Abstract

An instrument for angle measurement based on laser feedback has been designed. The measurement technique is based on the principle that when a wave plate placed into a feedback cavity rotates, its phase retardation varies. Phase retardation is a function of the rotating angle of the wave plate. Hence, the angle can be converted to phase retardation. The phase retardation is measured at certain characteristic points identified in the laser outputting curve that are then modulated by laser feedback. The angle of a rotating object can be measured if it is connected to the wave plate. The main advantages of this instrument are: high resolution, compact, flexible, low cost, effective power, and fast response.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2012

W. X. Chen, H. H. Li, S. L. Zhang, and X. W. Long, “Measurement of phase retardation of waveplate online based on laser feedback,” Rev. Sci. Instrum.83(1), 013101 (2012).
[CrossRef] [PubMed]

W. X. Chen, S. L. Zhang, and X. W. Long, “Internal stress measurement by laser feedback method,” Opt. Lett.37(13), 2433–2435 (2012).
[CrossRef] [PubMed]

2009

2008

2007

2006

2005

2003

2001

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

K. S. Dharmsaktu, A. Kumar, and K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTio3 crystal,” Opt. Lasers Eng.36(4), 331–344 (2001).
[CrossRef]

1998

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

1996

1995

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31(1), 113–119 (1995).
[CrossRef]

1992

R. S. Sirohi, A. R. Ganesan, and B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol.24(5), 257–261 (1992).
[CrossRef]

P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt.31(28), 6047–6055 (1992).
[CrossRef] [PubMed]

1989

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

1986

1984

G. G. Luther, R. D. Deslattes, and W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum.55(5), 747–750 (1984).
[CrossRef]

1983

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum.54(12), 1648–1652 (1983).
[CrossRef]

1982

Y. Koboyashi, Yamamoto, and M. Ito, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron.18(4), 582–595 (1982).

1963

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci.17, 180–182 (1963).

Bellon, L.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun.280(1), 1–9 (2007).
[CrossRef]

Chen, W. X.

W. X. Chen, H. H. Li, S. L. Zhang, and X. W. Long, “Measurement of phase retardation of waveplate online based on laser feedback,” Rev. Sci. Instrum.83(1), 013101 (2012).
[CrossRef] [PubMed]

W. X. Chen, S. L. Zhang, and X. W. Long, “Internal stress measurement by laser feedback method,” Opt. Lett.37(13), 2433–2435 (2012).
[CrossRef] [PubMed]

Chung, P. S.

Cui, L.

Deslattes, R. D.

G. G. Luther, R. D. Deslattes, and W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum.55(5), 747–750 (1984).
[CrossRef]

Dharmsaktu, K. S.

K. S. Dharmsaktu, A. Kumar, and K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTio3 crystal,” Opt. Lasers Eng.36(4), 331–344 (2001).
[CrossRef]

Donati, S.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31(1), 113–119 (1995).
[CrossRef]

Du, W.

Ganesan, A. R.

R. S. Sirohi, A. R. Ganesan, and B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol.24(5), 257–261 (1992).
[CrossRef]

Ge, Z.

Giuliani, G.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31(1), 113–119 (1995).
[CrossRef]

Greivenkamp, J. E.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

Huang, P. S.

Hussain, G.

Ikeda, H.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

Ikram, M.

Ito, M.

Y. Koboyashi, Yamamoto, and M. Ito, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron.18(4), 582–595 (1982).

Jin, G.

Kamada, O.

King, P. G. R.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci.17, 180–182 (1963).

Kiyono, S.

Koboyashi, Y.

Y. Koboyashi, Yamamoto, and M. Ito, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron.18(4), 582–595 (1982).

Kumar, A.

K. S. Dharmsaktu, A. Kumar, and K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTio3 crystal,” Opt. Lasers Eng.36(4), 331–344 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

Li, D.

Li, H. H.

W. X. Chen, H. H. Li, S. L. Zhang, and X. W. Long, “Measurement of phase retardation of waveplate online based on laser feedback,” Rev. Sci. Instrum.83(1), 013101 (2012).
[CrossRef] [PubMed]

Li, S.

Li, Y.

Long, X. W.

W. X. Chen, H. H. Li, S. L. Zhang, and X. W. Long, “Measurement of phase retardation of waveplate online based on laser feedback,” Rev. Sci. Instrum.83(1), 013101 (2012).
[CrossRef] [PubMed]

W. X. Chen, S. L. Zhang, and X. W. Long, “Internal stress measurement by laser feedback method,” Opt. Lett.37(13), 2433–2435 (2012).
[CrossRef] [PubMed]

Luther, G. G.

G. G. Luther, R. D. Deslattes, and W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum.55(5), 747–750 (1984).
[CrossRef]

Mao, W.

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31(1), 113–119 (1995).
[CrossRef]

Murata, K.

Naito, H.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

Nakamura, H.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

Nakano, Y.

Paolino, P.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun.280(1), 1–9 (2007).
[CrossRef]

Pati, G. S.

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

Roos, P. A.

Sasaki, O.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

Schuda, F. J.

