Abstract

The simultaneous and independent measurements of in-plane and out-of-plane displacements are significant issues to be solved in research. Here a novel system to realize single-spot two-dimensional (2D) displacement measurement of a noncooperative target is reported. The performance of the system is tested in the displacement measurement of an aluminum target with a rough surface. 2D random movement and 2D movement with different parameters of Lissajous figures are measured by the system. The ranges of the 2D displacement measurement reach 500 μm and the accuracies reach the submicron scale. The resolutions of the two dimensions are all better than 5 nm. The measurement system is based on laser heterodyne self-mixing interferometry with frequency multiplexing, which has advantages such as noncontact, nondestruction, nanometer-scale resolution and high sensitivity. The method is promising to be applied in 2D deformation tests of materials, 2D rotor vibration measurement, 2D positioning of particles, thermal expansion coefficient measurement, and other applications.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (7)

S. Donati, D. Rossi, and M. Norgia, “Single channel self-mixing interferometer measures simultaneously displacement and tilt and yaw angles of a reflective target,” IEEE J. Quantum Electron. 51, 1–8 (2015).
[Crossref]

K. Otsuka, “Self-mixing thin-slice solid-state laser Doppler velocimetry with much less than one feedback photon per Doppler cycle,” Opt. Lett. 40, 4603–4606 (2015).
[Crossref]

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

W. Wang, S. Zhang, and Y. Li, “Surface microstructure profilometry based on laser confocal feedback,” Rev. Sci. Instrum. 86, 103108 (2015).
[Crossref]

A. Safrani and I. Abdulhalim, “High-speed 3D imaging using two-wavelength parallel-phase-shift interferometry,” Opt. Lett. 40, 4651–4654 (2015).
[Crossref]

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: A tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photon. 7, 570–631 (2015).
[Crossref]

2014 (2)

2013 (1)

Y. Tan, W. Wang, C. Xu, and S. Zhang, “Laser confocal feedback tomography and nano-step height measurement,” Sci. Rep. 3, 2971 (2013).
[Crossref]

2012 (1)

2011 (1)

2009 (1)

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

2007 (1)

2006 (1)

1963 (1)

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 14 (1963).

Abdulhalim, I.

Berkovic, G.

Bertling, K.

Bhaduri, B.

Bosch, T.

Chen, J. C.

Czarske, J.

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

De Oliveira, I.

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Donati, S.

S. Donati, D. Rossi, and M. Norgia, “Single channel self-mixing interferometer measures simultaneously displacement and tilt and yaw angles of a reflective target,” IEEE J. Quantum Electron. 51, 1–8 (2015).
[Crossref]

Edwards, C.

Georges, M. P.

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Goddard, L. L.

Günther, P.

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

Guo, D.

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Hao, H.

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Hsieh, H. L.

Iwata, K.

Kikuta, H.

King, P. G. R.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 14 (1963).

Lee, J. Y.

Lerondel, G.

Li, D.

Li, Y.

W. Wang, S. Zhang, and Y. Li, “Surface microstructure profilometry based on laser confocal feedback,” Rev. Sci. Instrum. 86, 103108 (2015).
[Crossref]

Lim, Y. L.

Liu, Q.

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Medjahed, A.

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Nguyen, T. H.

Nikolic, M.

Norgia, M.

S. Donati, D. Rossi, and M. Norgia, “Single channel self-mixing interferometer measures simultaneously displacement and tilt and yaw angles of a reflective target,” IEEE J. Quantum Electron. 51, 1–8 (2015).
[Crossref]

Nöthen, M.

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

Otsuka, K.

Pan, B.

Park, C. S.

Pfister, T.

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

Pham, H.

Popescu, G.

Rakic, A. D.

Rossi, D.

S. Donati, D. Rossi, and M. Norgia, “Single channel self-mixing interferometer measures simultaneously displacement and tilt and yaw angles of a reflective target,” IEEE J. Quantum Electron. 51, 1–8 (2015).
[Crossref]

Safrani, A.

Shafir, E.

Shibuya, A.

