Three-dimensional model of thermal-induced optical phase shifts in rotation sensing

Xuyou Li; Weiwei Ling; Yanhui Wei; Zhenlong Xu

doi:10.3788/COL201513.090603

Journals >Chinese Optics Letters >Volume 13 >Issue 9 >Page 090603 > Article

Chinese Optics Letters
Vol. 13, Issue 9, 090603 (2015)

Three-dimensional model of thermal-induced optical phase shifts in rotation sensing

Xuyou Li, Weiwei Ling, Yanhui Wei^*, and Zhenlong Xu

Author Affiliations

Harbin Engineering University, College of Automation, Harbin, Heilongjiang 150001, China

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DOI: 10.3788/COL201513.090603 Cite this Article Set citation alerts

Xuyou Li, Weiwei Ling, Yanhui Wei, Zhenlong Xu. Three-dimensional model of thermal-induced optical phase shifts in rotation sensing[J]. Chinese Optics Letters, 2015, 13(9): 090603 Copy Citation Text

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Abstract

By studying the thermal-induced phase shift mechanism of an interferometric fiber-optic gyroscope (IFOG) sensing coil, a novel generalized expression based on a three-dimensional (3D) model is proposed. Compared with the traditional pure Shupe effect model, the simulation results show that the new 3D model, including elastic strain and the elasto-optical effect, can describe the thermal effect of the coils more accurately. Experiments with temperature change rates between

40 ° C

and 70°C are performed to verify the effectiveness of the proposed generalized expression. The results of our work can guide researchers in identifying countermeasures to reduce the thermal-induced bias error in IFOG.

ϕ (l) = β_{0} n \cdot l + β_{0} (\frac{\partial n}{\partial T} \cdot Δ T + n α \cdot Δ T) \cdot l,

(1)

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Ω_{E 1} (t) = \frac{n}{D L} (\frac{\partial n}{\partial T} + n α) \int_{- L / 2}^{L / 2} \dot{T} (s, t) (L - 2 s) d s,

(2)

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Δ ϕ (l) = β \cdot Δ l + l \cdot Δ β = β l \cdot \frac{Δ l}{l} + l \cdot \frac{Δ β}{Δ n} Δ n .

(3)

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Δ ϕ (l) = β_{0} l \cdot n ε_{z} + β_{0} l \cdot Δ n,

(4)

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Δ n = - \frac{1}{2} n^{2} (P_{11} ε_{x} + P_{12} ε_{y} + P_{12} ε_{z}),

(5)

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[\begin{array}{l} ε_{x} \\ ε_{y} \\ ε_{z} \\ ε_{y z} \\ ε_{z x} \\ ε_{x y} \end{array}] = [\begin{matrix} 1 / E & - v / E & - v / E & 0 & 0 & 0 \\ - ν / E & 1 / E & - ν / E & 0 & 0 & 0 \\ - ν / E & 1 / E & 1 / E & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 / G & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 / G & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 / G \end{matrix}] [\begin{array}{l} σ_{x} \\ σ_{y} \\ σ_{z} \\ σ_{y z} \\ σ_{z x} \\ σ_{x y} \end{array}],

(6)

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[\begin{array}{l} σ_{x} \\ σ_{y} \\ σ_{z} \\ σ_{y z} \\ σ_{z x} \\ σ_{x y} \end{array}] = [\begin{array}{l} - P_{h} \\ - P_{v} \\ 0 \\ 0 \\ 0 \\ 0 \end{array}] .

(7)

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P (T) = P_{h} = P_{v} .

(8)

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Δ φ (l) = β_{0} {\frac{2 ν n}{E} Δ P (T) + \frac{n^{3}}{2 E} [(1 - ν) \cdot p_{11} + (1 - 3 ν) \cdot p_{12}] Δ P (T)} l,

(9)

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Ω_{E 2} (t) = \frac{n}{D L} {\frac{2 ν}{E} + \frac{n^{2}}{2 E} [(1 - ν) \cdot p_{11} + (1 - 3 ν) \cdot p_{12}]} \times \int_{- L / 2}^{L / 2} \dot{P} (T (s, t)) (L - 2 s) d s,

(10)

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Ω_{E} (t) = Ω_{E 1} (t) + Ω_{E 2} (t) .

(11)

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Ω_{E} (t, T) = \frac{2 n}{D L} (\frac{\partial n}{\partial T} + n α (T)) \sum_{i}^{N_{cc w}} r_{i} \int_{0}^{2 π} \dot{T} |_{(r_{i}, θ, z_{i}, t)} (r_{i} θ + s_{i 0}) d θ + \frac{2 n}{D L} (\frac{\partial n}{\partial T} + n α (T)) \sum_{j}^{N_{c w}} r_{j} \int_{0}^{2 π} \dot{T} |_{(r_{j}, θ, z_{j}, t)} (r_{j} θ - s_{j 0}) d θ + \frac{2 n}{D L} {\frac{2 ν}{E} + \frac{n^{2}}{2 E} [(1 - ν) \cdot p_{11} + (1 - 3 ν) \cdot p_{12}]} \sum_{i}^{N_{cc w}} r_{i} \int_{0}^{2 π} \dot{P} |_{(r_{i}, θ, z_{i}, t)} (r_{i} θ + s_{i 0}) d θ + \frac{2 n}{D L} {\frac{2 ν}{E} + \frac{n^{2}}{2 E} [(1 - ν) \cdot p_{11} + (1 - 3 ν) \cdot p_{12}]} \sum_{j}^{N_{c w}} r_{j} \int_{0}^{2 π} \dot{P} |_{(r_{j}, θ, z_{j}, t)} (r_{j} θ - s_{j 0}) d θ,

(12)

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Xuyou Li, Weiwei Ling, Yanhui Wei, Zhenlong Xu. Three-dimensional model of thermal-induced optical phase shifts in rotation sensing[J]. Chinese Optics Letters, 2015, 13(9): 090603

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