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum.54(12), 1648–1652 (1983).
[CrossRef]

Shinohara, S.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

Singh, K.

K. S. Dharmsaktu, A. Kumar, and K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTio3 crystal,” Opt. Lasers Eng.36(4), 331–344 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, A. R. Ganesan, and B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol.24(5), 257–261 (1992).
[CrossRef]

Stephens, M.

Steward, G. J.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci.17, 180–182 (1963).

Sumi, M.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

Suzuki, T.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

Takeda, M.

Tan, B. C.

R. S. Sirohi, A. R. Ganesan, and B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol.24(5), 257–261 (1992).
[CrossRef]

Tan, Y. D.

Towler, W. R.

G. G. Luther, R. D. Deslattes, and W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum.55(5), 747–750 (1984).
[CrossRef]

Tripathi, R.

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

Wan, X. J.

Wen, F. J.

Wieman, C. E.

Xu, Z. G.

Yamamoto,

Y. Koboyashi, Yamamoto, and M. Ito, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron.18(4), 582–595 (1982).

Yang, C.

Yoshida, H.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

Zhang, E.

Zhang, S.

Zhang, S. L.

Zhang, Y. N.

Appl. Opt.

IEEE J. Quantum Electron.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31(1), 113–119 (1995).
[CrossRef]

Y. Koboyashi, Yamamoto, and M. Ito, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron.18(4), 582–595 (1982).

IEEE Trans. Instrum. Meas.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas.38(2), 574–577 (1989).
[CrossRef]

New Sci.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci.17, 180–182 (1963).

Opt. Commun.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun.280(1), 1–9 (2007).
[CrossRef]

Opt. Eng.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, “Small-rotating-angle measurement using an imaging method,” Opt. Eng.40(3), 426–432 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, and K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng.37(11), 2988–2997 (1998).
[CrossRef]

Opt. Express

Opt. Laser Technol.

R. S. Sirohi, A. R. Ganesan, and B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol.24(5), 257–261 (1992).
[CrossRef]

Opt. Lasers Eng.

K. S. Dharmsaktu, A. Kumar, and K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTio3 crystal,” Opt. Lasers Eng.36(4), 331–344 (2001).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

W. X. Chen, H. H. Li, S. L. Zhang, and X. W. Long, “Measurement of phase retardation of waveplate online based on laser feedback,” Rev. Sci. Instrum.83(1), 013101 (2012).
[CrossRef] [PubMed]

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum.54(12), 1648–1652 (1983).
[CrossRef]

G. G. Luther, R. D. Deslattes, and W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum.55(5), 747–750 (1984).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Setup for angle measurement. D, photo detector; S, wave plate; θ: rotating angle; M1, M2, high reflectors; ME, feedback mirror; PZT, piezoelectric transducer; AMP, voltage amplification; DA, digital–to–analog conversion; AD, analog–to–digital conversion.

Fig. 2
Fig. 2

Phenomenon of laser intensity transfer.

Fig. 3
Fig. 3

Relationship between phase retardation and polarization flipping point.

Fig. 4
Fig. 4

Phase retardation depending thickness and refractive index.

Fig. 5
Fig. 5

Schematic of optical interference of wave plate.

Fig. 6
Fig. 6

Experimental results of angle dependent phase retardation.

Equations (8)

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

δ=( t BC t AD + t FG t EH )× 90 o
δ 1 = 2πd λ [ ( n e e cos θ e n o o cos θ o )+( tan θ o tan θ e )sinθ( n e n o ) ]+ δ 0 ,
n o o = n o , n e e = n 2 o n 2 e +( n 2 o n 2 e ) sin 2 θ n 2 o ,
n o o sin( θ o )=sinθ, n e e sin( θ e )=sinθ,
n oo = n o , n ee = [ cos 2 ( θ e ) n e 2 + sin 2 ( θ e ) n o 2 ] 1/2 ,
r oab = sin(θ θ o ) sin(θ+ θ o ) , r eab = tg(θ θ e ) tg(θ+ θ e ) , r oba = sin(θ θ o ) sin(θ+ θ o ) , r eba = tg(θ θ e ) tg(θ+ θ e ) , t oab = 2sin( θ o )cosθ sin(θ+ θ o ) , t eab = 2sin( θ e )cosθ sin(θ+ θ e )cos(θ θ e ) , t oba = 2sinθcos θ o sin(θ+ θ o ) , t eba = 2sinθcos θ e sin(θ+ θ e )cos(θ θ e ) ,
E oo = E ' oo e (jωt φ o ) = E o t oab t oba exp( ik n oo d cos( θ o ) )[ 1+ r oba exp( 2ik n oo dcos( θ o ) ) ], E ee = E ' ee e (jωt φ e ) = E e t eab t eba exp( ik n ee d cos( θ e ) )[ 1+ r eba exp( 2ik n ee dcos( θ e ) ) ], δ 2 = φ e φ o ,
δ= δ 2 + δ 1 = φ e φ o + 2d λ [ ( n ee cos θ e n oo cos θ o )+( tan θ o tan θ e )sinθ( n e n o ) ],

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