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摘要:
相位生成载波(PGC)解调技术具有高灵敏度、线性度好和动态范围广的优点，因此广泛应用于分布式光纤传感器中。本文提出了一种单路微分相除和微分自相乘的PGC(PGC-SDD-DSM)解调算法，该解调算法对载波相位调制深度和光强度干扰均不敏感。仿真实验显示，与PGC单路微分相除(PGC-SDD)解调算法、传统的PGC微分交叉相乘(PGC-DCM)和PGC反正切(PGC-Arctan)解调算法相比较，改进的PGC解调算法具有最佳的解调效果。将改进的PGC解调算法应用在光纤干涉传感器中，实验结果表明改进的解调算法能有效抑制光强和载波调制深度引起的失真。待测信号的频率为1 kHz，幅度值为2 rad，在引入1.5 rad的载波调制深度和 0.7 rad的光强干扰深度时，实验系统中使用改进PGC解调算法的解调结果信纳比(SINAD)可以达到35.56 dB，与使用传统的PGC-DCM、PGC-Arctan和PGC-SDD解调算法相比较分别高出10.87 dB、24.19 dB和6.38 dB，同时系统的稳定性得到了提升。该技术有效地促进了光纤传感器领域的技术研究。
Abstract:The phase generated carrier (PGC) demodulation technique is widely used in distributed fiber-optic interferometric sensors, for its high sensitivity, good linearity, and large dynamic range. An improved PGC demodulation algorithm with single-path differential divide and the differential-self-multiplication (PGC-SDD-DSM) demodulation algorithm is proposed in this paper, the demodulation result of the PGC-SDD-DSM algorithm is not related to the carrier phase modulation depth (C) and light intensity disturbance (LID). The simulation and experiment results show that the proposed algorithm is insensitive to the C value, and compared with the single-path differential divide to PGC demodulation algorithm (PGC-SDD), the traditional differential-cross-multiplying (PGC-DCM) and PGC Arctangent (PGC-Arctan) demodulation algorithms, and the proposed algorithm has the best demodulation effect. When the proposed demodulation algorithm is applied in the optical fiber interferometric, it is found that the proposed algorithm can suppress the distortion caused by LID and C. The frequency of the signal to be demodulated is 1000 Hz, and the amplitude value is 2 rad. When the carrier modulation depth of 1.5 rad and the light intensity interference depth of 0.7 rad are introduced, the signal-to-noise and distortion ratio (SINAD) of the demodulation result using the improved PGC demodulation algorithm in the experimental system is 35.56 dB, which is 10.87 dB, 24.19 dB, and 6.38 dB higher than using traditional PGC-DCM, PGC-Arctan, and PGC-SDD demodulation algorithms, respectively. It is proved the system's stability improved effectively. This technology effectively promotes technical research in the fields of optical fiber sensors.
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Overview: Phase generated carrier demodulation is widely used in distributed fiber-optic interferometric sensors. Traditional PGC demodulation methods include the PGC-DCM (differential-cross-multiplying), the PGC-Arctan (PGC Arctangent) demodulation methods, and the PGC-SDD (single-path differential divide) demodulation scheme proposed by previous researchers. While the demodulation results of those demodulation algorithms are influenced by light intensity disturbance or phase modulation depth, which affects the stability of the demodulation system. Here, high stability and low harmonic distortion PGC demodulation technique with single-path differential divide and differential-self-multiplication (PGC-SDD-DSM) is proposed, and the demodulation result of which is not affected by light intensity and C value shift of the phase modulation depth. The simulation results show that when the C value is 1.5 rad, 2.0 rad, 2.5 rad, 3.0 rad, and 3.5 rad, the amplitude of PGC-DCM, PGC-Arctan, and PGC-SDD demodulation algorithm changes obviously, while the result of PGC-SDD-DSM demodulation algorithm hardly changes. The improved PGC demodulation algorithm is applied to the experiment system, the system composed of two Mach-Zehnder fiber-optic interference sensors verifies the performance of the proposed PGC demodulation algorithm. The first Mach-Zehnder sensor is used to generate light intensity interference, and the second one is used to generate PGC modulation signals and test signals. When the modulation depth C value is 1.5 rad, the time domain and frequency domain demodulation result show the improved PGC demodulation algorithm can suppress the interference of light intensity, and its demodulation result is better than the other three algorithms. The signal to noise and disturbance ratio (SINAD) of the demodulation signal using the proposed PGC algorithm is 35.56 dB, which is 10.87 dB, 24.19 dB, and 6.38 dB, higher than those of the PGC-DCM, PGC-Arctan, and PGC-SDD algorithms, respectively. For the improved PGC demodulation algorithm, when the phase modulation depth C changes from 1.5 rad to 3.5 rad, the total harmonic distortion (THD) varies from 0.02% to 0.05%, and the SINAD varies from 35 dB to 37 dB. Compared with the other three demodulation algorithms, the SINAD and THD of demodulation signal using the improved PGC demodulation algorithm are better than others and hardly change with the change of C value, which indicates that the PGC-SDD-DSM demodulation algorithm has higher stability and lower harmonic distortion. At the same time, the improved PGC demodulation algorithm can also demodulate aperiodic signals with better frequency response and amplitude response. It is believed that the proposed PGC demodulation algorithm can be further developed in the field of optical fiber sensors.
