Abstract

Ellipse fitting algorithm (EFA) has attracted tremendous interest in phase demodulation schemes to eliminate nonlinear errors, however, there is an inherent drawback that the EFA fails to work when the desired phase signal is small. A high precision and stabilization phase generated carrier (PGC) demodulation scheme using hyper least squares (LS) fitting of ellipse is proposed for the first time, to our best knowledge. The contaminated quadrature signals obtained after mixing and low pass filtering are processed by a hyper LS based EFA to eliminate nonlinear errors. Hyper LS relies on algebraic distance minimization with a carefully chosen scale normalization and statistical bias is eliminated up to second order noise terms, which is far superior to the traditional LS. The temporary stability of the fitting result is used to resolve the drawback of the EFA. A module for judging the ellipse arc of quadrature signals is developed. The EFA is executed when the Lissajous figure is larger than 1/4 ellipse arc, otherwise the fitting result of the previous executed EFA is used to correct the ellipse. Experimental results show that the proposed scheme is highly precise and stable regardless of the desired signal amplitude. It has a high response linearity of 99.997%, a minimum detectable phase of 3.16 μrad and a large dynamic range of 123.52 dB @1 kHz & 1% THD.

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