Steward, G. J.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 14 (1963).

Sun, L.

Taimre, T.

Tan, Y.

S. Zhang, S. Zhang, Y. Tan, and L. Sun, “Common-path heterodyne self-mixing interferometry with polarization and frequency multiplexing,” Opt. Lett. 41, 4827–4830 (2016).
[Crossref]

Y. Tan, W. Wang, C. Xu, and S. Zhang, “Laser confocal feedback tomography and nano-step height measurement,” Sci. Rep. 3, 2971 (2013).
[Crossref]

Tao, Y.

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Vandenrijt, J. F.

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Wan, X.

Wang, M.

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Wang, W.

W. Wang, S. Zhang, and Y. Li, “Surface microstructure profilometry based on laser confocal feedback,” Rev. Sci. Instrum. 86, 103108 (2015).
[Crossref]

Y. Tan, W. Wang, C. Xu, and S. Zhang, “Laser confocal feedback tomography and nano-step height measurement,” Sci. Rep. 3, 2971 (2013).
[Crossref]

Xu, C.

Y. Tan, W. Wang, C. Xu, and S. Zhang, “Laser confocal feedback tomography and nano-step height measurement,” Sci. Rep. 3, 2971 (2013).
[Crossref]

Yan, H.

Zemmamouche, R.

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Zhang, J.

Zhang, S.

Zhou, R.

Adv. Opt. Photon. (3)

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

S. Donati, D. Rossi, and M. Norgia, “Single channel self-mixing interferometer measures simultaneously displacement and tilt and yaw angles of a reflective target,” IEEE J. Quantum Electron. 51, 1–8 (2015).
[Crossref]

Meas. Sci. Technol. (1)

T. Pfister, P. Günther, M. Nöthen, and J. Czarske, “Heterodyne laser Doppler distance sensor with phase coding measuring stationary as well as laterally and axially moving objects,” Meas. Sci. Technol. 21, 025302 (2009).
[Crossref]

New Sci. (1)

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 14 (1963).

Opt. Commun. (1)

Y. Tao, M. Wang, D. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340, 141–150 (2015).
[Crossref]

Opt. Eng. (1)

R. Zemmamouche, J. F. Vandenrijt, A. Medjahed, I. De Oliveira, and M. P. Georges, “Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry,” Opt. Eng. 54, 084110 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Rev. Sci. Instrum. (1)

W. Wang, S. Zhang, and Y. Li, “Surface microstructure profilometry based on laser confocal feedback,” Rev. Sci. Instrum. 86, 103108 (2015).
[Crossref]

Sci. Rep. (1)

Y. Tan, W. Wang, C. Xu, and S. Zhang, “Laser confocal feedback tomography and nano-step height measurement,” Sci. Rep. 3, 2971 (2013).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the experimental set up. ML is the microchip laser; BS 1 , BS 2 , and BS 3 are the beam splitters; L is the optical lens; AOM 1 , AOM 2 , and AOM 3 are the acousto-optic modulators; R 1 , R 2 , R 3 , and R 4 , are reflectors; Iso is the optical isolator; T is the target; and PD is the photodetector.
Fig. 2.
Fig. 2. Schematic diagram of the optical path. S in is the in-plane displacement; S out is the out-of-plane displacement; B 1 , B 2 are the measuring beams; B 3 is the scattering beam; θ 1 is the angle between the direction of B 1 and the target’s movement; θ is the angle between the direction of B 1 and B 3 ; θ is the angle between the direction of B 2 and B 3 ; and S isthe incident spot of the two measuring beams.
Fig. 3.
Fig. 3. (a) Results of the calculation θ ; (b) the results of the calculation θ .
Fig. 4.
Fig. 4. Results of the circular Lissajous figures. The blue dashed line is the experiment; the red circular mark line is the simulation.
Fig. 5.
Fig. 5. Schematic of the mechanical set up. X is the axis of the in-plane displacement; Y is the axis of the out-of-plane displacement; X1 is the axis of Stage_1; and Y1 is the axis of Stage_2.
Fig. 6.
Fig. 6. Results of the circular Lissajous figures. The blue dashed line is the experiment; the red circular mark line is the modified simulation.
Fig. 7.
Fig. 7. Results of the radial error.
Fig. 8.
Fig. 8. Results of various Lissajous figures. The blue dashed line is the experiment; the red circular mark line is the simulation; (a)  f x = f y , φ y φ x = π / 4 , A = 5    μm ; (b)  f x = f y , φ y φ x = π / 4 , A = 240    μm ; (c)  f x = f y , φ y = φ x , A = 5    μm ; (d)  f x = f y , φ y = φ x , A = 240    μm ; (e)  f x : f y = 2 : 1 , φ y φ x = π / 2 , A = 5    μm ; and (f)  f x : f y = 2 : 1 , φ y φ x = π / 2 , A = 240    μm .
Fig. 9.
Fig. 9. Results of the random motion. The blue dashed line is the experiment; the red circular mark is the simulation.
Fig. 10.
Fig. 10. Results of the step test experiment.

