Multipoint sensing with a low-coherence source using single-arm frequency-shifted interferometry

Yiwei Zhang; Fei Ye; Bing Qi; Li Qian

doi:10.1364/AO.55.005526

Applied Optics
Vol. 55,
Issue 21,
pp. 5526-5530
(2016)
•https://doi.org/10.1364/AO.55.005526

Multipoint sensing with a low-coherence source using single-arm frequency-shifted interferometry

Yiwei Zhang, Fei Ye, Bing Qi, and Li Qian

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Yiwei Zhang, Fei Ye, Bing Qi, and Li Qian, "Multipoint sensing with a low-coherence source using single-arm frequency-shifted interferometry," Appl. Opt. 55, 5526-5530 (2016)

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Table of Contents Category
- Fiber Optics and Optical Communications
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: March 28, 2016
- Revised Manuscript: June 15, 2016
- Manuscript Accepted: June 16, 2016
- Published: July 12, 2016

Abstract

We demonstrate that multiple-site sensing along an optical fiber can be done with incoherent continuous-wave light. Using a broadband low-coherence noise source, a slow detector, and an optical modulator, we construct a single-arm frequency-shifted interferometer (SA-FSI) capable of simultaneously sensing multiple weak-reflection sites distributed either in parallel or in series along fiber links. By scanning the driving frequency of an electro-optic amplitude modulator in the range of 2.7–3.2 GHz at steps of 41.7 KHz, we demonstrate a spatial resolution of 0.3 m and a measurement range of over 1 km.

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Field Components After the 1st Modulation	Field Components After the 2nd Modulation (On Return)
$E_{1 ν}^{'} = J_{0} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \cos (2 π ν t + φ_{ν})$	$E_{1 ν}^{''} = J_{0}^{2} (α \frac{π}{2}) \cos^{2} [\frac{π}{2} ϵ] \cos (2 π ν t + φ_{ν})$
	$E_{2 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π ν t - 2 π f (t + δ t) + φ_{ν})$
	$E_{3 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π ν t + 2 π f (t + δ t) + φ_{ν})$
$E_{2 ν}^{'} = - J_{1} (α \frac{π}{2}) \sin [\frac{π}{2} ϵ] \cos (2 π t (ν - f) + φ_{ν})$	$E_{4 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π (ν - f) t + φ_{ν})$
	$E_{5 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν - f) t - 2 π f (t + δ t) + φ_{ν})$
	$E_{6 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν - f) t + 2 π f (t + δ t) + φ_{ν})$
$E_{3 ν}^{'} = - J_{1} (α \frac{π}{2}) \sin [\frac{π}{2} ϵ] \cos (2 π t (ν + f) + φ_{ν})$	$E_{7 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π (ν + f) t + φ_{ν})$
	$E_{8 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν + f) t - 2 π f (t + δ t) + φ_{ν})$
	$E_{9 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν + f) t + 2 π f (t + δ t) + φ_{ν})$

Methods	$d_{12} (m)$	$d_{23} (m)$	$d_{45} (m)$
Ruler	$2.08 \pm 0.01$	$5.07 \pm 0.02$	$0.320 \pm 0.005$
SA-FSI	$2.08 \pm 0.05$	$5.06 \pm 0.05$	$0.32 \pm 0.05$

Methods	$d_{12} (m)$	$d_{23} (m)$	$d_{34} (m)$
SA-FSI	$1.11 \pm 0.05$	$999.05 \pm 0.05$	$1.06 \pm 0.05$
Ruler	$1.10 \pm 0.01$	×	$1.09 \pm 0.01$
TOF	×	$998.98 \pm 0.10$	×

Field Components After the 1st Modulation	Field Components After the 2nd Modulation (On Return)
$E_{1 ν}^{'} = J_{0} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \cos (2 π ν t + φ_{ν})$	$E_{1 ν}^{''} = J_{0}^{2} (α \frac{π}{2}) \cos^{2} [\frac{π}{2} ϵ] \cos (2 π ν t + φ_{ν})$
	$E_{2 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π ν t - 2 π f (t + δ t) + φ_{ν})$
	$E_{3 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π ν t + 2 π f (t + δ t) + φ_{ν})$
$E_{2 ν}^{'} = - J_{1} (α \frac{π}{2}) \sin [\frac{π}{2} ϵ] \cos (2 π t (ν - f) + φ_{ν})$	$E_{4 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π (ν - f) t + φ_{ν})$
	$E_{5 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν - f) t - 2 π f (t + δ t) + φ_{ν})$
	$E_{6 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν - f) t + 2 π f (t + δ t) + φ_{ν})$
$E_{3 ν}^{'} = - J_{1} (α \frac{π}{2}) \sin [\frac{π}{2} ϵ] \cos (2 π t (ν + f) + φ_{ν})$	$E_{7 ν}^{''} = - J_{0} (α \frac{π}{2}) J_{1} (α \frac{π}{2}) \cos [\frac{π}{2} ϵ] \sin [\frac{π}{2} ϵ] \cos (2 π (ν + f) t + φ_{ν})$
	$E_{8 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν + f) t - 2 π f (t + δ t) + φ_{ν})$
	$E_{9 ν}^{''} = J_{1}^{2} (α \frac{π}{2}) \sin^{2} [\frac{π}{2} ϵ] \cos (2 π (ν + f) t + 2 π f (t + δ t) + φ_{ν})$

Methods	$d_{12} (m)$	$d_{23} (m)$	$d_{45} (m)$
Ruler	$2.08 \pm 0.01$	$5.07 \pm 0.02$	$0.320 \pm 0.005$
SA-FSI	$2.08 \pm 0.05$	$5.06 \pm 0.05$	$0.32 \pm 0.05$

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Applied Optics