Principles and Applications of Optical Fiber Distributed Acoustic Sensors

Zuyuan He; Qingwen Liu

doi:10.3788/LOP202158.1306001

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 13 >Page 1306001 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 13, 1306001 (2021)

Principles and Applications of Optical Fiber Distributed Acoustic Sensors

Zuyuan He^* and Qingwen Liu

Author Affiliations

State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China

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DOI: 10.3788/LOP202158.1306001 Cite this Article Set citation alerts

Zuyuan He, Qingwen Liu. Principles and Applications of Optical Fiber Distributed Acoustic Sensors[J]. Laser & Optoelectronics Progress, 2021, 58(13): 1306001 Copy Citation Text

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Abstract

Optical fiber based distributed acoustic sensor (DAS) is one of the most attractive and well developed fiber sensing technologies in the recent decade. It can simultaneously detect and recover the waveforms of multiple mechanical vibrations along the sensing fiber with high sampling rate, providing abundant information of the environment, which has great potential applications in perimeter fence security, oil and gas exploration, seismic waveform detection, and other fields. This paper first reviews the principles involved in DAS system, including three types of reflectometry to locate the Rayleigh backscattering (RBS) along the long distance fiber, and the two methods to recover the vibration waveform using RBS signal. Then two typical applications of DAS system are reviewed, and finally the possible research trends of DAS technology are discussed.

Keywords

distributed acoustic sensor fiber sensor optical communications Rayleigh backscattering reflectometry

z = \frac{c τ}{2 n}

，（1）

s (t) = w (\frac{t}{T_{p}}) e x p (j 2 π f_{0} t)

，（2）

E_{l} (t) = \sqrt[]{P_{l}} e x p (j 2 π ν_{0} t),

（3）

E_{p} (t) = \sqrt[]{P_{p}} w (\frac{t}{T_{p}}) e x p (j 2 π ν_{0} t + j 2 π f_{0} t),

（4）

E_{R} (t) = \sum_{i = 1}^{N} E_{i} w (\frac{t - τ_{i}}{T_{p}}) e x p [j 2 π ν_{0} (t - τ_{i}) + j 2 π f_{0} (t - τ_{i})],

（5）

i (t) \propto R e {E_{R} (t) \cdot E_{l}^{*} (t)} = \sum_{i = 1}^{N} A_{i} w (\frac{t - τ_{i}}{T_{p}}) c o s [2 π f_{0} (t - τ_{i}) - 2 π ν_{0} τ_{i}],

（6）

i (t) = \int_{0}^{T_{F}} A (τ) w (\frac{t - τ}{T_{p}}) e x p [j 2 π f_{0} (t - τ) - j 2 π ν_{0} τ] d τ = h (t) \otimes s (t),

（7）

h (t) = A (t) e x p (- j 2 π ν_{0} t)

。（8）

Z_{S R} = \frac{c T_{p}}{2 n}

。（9）

E_{l} (t) = \sqrt[]{P_{l}} w (\frac{t}{T_{s}}) e x p [j 2 π ν_{0} t + j π γ t^{2} + j ϕ (t)],

（10）

E^{R B S} (t) = \int_{0}^{T_{F}} E (τ) w (\frac{t - τ}{T_{s}}) e x p \{j [2 π ν_{0} (t - τ) + π γ {(t - τ)}^{2}]\} d τ

，（11）

i (t) \propto \int_{0}^{T_{F}} A (τ) c o s (2 π γ τ t + 2 π ν_{0} τ - π γ τ^{2}) \cdot w (\frac{t}{T_{s}}) d τ

。（12）

F (f) = \int_{0}^{T_{F}} A (τ) e x p (j 2 π ν_{0} τ - j π γ τ^{2}) W (f - γ τ) \cdot d τ = H (f) \otimes W (f)

，（13）

H (f) = A (f) e x p [j (2 π ν_{0} f / γ - π f^{2} / γ)]

。（14）

|W (f)| = |\frac{s i n (π f T_{s})}{π f}|

。（15）

Z_{S R} = \frac{c}{2 n} \cdot \frac{Δ f}{γ} = \frac{c}{2 n Δ F},

（16）

E_{p} (t) = \sqrt[]{P_{p}} w (\frac{t}{T_{p}}) e x p [j (2 π ν_{0} t + 2 π f_{0} t + π γ t^{2})]

。（17）

i (t) = \int_{0}^{T_{F}} A (τ) w (\frac{t - τ}{T_{p}}) e x p [j 2 π f_{0} (t - τ) + j π γ {(t - τ)}^{2} - j 2 π ν_{0} τ] d τ = h (t) \otimes s (t) 。

（18）

I (t) = h (t) \otimes s (t) \otimes s^{*} (- t) = h (t) \otimes S (t),

（19）

S (t) = W (\frac{t}{2 T_{p}}) \frac{s i n [π γ t (T_{p} - | t |)]}{π γ t} \times e x p [- j 2 π (f_{0} + \frac{γ T_{p}}{2}) t] 。

（20）

Z_{S R} = \frac{c}{2 n Δ F}

。（21）

Φ (z, 0) = 2 \int_{0}^{z} β n (x) d x = 2 β n z,

（22）

Φ (z, ε) = 2 \int_{0}^{z} β n (x) d x = 2 β n z_{A} + 2 β (n + C_{ε} ε) (1 + ε) (z - z_{A})

。（23）

Φ (z, 0) = 2 \int_{0}^{z} β n (x) d x = 2 β n (z - z_{B} + z_{A}) + 2 β (n + C_{ε} ε) (1 + ε) (z_{B} - z_{A}) 。

（24）

Φ_{L} (0) = Φ (z, 0) - Φ (z - L, 0) = 2 β n L 。

（25）

Φ_{L} (ε) = Φ (z, ε) - Φ (z - L, ε) = 2 β (n + C_{ε} ε) (1 + ε) L 。

（26）

Δ Φ_{L} (ε) = Φ_{L} (ε) - Φ_{L} (0) = 2 β (n ε + C_{ε} ε + C_{ε} ε^{2}) L

。（27）

Δ Φ_{L} (ε) = 2 β (n + C_{ε}) ε L 。

（28）

σ_{θ}^{2} = \frac{1}{S_{N R}}

。（29）

\frac{Δ ν}{ν_{0}} = \frac{Δ n}{n} = - K_{ε} ε,

（30）

Zuyuan He, Qingwen Liu. Principles and Applications of Optical Fiber Distributed Acoustic Sensors[J]. Laser & Optoelectronics Progress, 2021, 58(13): 1306001

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