Equations (17)

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Δ I 1 ( Ω 1 ) I s = κ 1 G ( Ω 1 ) cos ( Ω 1 t + φ 1 + ϕ 1 ) , Δ I 2 ( Ω 2 ) I s = κ 2 G ( Ω 2 ) cos ( Ω 2 t + φ 2 + ϕ 2 ) ,
f 1 = f 1 1 + v / c cos ( θ 1 ) 1 v / c cos ( θ 1 + θ ) , f 2 = f 2 1 + v / c cos ( θ 1 + θ + θ ) 1 v / c cos ( θ 1 + θ ) ,
Δ f 1 = f 1 f 1 = f 1 v c ( cos θ 1 + cos ( θ 1 + θ ) ) , Δ f 2 = f 2 f 2 = f 2 v c ( cos ( θ 1 + θ + θ ) + cos ( θ 1 + θ ) ) .
Δ f 1 d t = 1 2 π Δ ω 1 d t = 1 2 π φ 1 , Δ f 2 d t = 1 2 π Δ ω 2 d t = 1 2 π φ 2 .
φ 1 = 2 π λ S ( cos θ 1 + cos ( θ 1 + θ ) ) , φ 2 = 2 π λ S ( cos ( θ 1 + θ + θ ) + cos ( θ 1 + θ ) ) .
0 t v d t = S , 0 t v sin ( θ 1 + θ ) d t = S in , 0 t v cos ( θ 1 + θ ) d t = S out .
S in = λ 2 π · φ 1 ( 1 + cos θ ) φ 2 ( 1 + cos θ ) sin θ + sin θ + sin ( θ + θ ) , S out = λ 2 π · φ 1 sin θ + φ 2 sin θ sin θ + sin θ + sin ( θ + θ ) .
φ 1 = 2 π λ S in sin θ , φ 2 = 2 π λ S in sin θ .
x = A sin ( 2 π f x + φ x ) = 10 sin ( 2 π f ) , y = A sin ( 2 π f y + φ y ) = 10 sin ( 2 π f + π / 2 ) .
α = arctan ( S out S in ) 87.02 ° .
x 1 = 10 sin ( 2 π f ) , y 1 = 10 sin ( 2 π f + π / 2 ) , x = x 1 + y 1 · cos ( α ) , y = y 1 · sin ( α ) .
x = ρ cos θ , y = ρ sin θ .
( ρ cos θ ρ sin θ / tan α ) 2 + ( ρ sin θ / sin α ) 2 = 10 2 .
σ = 1 N 1 N ( r r ) 2 = 0.0671    μm ,
f D 1 = v λ sin θ , f D 2 = v λ sin θ .
f D 1 = v λ ( 1 cos θ ) , f D 2 = v λ ( 1 cos θ ) .
v max _ in = min { | f D λ sin θ | , | f D λ sin θ | } 4.55    mm / s , v max _ out = min { | f D λ 1 cos θ | , | f D λ 1 cos θ | } 0.54    mm / s .

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