Comparison of Amplitude-Frequency Response Characteristics Between DCM and Arctan Algorithms in <i>ϕ</i>-OTDR
Tingyu Wang, Jianzhong Zhang, Zhe Ma, Ming Liu, Xiang He, Weizhe Li, Binyuan Yang, Mingjiang Zhang
Abstract
In phase-sensitive optical time-domain reflectometry ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> -OTDR) systems, DCM and Arctan demodulation algorithms are typically used to recover the information on vibration events along the fiber. The amplitude-frequency response characteristics of the DCM and Arctan algorithms are investigated and compared using a 3×3 coupler demodulation technique. We first testify the demodulation capability of the DCM and Arctan algorithms through experiments in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> -OTDR. Then the amplitude-frequency response ranges of the two algorithms are analyzed according to the demodulated phase error distribution from both the experiment and simulation. It is shown that the Arctan algorithm has a wider amplitude-frequency range than the DCM algorithm. The phase error generation mechanism is also investigated and we find that, in a noise-free condition, the phase errors still appear with use of the DCM algorithm, which cannot be explained by the general perspective that the phase errors arise from the sensitivity of the differential operator to noise. For both algorithms the phase error is related to the amplitude ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ) and frequency ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> ) of the vibration signal, and pulse repetition frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${f}_{\text{pulse}}$</tex-math></inline-formula> ). When the phase error tolerance is less than 0.1, the expression of the amplitude-frequency response characteristic of DCM algorithm is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.7({D + 1})f \leq {f}_{\text{pulse}}$</tex-math></inline-formula> , whereas that of the Arctan algorithm is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2Df \leq {f}_{\text{pulse}}$</tex-math></inline-formula> .