Analysis and elimination of bias error in a fiber-optic current sensor

Xiaxiao Wang; Zijie Zhao; Chuansheng Li; Jia Yu; Zhenjie Wang

doi:10.1364/AO.56.008887

Applied Optics
Vol. 56,
Issue 32,
pp. 8887-8895
(2017)
•https://doi.org/10.1364/AO.56.008887

Analysis and elimination of bias error in a fiber-optic current sensor

Xiaxiao Wang, Zijie Zhao, Chuansheng Li, Jia Yu, and Zhenjie Wang

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Xiaxiao Wang, Zijie Zhao, Chuansheng Li, Jia Yu, and Zhenjie Wang, "Analysis and elimination of bias error in a fiber-optic current sensor," Appl. Opt. 56, 8887-8895 (2017)

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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: August 8, 2017
- Revised Manuscript: October 3, 2017
- Manuscript Accepted: October 4, 2017
- Published: November 3, 2017

Abstract

Bias error, along with scale factor, is a key factor that affects the measurement accuracy of the fiber-optic current sensor. Because of polarization crosstalk, the coherence of parasitic interference signals could be rebuilt and form an output independent of the current to be measured, i.e., the bias error. The bias error is a variable of the birefringence optical path difference. Hence, when the temperature changes, the bias error shows a quasi-periodical tendency whose envelope curve reflects the coherence function of light source. By identifying the key factors of bias error and setting the propagation directions of a super-luminescent diode, polarization-maintaining coupler and polarizer to fast axis, it is possible to eliminate the coherence of parasitic interference signals. Experiments show that the maximum bias error decreases by one order of magnitude at temperatures between $- 40 ° C$ to 60°C.

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Device	Parameter	Value
High-polarization SLD	$P$ (Optical power)	900 μW
	$d$ (Degree of polarization)	0.97
	$θ_{s}$ (Coupling angle of output fiber)	3°
PM coupler	$θ_{c 1}$ (Coupling angle of input fiber between Port 1 to Port 3)	2.5°
	$θ_{c 2}$ (Coupling angle of input fiber between Port 3 to Port 2)	2.5°
	Splitting ratio	$1 ∶ 1$
Polarizer	Extinction ratio	30 dB
	$θ_{p 1}$ (Coupling angle of input fiber)	1.8°
	$θ_{p 1}$ (Coupling angle of output fiber)	1.8°
Phase modulator	$θ_{m 1}$ (Coupling angle of input fiber)	2°
Phase modulator	$θ_{m 2}$ (Coupling angle of output fiber)	2°
Splice	$θ_{1}$ (Splice between SLD and PM coupler port 1)	1°
	$θ_{2}$ (Splice between PM coupler port 3 and polarizer)	1°
	$θ_{3}$ (Splice between polarizer and modulator)	46°
	$θ_{4}$ (Splice between modulator and PM fiber delayer)	1.5°
	$θ_{5}$ (Splice between PM fiber delayer and $λ / 4$ retarder)	46.5°

$Δ ϕ_{x k}$ and $Δ ϕ_{y k}$	$B_{x k} (\cdot 10^{- 7})$	$B_{x k}^{'} (\cdot 10^{- 7})$	$B_{y k} (\cdot 10^{- 7})$	$B_{y k}^{'} (\cdot 10^{- 7})$
$Δ ϕ (L_{s} + L_{c 1} + L_{p 2})$	4	−3	−3	4
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2})$	−1328	1239	1328	−1239
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} - L_{p 2})$	1	−1	−1	1
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−45	42	45	−42
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	48	−45	−48	45
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2})$	−441	412	441	−412
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−15	14	15	−14
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	16	−15	−16	15
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2})$	−1029	1103	1103	−1029
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−35	37	37	−35
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	37	−40	−40	37
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} + L_{m 2})$	2	−2	−2	2
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} - L_{m 2})$	2	−2	−2	2
$Δ ϕ (L_{p 1} + L_{p 2})$	−411	440	440	−411
$Δ ϕ (L_{p 2})$	−739	792	792	−739
$Δ ϕ (L_{p 2} + L_{m 1})$	−25	27	27	−25
$Δ ϕ (L_{p 2} - L_{m 1})$	27	−29	−29	27
$Δ ϕ (L_{p 2} + L_{m 2})$	1	−1	−1	1
$Δ ϕ (L_{p 2} - L_{m 2})$	1	−2	−2	1
$Δ ϕ (L_{p 1} + L_{p 2} + L_{m 1})$	−14	15	15	−14
$Δ ϕ (L_{p 1} + L_{p 2} - L_{m 1})$	15	−16	−16	15

