Enhancing the Dynamic Strain Range of Phase-Sensitive Optical Time Domain Reflectometry Using Least Squares Linear Programming Phase Unwrapping Method

Due to the inherent $\pi $ -phase constraint in phase unwrapping algorithms, the dynamic strain range of phase-sensitive optical time domain reflectometry ( $\Phi $ -OTDR) is significantly limited. $\Phi $ -OTDR with modified architectures have proven effective in expanding the dynamic strain range. However, such methods still subject to the $\pi $ -phase constraint, resulting in inconsistent enhancement of the dynamic strain range across the frequency response bandwidth. This work innovatively proposes a least squares linear programming phase unwrapping (ls-LPPU) algorithm, which determines the wrapping orders under large dynamic strains by minimizing the squared optical path difference between two wavelengths, thereby achieving temporally independent phase unwrapping. Experimental results demonstrate that the proposed method achieves precise restoration of large dynamic strains ranging from 13.8 to $44.6~\mu \varepsilon $ , representing an enhancement of at least 90-fold. Furthermore, under a pulse repetition frequency of 10 kHz, error-free recovery of large dynamic strains with frequencies spanning 0.9–4.5 kHz is realized. The ls-LPPU algorithm facilitates the restoration of large dynamic strains by directly obtaining the phase wrapped orders. Meanwhile, its temporally independent characteristic eliminates the $\pi $ -phase constraint, achieving the decoupling of dynamic strain extension and frequency response bandwidth.