An improved phase generated carrier demodulation algorithm of fiber optic fabry-perot sensor
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摘要:
为解决相位生成载波-反正切解调算法(PGC-Atan)的非线性失真问题，搭建了基于改进型PGC-Atan算法的非本征型法珀传感器(EFPI)解调系统。首先，理论分析了载波相位调制深度(C)偏离最优值、伴生调幅、载波相位延迟等非线性因素对经典PGC-Atan算法中参与反正切运算的正弦与余弦两路信号的影响。然后，针对外调制或伴生调幅较小的情况，提出了一种基于系数补偿的改进型PGC-Atan算法(PGC-CC-Atan)。该算法通过构造与C值和载波相位延迟有关的系数，消除反正切运算中的非线性参数。针对内调制情况，提出了一种基于椭圆拟合的改进型PGC-Atan算法(PGC-EF-Atan)。该算法通过基于分块矩阵的最小二乘法拟合椭圆并提取3个椭圆参数，进而将受非线性因素影响的正弦与余弦两路信号校正为正交信号。最后，通过仿真验证了改进型算法的正确性，并采用高调制特性的垂直腔面发射激光器(VCSEL)和常规腔长的EFPI等搭建PGC解调系统，对比经典PGC-Atan算法与两种改进型算法的解调性能，证实了改进型算法非线性失真抑制的有效性。实验结果表明：一定C值范围内，两种改进型算法可在非线性因素影响下有效解调。PGC-EF-Atan算法相较于PGC-CC-Atan算法，解调信纳比提升了11.602 dB，总谐波失真降低了10.951%。两种改进型算法中，PGC-EF-Atan算法对非线性失真的抑制效果更好，且解调线性度良好，准确度高。
Abstract:To address the issue of non-linear distortion in the Phase Generated Carrier-Antitangent demodulation (PGC-Atan) algorithm, we have developed an extrinsic Fabry-Perot Interferometer (EFPI) sensor demodulation system based on an improved PGC-Atan algorithm. The theoretical analysis focuses on the affect of nonlinear factors on sine and cosine signals used in arctangent operation of the PGC-Atan algorithm. Such factors include deviations from optimal values of the phase modulation depth (C), companion amplitude modulation, and carrier phase delay. As a solution, we propose an improved PGC-Atan algorithm based on a correction coefficient (PGC-CC-Atan) suitable for external modulation or the case of low companion amplitude modulation scenarios. The PGC-CC-Atan algorithm generates a coefficient relating to C and carrier phase delay while excluding nonlinear parameters in the arctangent operation. Furthermore, an improved PGC-Atan algorithm that utilizes an elliptic fitting algorithm (PGC-EF-Atan) is proposed for internal modulation. The ellipse fitting technique is employed to fit the eclipse using the least squares method based on a matrix block decomposition. The pair of signals that are influenced by nonlinear factors are corrected and transformed into orthogonal signals utilizing three parameters of the ellipse. Finally, the correctness of the two improved algorithms is verified through simulations and experiments. The PGC demodulation system comprises a high d
v /di VCSEL laser and a conventional cavity length F-P sensor. By comparing the demodulation performance of the PGC-Atan algorithm with that of the two improved algorithms, their effectiveness in suppressing nonlinear distortion is verified. Experimental results indicate that the two improved algorithms exhibit effective demodulation in the presence of nonlinear factors within a specific range of C values. The signal-to-noise and distortion ratio (SINAD) of demodulation result obtained from PGC-EF-Atan algorithm surpasses that of the PGC-CC-Atan algorithm by 11.602 dB, while the Total Harmonic Distortion (THD) is reduced by 10.951%. Between the two improved algorithms, the PGC-EF-Atan algorithm possesses superior demodulation linearity, accuracy, and nonlinear distortion suppression performance. -
图 4 C值从0.1 rad变化到6.1 rad时3种算法的仿真结果与J1(C)/J2(C)的变化趋势
Figure 4. Simulation results of the three algorithms and the variation trend of J1(C)/J2(C) when C deviates from 0.1 rad to 6.1 rad
图 5 两种非线性因素影响下3种算法的仿真结果
Figure 5. Simulation results of the three algorithms under the influence of the two nonlinear factors
图 6 3种非线性因素影响下PGC-CC-Atan算法仿真结果
Figure 6. Simulation results of PGC-CC-Atan algorithm under the influence of the three nonlinear factors
图 7 3种非线性因素影响下PGC-EF-Atan算法仿真结果
Figure 7. Simulation results of PGC-EF-Atan algorithm under the influence of the three nonlinear factors
图 9 不同C值下两种改进型算法解调结果与参考解调仪结果对比
Figure 9. Comparison between the demodulation results of the two algorithms under different C and the calibration results of the reference demodulator
图 10 原始信号（a）波形图与（b）频谱图
Figure 10. (a) The waveform and (b) spectrum of the original signal
图 12 PGC-CC-Atan算法解调结果。(a)波形图；(b)频谱图
Figure 12. Demodulation results using PGC-CC-Atan algorithm. (a) Waveform; (b) spectrum
图 11 经典PGC-Atan算法解调结果。(a)波形图；(b)频谱图
Figure 11. Demodulation results using PGC-Atan algorithm. (a) Waveform; (b) spectrum
图 13 PGC-EF-Atan算法解调结果。(a)波形图；(b)频谱图；(c)P(t)与Q(t)形成的李萨如图
Figure 13. Demodulation results of PGC-EF-Atan algorithm. (a) Waveform; (b) spectrum; (c) Lissajous figure of P(t) and Q(t)
图 14 PGC-EF-Atan算法解调结果与参考解调仪标定结果对比
Figure 14. Comparison between the demodulation results of PGC-EF-Atan algorithm and the calibration results of the reference demodulator
表 1 3种解调算法的性能对比
Table 1. Performance comparison of the three demodulation algorithms
解调方法 幅值/rad SINAD/dB THD PGC-Atan 1.494 13.063 21.276% PGC-CC-Atan 0.947 15.189 12.562% PGC-EF-Atan 0.910 26.791 1.611% 
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