High Accuracy Distributed Strain Sensing Based on Fractional Cyclic Shift With Nondestructive Phase Unwrapping in OFDR

The relative phase method in strain demodulation based on optical frequency domain reflectometry (OFDR) has received much attention for its high accuracy and spatial resolution, but has the unique phase wrapping problem with different proposed solutions. Some relative phase information is lost in these solutions, and the complex algorithms make it difficult to implement in devices. This article proposes a fractional cyclic shift method that matches any slope, which provides a nondestructive solution to phase wrapping and is easy to implement. Additionally, this article presents the theory of cyclic shifts with zero padding, conversion formulae for fractional shift points, and the mathematical relationship between relative phase slope and optical frequency domain shift under the same strain. Using fractional cyclic shift and peak finding method based on variance statistic, this article accurately determines the start and end positions of the strain, providing basic strain phase information. Finally, the method achieves the strain measurement with spatial resolution of 0.907 mm, distance of 36.7 m, strain accuracy of $0.5~\mu \varepsilon $ , maximum error of $0.2~\mu \varepsilon $ , and standard deviation of $0.077~\mu \varepsilon $ through bidirectional Chebyshev low-pass filtering, providing low-error strain demodulation with sub-millimeter resolution in the medium distance. This article also compares different filtering methods finding that bidirectional Chebyshev filtering avoids phase distortion and has one-third the error of finite impulse response (FIR) filtering with different windows.