Reducing Recovery Signal Distortion of the $\phi$-OTDR Based on 3×3 Coupler Demodulation Using Ellipse Fitting Algorithm

3 × 3 coupler demodulation method is widely used in
$\phi$
-OTDR because of its large dynamic range, high response bandwidth and simple structure. However, when the 3 × 3 coupler undergoes a severe amplitude and/or phase mismatch in practical applications, the demodulation results would produce severe distortions and may lead to nuisance alarms in static conditions. For this deficiency, Ellipse Fitting Algorithm (EFA) and two-path Differential Cross Multiply (DCM) algorithm are proposed in this paper. EFA calculates the characteristic parameters of outputs of the 3 × 3 coupler based on the least square method, and then generates two corrected orthogonal waveforms that are provided to the DCM algorithm for demodulation. The experimental results show that the proposed EFA-DCM method can improve signal-to-noise ratio by up to 31.74 dB compared to the three-path DCM method, and by up to 14.19 dB compared to the improved two-path DCM method we proposed before. Furthermore, under static measurement conditions, EFA-DCM method can reduce the nuisance alarms that induced by the three-path DCM method by 87%. These results show that the EFA-DCM method can significantly reduce the recovery signal distortion and nuisance alarms, and may further promote wide application of 3 × 3 coupler demodulation method.