Abstract

The deviation of wave plates’ optical axes from their intended angles, which may result from either instability or assembly error, is the main cause of quadrature phase error in homodyne quadrature laser interferometers (HQLIs). The quadrature phase error sensitivity to wave plate angle deviations, which is an effective measure of HQLI robustness, is further amplified by beam splitter imperfections. In this paper, a new HQLI design involving non-polarization beam splitting is presented, and a method of making this HQLI robust by yawing the wave plates in the measurement and reference arms is proposed. The theoretical analysis results indicate that ultra-low quadrature phase error sensitivities to wave plate angle deviations can be realized and that non-polarizing beam splitter imperfections can be adequately compensated for. The experimental results demonstrate that the proposed method can reduce the quadrature phase error sensitivity by more than 1 order of magnitude, from a theoretical value of 1.4°/1° to 0.05°/1°.

© 2016 Optical Society of America

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References

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2015 (2)

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

P. Hu, J. Zhu, X. Zhai, and J. Tan, “DC-offset-free homodyne interferometer and its nonlinearity compensation,” Opt. Express 23(7), 8399–8408 (2015).
[Crossref] [PubMed]

2014 (1)

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

2012 (1)

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

2011 (1)

2009 (3)

2008 (1)

2005 (1)

2001 (1)

T. Eom, J. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12(10), 1734–1738 (2001).
[Crossref]

1995 (1)

Ahn, J.

Buchta, Z.

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

Cip, O.

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

Eom, T.

T. Eom, J. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12(10), 1734–1738 (2001).
[Crossref]

Gonda, S.

Gregorcic, P.

Guo, X.

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

He, W.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Hu, P.

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

P. Hu, J. Zhu, X. Zhai, and J. Tan, “DC-offset-free homodyne interferometer and its nonlinearity compensation,” Opt. Express 23(7), 8399–8408 (2015).
[Crossref] [PubMed]

Huang, Q.

Jeong, K.

T. Eom, J. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12(10), 1734–1738 (2001).
[Crossref]

Kang, C. S.

Kang, C.-S.

Keem, T.

Kim, J.

T. Eom, J. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12(10), 1734–1738 (2001).
[Crossref]

Kim, J. W.

Kim, J.-A.

Kim, S.

Kurosawa, T.

Lazar, J.

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

Misumi, I.

Monzón, J. J.

Možina, J.

Pisani, M.

Požar, T.

Rerucha, S.

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

Sánchez-Soto, L. L.

Sarbort, M.

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

Shen, R.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Tan, J.

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

P. Hu, J. Zhu, X. Zhai, and J. Tan, “DC-offset-free homodyne interferometer and its nonlinearity compensation,” Opt. Express 23(7), 8399–8408 (2015).
[Crossref] [PubMed]

Wang, C.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Yu, M.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Zhai, X.

Zhang, X.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Zhu, J.

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

P. Hu, J. Zhu, X. Zhai, and J. Tan, “DC-offset-free homodyne interferometer and its nonlinearity compensation,” Opt. Express 23(7), 8399–8408 (2015).
[Crossref] [PubMed]

Appl. Opt. (3)

Meas. Sci. Technol. (2)

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

T. Eom, J. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12(10), 1734–1738 (2001).
[Crossref]

Opt. Express (5)

Sensors (Basel) (2)

S. Rerucha, Z. Buchta, M. Sarbort, J. Lazar, and O. Cip, “Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry,” Sensors (Basel) 12(12), 14095–14112 (2012).
[Crossref] [PubMed]

P. Hu, J. Zhu, X. Guo, and J. Tan, “Compensation for the variable cyclic error in homodyne laser interferometers,” Sensors (Basel) 15(2), 3090–3106 (2015).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of HQLI (top view). Optical Faraday Isolator (OFI), Quarter Wave Plate (QWP), Half Wave Plate (HWP), Non-polarizing Beam Splitter (NBS), Reference Mirror (RM), Target Mirror (TM), Piezoelectric Transducer (PZT), Wollaston Prism (WP), Photodiode (PD).
Fig. 2
Fig. 2 (a) NBS structure and beam-splitting cases with beam entering through (b) face A, (c) face B, (d) face C, and (e) face D.
Fig. 3
Fig. 3 Experimental setup for determining Jones matrices of NBS. Detection Module (DM).
Fig. 4
Fig. 4 Quadrature phase error introduced by wave plate angle deviation. When one wave plate’s angular deviation was analyzed, those of the other two wave plates were set to zero.
Fig. 5
Fig. 5 Views of zero-order wave plate: (a) 3-D view of wave plate; (b) optical path of wave plate when yawing. Optical Axis (OA), ordinary light (o light), extraordinary light (e light).
Fig. 6
Fig. 6 Phase retardation after yawing: (a) HWP; (b) QWP.
Fig. 7
Fig. 7 Quadrature phase errors introduced by angular deviations of wave plates after yawing HWP and QWP1. When one wave plate’s angular deviation was analyzed, those of the other two wave plates were set to zero. “Before” and “After” indicate “before yawing” and “after yawing,” respectively.
Fig. 8
Fig. 8 Procedure used to improve HQLI robustness.
Fig. 9
Fig. 9 Experimentally measured quadrature phase errors vs. wave plate optical axis angles after assembly for (a) HWP, (b) QWP1, and (c) QWP2.
Fig. 10
Fig. 10 Cyclic nonlinearity error after applying proposed method of achieving robustness.

Tables (1)

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Table 1 Transmission and reflection Jones matrices of NBS shown in Fig. 1.

Equations (11)

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I n = A 0 sin[δ+(n1) π 2 ]+Q,n=14,
I x =2 A 0 sinδ and I y =2 A 0 cosδ.
u(t)= λ 4π ( arctan I x I y +mπ ),m=0,±1,±2,.
B T = 2 2 [ 1 0 0 1 ] and B R = 2 2 [ 1 0 0 1 ],
B Ti =[ t pi 0 0 t si e i τ i ] and B Ri =[ r pi 0 0 r si e i δ i ], i=A,B,C,D,
a= I o b= I e | I min | | I max | = a 2 + b 2 a 4 + b 4 +2 a 2 b 2 cos( 2 δ 0 ) a 2 + b 2 + a 4 + b 4 +2 a 2 b 2 cos( 2 δ 0 ) .
[ Ε x t Ε y t ]= B TA [ Ε x Ε y ], [ Ε x r Ε y r ]= B RA [ Ε x Ε y ]
I 1 = I 0 8 ( 1+cosδ ) I 2 = I 0 8 ( 1+cos( δ+MR ) ) I 3 = I 0 16 ( 2+sinM+sinR+cosδ+cos( δ+MR )+sin( δ+M )sin( δR ) ), I 4 = I 0 16 ( 2sinMsinR+cosδ+cos( δ+MR )sin( δ+M )+sin( δR ) )
Γ H = 199 and Γ Q = 119.2 .
Γ= 2π λ | n o n e || d 1 d 2 |,
Γ = 2π λ | n o 2 d 1 n o 2 sin 2 β + n t 2 d 2 n t 2 sin 2 β n e 2 d 1 n e 2 sin 2 β n o 2 d 2 n o 2 sin 2 β |,

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