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Chinese Optics Letters
Vol. 15, Issue 10, 101201 (2017)

Large-range displacement measurement using sinusoidal phase-modulating laser diode interferometer

Ming Zhang^1、2、*, Chang Ni^1、2, Yu Zhu^1、2, Leijie Wang^1、2, Chuxiong Hu^1、2, and Jinchun Hu^1、2

Author Affiliations

¹State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

²Beijing Laboratory of Precision/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China

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DOI: 10.3788/COL201715.101201 Cite this Article Set citation alerts

Ming Zhang, Chang Ni, Yu Zhu, Leijie Wang, Chuxiong Hu, Jinchun Hu. Large-range displacement measurement using sinusoidal phase-modulating laser diode interferometer[J]. Chinese Optics Letters, 2017, 15(10): 101201 Copy Citation Text

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Abstract

A signal processing method of realizing a large-range displacement measurement in a sinusoidal phase-modulating laser diode interferometer is proposed. The method of obtaining the dynamic value of the effective sinusoidal phase-modulating depth is detailed, and the residual amplitude modulation is also taken into account. Numerical simulations and experiments are carried out to compare this method with the traditional one. We prove that, with this method, the sinusoidal phase-modulating laser diode interferometer can realize a centimeter-level displacement measurement range with high precision, which is much better than the traditional method.

s (t) = E_{1} + E_{2} \cos [4 π x (t) / λ + m \cos (ω t)],

(1)

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m = a x (t) = a [x_{0} + Δ x (t)],

(2)

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S_{1} (t) = - 2 E_{2} J_{1} (m) \times \sin [4 π x (t) / λ], S_{2} (t) = - 2 E_{2} J_{2} (m) \times \cos [4 π x (t) / λ] .

(3)

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Δ x (t) = \frac{N λ}{4} + \arctan [\frac{S_{1} (t) / J_{1} (m)}{S_{2} (t) / J_{2} (m)}] \times \frac{λ}{4 π} .

(4)

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m_{r} (t_{i}) = a x_{0} + a Δ x (t_{i}) = m_{0} + a Δ x (t_{i}),

(5)

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Δ x (t_{i + 1}) = \frac{N λ}{4} + \arctan [\frac{S_{1} (t_{i + 1}) / J_{1} (m_{r} (t_{i}))}{S_{2} (t_{i + 1}) / J_{2} (m_{r} (t_{i}))}] \times \frac{λ}{4 π} .

(6)

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A_{1} (t) = | 2 E_{2} J_{1} (m_{r} (t)) |, A_{2} (t) = | 2 E_{2} J_{2} (m_{r} (t)) | .

(7)

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f (m_{r} (t)) = \frac{A_{2} (t)}{A_{1} (t)} = | \frac{J_{2} (m_{r} (t))}{J_{1} (m_{r} (t))} | .

(8)

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s_{RAM} (t) = [1 + k \cos (ω t)] {E_{1} + E_{2} \cos [4 π x (t) / λ + m \cos (ω t)]},

(9)

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S_{R 1} (t) = k E_{1} / 2 - 2 E_{2} J_{1} (m) \times \sin [4 π x (t) / λ] + k E_{2} [J_{0} (m) - J_{2} (m)] \times \cos [4 π x (t) / λ], S_{R 2} (t) = - 2 E_{2} J_{2} (m) \times \cos [4 π x (t) / λ] - k E_{2} [J_{1} (m) - J_{3} (m)] \times \sin [4 π x (t) / λ], S_{R 3} (t) = 2 E_{2} J_{3} (m) \times \sin [4 π x (t) / λ] - k E_{2} [J_{2} (m) - J_{4} (m)] \times \cos [4 π x (t) / λ],

(10)

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f (m_{r} (t)) = \frac{\sqrt{{[2 J_{3} (m_{r} (t))]}^{2} + k^{2} {[J_{2} (m_{r} (t)) - J_{4} (m_{r} (t))]}^{2}}}{\sqrt{{[2 J_{2} (m_{r} (t))]}^{2} + k^{2} {[J_{1} (m_{r} (t)) - J_{3} (m_{r} (t))]}^{2}}} .

(11)

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[\begin{matrix} S_{R 2} (t) \\ S_{R 3} (t) \end{matrix}] = [\begin{matrix} A_{11} (t) & A_{12} (t) \\ A_{21} (t) & A_{22} (t) \end{matrix}] [\begin{matrix} E_{2} \sin [4 π x (t) / λ] \\ E_{2} \cos [4 π x (t) / λ] \end{matrix}],

(12)

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{\begin{cases} A_{11} (t) = - k {J_{1} [m_{r} (t)] - J_{3} [m_{r} (t)]}, \\ A_{12} (t) = - 2 J_{2} [m_{r} (t)], \\ A_{21} (t) = 2 J_{3} [m_{r} (t)], \\ A_{22} (t) = - k {J_{2} [m_{r} (t)] - J_{4} [m_{r} (t)]} . \end{cases}

(13)

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Δ x (t) = \frac{N λ}{4} + \arctan {\frac{E_{2} \sin [4 π x (t) / λ]}{E_{2} \cos [4 π x (t) / λ]}} \times \frac{λ}{4 π} .

(14)

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\frac{1 mm / s}{785 nm} \times 4 \approx 5096 Hz .

(15)

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Ming Zhang, Chang Ni, Yu Zhu, Leijie Wang, Chuxiong Hu, Jinchun Hu. Large-range displacement measurement using sinusoidal phase-modulating laser diode interferometer[J]. Chinese Optics Letters, 2017, 15(10): 101201

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