Comparison of Amplitude-Frequency Response Characteristics Between DCM and Arctan Algorithms in ϕ-OTDR

In phase-sensitive optical time-domain reflectometry (
$\varphi$
-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
$\varphi$
-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 (
D
) and frequency (
f
) of the vibration signal, and pulse repetition frequency (
${f}_{\text{pulse}}$
). When the phase error tolerance is less than 0.1, the expression of the amplitude-frequency response characteristic of DCM algorithm is
$5.7({D + 1})f \leq {f}_{\text{pulse}}$
, whereas that of the Arctan algorithm is
$2Df \leq {f}_{\text{pulse}}$
.