Fiber Length	Propagation Direction	Case 1	Case 2
$L_{s}$	Fast axis	1.5 m	1.4 m
$L_{c 1}$	Fast axis	2 m	0.6 m
$L_{c 2}$	Fast axis	2.2 m	1.5 m
$L_{p 1}$	Slow axis	1.1 m	1 m
$L_{p 2}$	Slow axis	1.1 m	1.1 m

Device	Parameter	Value
High-polarization SLD	$P$ (Optical power)	900 μW
	$d$ (Degree of polarization)	0.97
	$θ_{s}$ (Coupling angle of output fiber)	3°
PM coupler	$θ_{c 1}$ (Coupling angle of input fiber between Port 1 to Port 3)	2.5°
	$θ_{c 2}$ (Coupling angle of input fiber between Port 3 to Port 2)	2.5°
	Splitting ratio	$1 ∶ 1$
Polarizer	Extinction ratio	30 dB
	$θ_{p 1}$ (Coupling angle of input fiber)	1.8°
	$θ_{p 1}$ (Coupling angle of output fiber)	1.8°
Phase modulator	$θ_{m 1}$ (Coupling angle of input fiber)	2°
Phase modulator	$θ_{m 2}$ (Coupling angle of output fiber)	2°
Splice	$θ_{1}$ (Splice between SLD and PM coupler port 1)	1°
	$θ_{2}$ (Splice between PM coupler port 3 and polarizer)	1°
	$θ_{3}$ (Splice between polarizer and modulator)	46°
	$θ_{4}$ (Splice between modulator and PM fiber delayer)	1.5°
	$θ_{5}$ (Splice between PM fiber delayer and $λ / 4$ retarder)	46.5°

$Δ ϕ_{x k}$ and $Δ ϕ_{y k}$	$B_{x k} (\cdot 10^{- 7})$	$B_{x k}^{'} (\cdot 10^{- 7})$	$B_{y k} (\cdot 10^{- 7})$	$B_{y k}^{'} (\cdot 10^{- 7})$
$Δ ϕ (L_{s} + L_{c 1} + L_{p 2})$	4	−3	−3	4
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2})$	−1328	1239	1328	−1239
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} - L_{p 2})$	1	−1	−1	1
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−45	42	45	−42
$Δ ϕ (L_{s} + L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	48	−45	−48	45
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2})$	−441	412	441	−412
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−15	14	15	−14
$Δ ϕ (L_{c 1} + L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	16	−15	−16	15
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2})$	−1029	1103	1103	−1029
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} + L_{m 1})$	−35	37	37	−35
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} - L_{m 1})$	37	−40	−40	37
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} + L_{m 2})$	2	−2	−2	2
$Δ ϕ (L_{c 2} + L_{p 1} + L_{p 2} - L_{m 2})$	2	−2	−2	2
$Δ ϕ (L_{p 1} + L_{p 2})$	−411	440	440	−411
$Δ ϕ (L_{p 2})$	−739	792	792	−739
$Δ ϕ (L_{p 2} + L_{m 1})$	−25	27	27	−25
$Δ ϕ (L_{p 2} - L_{m 1})$	27	−29	−29	27
$Δ ϕ (L_{p 2} + L_{m 2})$	1	−1	−1	1
$Δ ϕ (L_{p 2} - L_{m 2})$	1	−2	−2	1
$Δ ϕ (L_{p 1} + L_{p 2} + L_{m 1})$	−14	15	15	−14
$Δ ϕ (L_{p 1} + L_{p 2} - L_{m 1})$	15	−16	−16	15

Abstract

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Equations (22)

Applied Optics