This paper proposes a phase generated carrier (PGC) demodulation scheme for sinusoidal phase modulation interferometer (SPMI) that does not require a second harmonic carrier signal. In this scheme, an in-phase interference signal component with direct current (DC) bias is obtained by low-pass filtering the original interference signal, and a quadrature interference signal component is obtained by conventional means. The Lissajous figure formed by these two quadrature interference signal components is an ellipse whose center deviates from the origin of the I-Q coordinates. By fitting this ellipse, the major and minor axes and the center coordinates can be obtained. These elliptic parameters are then used to eliminate DC bias and normalize the amplitude of the quadrature signal components. Finally, the phase demodulation of the interference signal can be realized by using arctangent algorithm or differential cross multiplication (DCM) algorithm. The results of simulation and experiment have verified the validity and accuracy of the proposed PGC demodulation scheme, and show that it is insensitive to the phase modulation depth C. Compared with conventional PGC demodulation, this scheme requires lower depth of carrier phase modulation. The vibration measurement results indicate that the average signal-to-noise and distortion Ratio (SINAD) and total harmonic distortion (THD) values of demodulation results in the frequency range of 130 Hz to 250 Hz are 34 dB and -33 dB respectively. The proposed PGC demodulation scheme shows good performance in displacement measurement using SPMI.

中文翻译：

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不使用二次谐波载波信号的零差干涉仪李萨如椭圆拟合PGC解调方案

本文提出了一种用于正弦相位调制干涉仪（SPMI）的相位生成载波（PGC）解调方案，该方案不需要二次谐波载波信号。该方案通过对原始干扰信号进行低通滤波得到带有直流偏置的同相干扰信号分量，并通过常规手段得到正交干扰信号分量。这两个正交干扰信号分量形成的李萨如图是一个椭圆，其中心偏离IQ坐标原点。通过拟合这个椭圆，可以获得长轴和短轴以及中心坐标。然后使用这些椭圆参数来消除直流偏置并标准化正交信号分量的幅度。最后，可以利用反正切算法或微分互乘(DCM)算法实现干扰信号的相位解调。仿真和实验结果验证了所提出的PGC解调方案的有效性和准确性，并表明该方案对相位调制深度C不敏感。与传统PGC解调相比，该方案需要较低的载波相位调制深度。振动测量结果表明，解调结果在130 Hz~250 Hz频率范围内的平均信噪比和失真比（SINAD）和总谐波失真（THD）值分别为34 dB和-33 dB。所提出的 PGC 解调方案在使用 SPMI 的位移测量中表现出良好的性能。