A PGC demodulation scheme based on the Lissajous ellipse fitting for homodyne interferometer without using second harmonic carrier signal

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.