Abstract

A simple and high-accuracy self-mixing interferometer based on single high-order orthogonally polarized feedback effects is presented. The single high-order feedback effect is realized when dual-frequency laser reflects numerous times in a Fabry-Perot cavity and then goes back to the laser resonator along the same route. In this case, two orthogonally polarized feedback fringes with nanoscale resolution are obtained. This self-mixing interferometer has the advantages of higher sensitivity to weak signal than that of conventional interferometer. In addition, two orthogonally polarized fringes are useful for discriminating the moving direction of measured object. The experiment of measuring 2.5nm step is conducted, which shows a great potential in nanometrology.

© 2015 Optical Society of America

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References

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    [Crossref]
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2014 (1)

S. Sudo and K. Otsuka, “Measurements of liquid surface fluctuations using a self-mixing solid-state laser,” J. Appl. Phys. 115(23), 233103 (2014).
[Crossref]

2013 (1)

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

2012 (1)

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

2010 (1)

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (1)

H. J. Kimble, B. L. Lev, and J. Ye, “Optical interferometers with reduced sensitivity to thermal noise,” Phys. Rev. Lett. 101(26), 260602 (2008).
[Crossref] [PubMed]

2006 (1)

2002 (3)

1981 (1)

Ahn, J.

Boisen, A.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Cai, X.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

David, C.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

Deng, J.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Donath, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

Du, Z.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Dubovitsky, S.

Greve, A.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Heydemann, P. L. M.

Huang, W.

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

Huang, Y.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Hvam, J. M.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Kang, C. S.

Kim, J. A.

Kim, J. W.

Kim, S.

Kimble, H. J.

H. J. Kimble, B. L. Lev, and J. Ye, “Optical interferometers with reduced sensitivity to thermal noise,” Phys. Rev. Lett. 101(26), 260602 (2008).
[Crossref] [PubMed]

Larsson, D.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Lay, O. P.

Lev, B. L.

H. J. Kimble, B. L. Lev, and J. Ye, “Optical interferometers with reduced sensitivity to thermal noise,” Phys. Rev. Lett. 101(26), 260602 (2008).
[Crossref] [PubMed]

Lu, L.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Luo, X.

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

Mao, W.

Otsuka, K.

S. Sudo and K. Otsuka, “Measurements of liquid surface fluctuations using a self-mixing solid-state laser,” J. Appl. Phys. 115(23), 233103 (2014).
[Crossref]

Peggs, G. N.

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys Eng Sci 360(1794), 953–968 (2002).
[Crossref] [PubMed]

Rutishauser, S.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

Seidel, D. J.

Sudo, S.

S. Sudo and K. Otsuka, “Measurements of liquid surface fluctuations using a self-mixing solid-state laser,” J. Appl. Phys. 115(23), 233103 (2014).
[Crossref]

Tan, Y.

Wang, L.

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

Wang, X.

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

Yacoot, A.

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys Eng Sci 360(1794), 953–968 (2002).
[Crossref] [PubMed]

Ye, J.

H. J. Kimble, B. L. Lev, and J. Ye, “Optical interferometers with reduced sensitivity to thermal noise,” Phys. Rev. Lett. 101(26), 260602 (2008).
[Crossref] [PubMed]

Yu, B.

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Yvind, K.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Zanette, I.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

Zhang, S.

Zhang, Y.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

IEEE Photonics J. (1)

L. Wang, X. Luo, X. Wang, and W. Huang, “Obtaining high fringe precision in self-mixing interference using a simple external reflecting mirror,” IEEE Photonics J. 5(3), 6500207 (2013).
[Crossref]

J. Appl. Phys. (2)

S. Sudo and K. Otsuka, “Measurements of liquid surface fluctuations using a self-mixing solid-state laser,” J. Appl. Phys. 115(23), 233103 (2014).
[Crossref]

Y. Huang, Z. Du, J. Deng, X. Cai, B. Yu, and L. Lu, “A study of vibration system characteristics based on laser self-mixing interference effect,” J. Appl. Phys. 112(2), 023106 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Philos Trans A Math Phys Eng Sci (1)

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys Eng Sci 360(1794), 953–968 (2002).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional X-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[Crossref] [PubMed]

H. J. Kimble, B. L. Lev, and J. Ye, “Optical interferometers with reduced sensitivity to thermal noise,” Phys. Rev. Lett. 101(26), 260602 (2008).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Schematic of the experimental setup. M1, M2: laser mirrors; ML, MR: mirrors; Q: quartz crystal; PBS: Polarization beam splitter; D1, D2: photoelectric detectors; R: Resistance wire C: electric cabinet; PI: nanometer positioning stage; OS: oscilloscope.
Fig. 2
Fig. 2 Single high-order feedback effects. (a) Photo of light spots in Fabry-Perot feedback cavity, (b)~(d) intensity modulations and phase behaviors in the single high-order feedback.
Fig. 3
Fig. 3 The resolution and zero drifts test results. (a), the measurement result of 2.5 nm step. (b), the zero drifts of SMI in common laboratory.
Fig. 4
Fig. 4 Displacement measurement results. (a), displacement measurement results in 100μm range by SMI. (b), the rms error in the displacement is determined from the difference between a linear least-squares fit and the measurement data.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

QΔa<a
Q(a+Δa)<L<(Q+1)a
b>QΔb
L=[Q(a+Δa)+(Q+1)a]/2
N=Δl/(λ/2)
Δb=N×(λ/2)/[29×(1n×sinαsinβ)]
I o = I o0 + η o cos( ω o 2l c ) I e = I e 0 + η e cos( ω e 2l c )
I o = I o0 { 1+ K 2d N=1 q t 2 2 r 3 N r 2 N2 f N cos( N ω o 2l c ) } I e = I e 0 { 1+ K 2d N=1 q t 2 2 r 3 N r 2 N2 f N cos( N ω e 2l c ) }
f N = s N / π r 2
I o = I o0 { 1+ ε o η o f N cos( q ω o 2L c ) } I e = I e 0 { 1+ ε e η e f N cos( q ω e 2L c ) }

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