Phase Error Evaluation via Differentiation and Cross-Multiplication Demodulation in Phase-Sensitive Optical Time-Domain Reflectometry

Abstract

Phase-sensitive optical time-domain reflectometry (φOTDR) is a technology for distributed vibration sensing, where vibration amplitudes are determined by recovering the phase of the backscattered light. Measurement noise induces phase errors, which degrades sensing performance. The phase errors, using a differentiation and cross-multiplication (DCM) algorithm, are investigated theoretically and experimentally in a φOTDR system based on a phase retrieval configuration consisting of an imbalanced Mach–Zehnder interferometer (IMZI) and a 3 × 3 coupler. Analysis shows that phase error is highly dependent on the AC component of the obtained signal, essentially being inversely proportional to the product of the power of the light backscattered from two locations. An analytical expression was derived to estimate the phase error and was confirmed by experiment. When applied to the same measurement data, the error is found to be slightly smaller than that obtained using in-phase/quadrature (I/Q) demodulation. The error, however, increases for longer measurement times.