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图 2 C=1.5 rad、2.0 rad、2.5 rad、3.0 rad和3.5 rad时不同PGC算法解调结果。
Figure 2. Demodulation signals of different PGC demodulation algorithms with C=1.5 rad, 2.0 rad, 2.5 rad, 3.0 rad and 3.5 rad.
图 5 当C=1.5 rad时不同PGC算法的解调时域结果。
Figure 5. Demodulation time domain results of different PGC algorithms when C=1.5 rad.
图 6 当C=1.5 rad时不同PGC算法的解调频域结果。
Figure 6. Frequency spectrums of the demodulation results of different PGC algorithms when C=1.5 rad.
图 7 对不同的调制深度C值对应的THD
Figure 7. THD of the proposed PGC algorithm with modulation depth C
图 8 对不同的调制深度C值对应的SINAD
Figure 8. SINAD of the proposed PGC algorithm with modulation depth C
图 9 解调波形(红色)和原始波形(蓝色)
Figure 9. Demodulated signal waveform (red) and original signal (blue)
图 10 解调波形(绿色)和原始波形(蓝色)
Figure 10. Demodulated signal waveform (green) and original signal (blue)
图 11 基于PGC-SDD-DSM算法解调系统的动态范围
Figure 11. Dynamic range of the demodulation system based on the PGC-SDD-DSM algorithm
表 1 四种算法的性能比较
Table 1. Comparisons of four PGC demodulation algorithms
Parameters Demodulation formula Modulation depth(C) Light intensity
disturbance(LID)Total harmonic
distortion(THD)PGC-DCM ${S_{{\rm{PGC}} - {\rm{DCM}}}}\left( t \right) = {B^2}GH{{\rm{J}}_1}\left( C \right){{\rm{J}}_2}\left( C \right)\varphi \left( t \right)$ Sensitive Sensitive Low THD PGC-Arctan $ {S_{{\rm{PGC}} - {{\rm{Arctan}}} }}\left( t \right) = {{\rm{arctan}}} \left\{ {\left[ {\dfrac{{G{{\rm{J}}_1}\left( C \right)}}{{H{{\rm{J}}_2}\left( C \right)}}} \right]\tan \varphi \left( t \right)} \right\} $ Sensitive Non-sensitive High THD PGC-SDD ${S_{ {\rm{PGC} } - {\rm{SDD} } } }\left( t \right) = [{{\rm{J}}_1}\left( C \right)/{{\rm{J}}_2}\left( C \right)] \cdot \varphi \left( t \right)$ Sensitive Non-sensitive Low THD PGC-SDD-DSM ${S_{{\rm{PGC}} -{\rm{ SDD}} -{\rm{ DSM}}}} = \varphi \left( t \right)$ Non-sensitive Non-sensitive Low THD 
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表 2 四种算法的解调结果性能对比
Table 2. Performance comparison of demodulation results of four algorithms
PGC-DCM PGC-Arctan PGC-SDD PGC-SDD-DSM SINAD/dB 24.69 11.37 29.18 35.56 THD/ (%) 0.060 0.690 0.057 0.047
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