Ameliorated 3 × 3 coupler phase demodulation scheme using Gauss–Newton iteration algorithm

To solve the asymmetry problem of the 3×3 coupler, we propose an ellipse fitting algorithm (EFA) based on the Gauss–Newton iteration (GNI) algorithm in a 3×3 coupler demodulation system. The GNI algorithm uses a Taylor series expansion to approximate the Sampson error. In the optimization process, the approximation information of the gradient and Hessian matrix is used to improve the demodulation precision and convergence speed. However, the EFA may fail under small stimulus signals. The ellipse correction parameters have temporary stability, and we design a phase shift judgment module. If the phase shift exceeds π, the EFA is executed, and the ellipse correction parameters are updated in real time. Otherwise, the preset parameters are used for ellipse correction. Experiments have established that the ameliorated algorithm has a high signal-to-noise and distortion ratio. The total harmonic distortion of the proposed GNI algorithm is improved by 11.76% and 0.22% compared with the Naval Research Laboratory algorithm and the EFA based on the least squares algorithm, respectively. Its response linearity is as high as 99.992%, with a minimum detectable phase of 3.16 μrad/Hz and a large dynamic range of 148.84 dB. The proposed demodulation algorithm can eliminate nonlinear errors and has higher accuracy and reliability.