.1109/JLT.1986.1074677 [18] PAN Z, LIANG K, YE Q, et al. Phase-sensitive OTDR system based on digital coherent detection[J]. Proceedings of the SPIE, 2011, 8311: 83110S. doi: 10.1117/12.905657