Algorithm for interferometric phase signal demodulation using a 3×3 coupler

Accurate phase demodulation is essential for high-precision interferometric sensing with 3 × 3 couplers, but conventional methods are often limited by noise sensitivity and channel mismatches. We propose a robust phase demodulation algorithm that combines principal component analysis (PCA) with nonlinear least-squares ellipse fitting (EFA). The algorithm projects measured signals onto a unified two-dimensional subspace using PCA, enhancing noise suppression and ensuring global consistency during phase fitting. By employing trust-region reflective (TRF) optimization for ellipse fitting, the method achieves high stability and accuracy even in challenging scenarios. Experimental results show that, compared to traditional pairwise EFA, the proposed PCA-EFA approach improves mean SNR by 4.26 dB and reduces THD by 3.27% on average. The algorithm also achieves excellent amplitude linearity (R² = 99.9908%) and remains robust for phase amplitudes as low as π/8. These results demonstrate substantial advantages in accuracy, robustness, and noise immunity, making it highly suitable for advanced interferometric sensing applications.