Abstract

The principles, experimental apparatus, and advantages of the use of an optical feedback technique for extended displacement measurements based on the use of a dual-diode laser configuration are described. This device is capable of creating a synthetic wavelength from the two lasers simultaneously through the frequency selectivity of the individual lasers, which respond only to their own wavelength. Theoretical analysis and experimental evidence are presented to show the feasibility of the measurement method and the simplicity of its operation.

© 1994 Optical Society of America

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  1. S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser Doppler velocimeter,” Appl. Opt. 25, 1417–1419 (1986).
    [Crossref] [PubMed]
  2. P. J. de Groot, G. M. Gallatin, S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. 27, 4475–4480 (1988).
    [Crossref] [PubMed]
  3. A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
    [Crossref]
  4. W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
    [Crossref]
  5. E. T. Shimizu, “Directional discrimination in the self-mixing type laser Doppler velocimeter,” Appl. Opt. 26, 4541–4544 (1987).
    [Crossref] [PubMed]
  6. W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Fiber-optic Doppler velocimeter that incorporates active optical feedback from a diode laser,” Opt. Lett. 17, 819–821 (1992).
    [Crossref] [PubMed]
  7. W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
    [Crossref] [PubMed]
  8. P. J. de Groot, G. M. Gallatin, “Backscatter-modulation velocimetry with an external cavity laser diode,” Opt. Lett. 14, 165–167 (1989).
    [Crossref] [PubMed]
  9. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [Crossref]
  10. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [Crossref]
  11. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [Crossref] [PubMed]
  12. G. Beheim, “Fiber-optic interferometry using frequency modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
    [Crossref] [PubMed]
  13. A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).
  14. L. Wosinski, M. Breidne, “An in-situ fiber interferometer for measuring quasi-conical diamond-turned surfaces,” in In-Process Optical Measurements and Industrial Methods, P. Langenbeck, H. A. Macleod, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1266, 138–141 (1990).
  15. M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. De Paula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1990).
  16. P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
    [Crossref] [PubMed]
  17. P. de Groot, J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett. 17, 1626–1628 (1992).
    [Crossref] [PubMed]
  18. L. M. Smith, C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28, 3339–3342 (1989).
    [Crossref] [PubMed]
  19. K. Petermann, Laser Diode Modulation and Noise (Kluwer, Dordrecht, The Netherlands, 1991), Chap. 9, pp. 250–290.
  20. O. Sasaki, K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
    [Crossref] [PubMed]

1993 (1)

1992 (2)

1991 (1)

1989 (2)

1988 (3)

1987 (1)

1986 (3)

1984 (1)

1980 (1)

A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
[Crossref]

Beheim, G.

Boyle, W. J. O.

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Fiber-optic Doppler velocimeter that incorporates active optical feedback from a diode laser,” Opt. Lett. 17, 819–821 (1992).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
[Crossref]

Breidne, M.

L. Wosinski, M. Breidne, “An in-situ fiber interferometer for measuring quasi-conical diamond-turned surfaces,” in In-Process Optical Measurements and Industrial Methods, P. Langenbeck, H. A. Macleod, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1266, 138–141 (1990).

Cheng, Y.

Christenson, E.

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. De Paula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1990).

Dandridge, A.

A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
[Crossref]

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).

de Groot, P.

de Groot, P. J.

den Boef, A. J.

Dobson, C. C.

Gallatin, G. M.

Giallorenzi, T. G.

A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
[Crossref]

Grattan, K. T. V.

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Fiber-optic Doppler velocimeter that incorporates active optical feedback from a diode laser,” Opt. Lett. 17, 819–821 (1992).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
[Crossref]

Kersey, A. D.

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).

Macomber, S. H.

McGarvey, J.

Miles, R. O.

A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
[Crossref]

Mochizuki, A.

Palmer, A. W.

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Fiber-optic Doppler velocimeter that incorporates active optical feedback from a diode laser,” Opt. Lett. 17, 819–821 (1992).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
[Crossref]

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise (Kluwer, Dordrecht, The Netherlands, 1991), Chap. 9, pp. 250–290.

Sasaki, O.

Shimizu, E. T.

Shinohara, S.

Smith, L. M.

Sumi, M.

Takahashi, K.

Tucker, M.

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. De Paula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1990).

Wang, W. M.

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Fiber-optic Doppler velocimeter that incorporates active optical feedback from a diode laser,” Opt. Lett. 17, 819–821 (1992).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
[Crossref]

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[Crossref]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[Crossref]

Wosinski, L.

L. Wosinski, M. Breidne, “An in-situ fiber interferometer for measuring quasi-conical diamond-turned surfaces,” in In-Process Optical Measurements and Industrial Methods, P. Langenbeck, H. A. Macleod, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1266, 138–141 (1990).

Wyant, J. C.

Yoshida, H.

Appl. Opt. (10)

S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser Doppler velocimeter,” Appl. Opt. 25, 1417–1419 (1986).
[Crossref] [PubMed]

P. J. de Groot, G. M. Gallatin, S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. 27, 4475–4480 (1988).
[Crossref] [PubMed]

E. T. Shimizu, “Directional discrimination in the self-mixing type laser Doppler velocimeter,” Appl. Opt. 26, 4541–4544 (1987).
[Crossref] [PubMed]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
[Crossref]

Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[Crossref] [PubMed]

G. Beheim, “Fiber-optic interferometry using frequency modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
[Crossref] [PubMed]

P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
[Crossref] [PubMed]

L. M. Smith, C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28, 3339–3342 (1989).
[Crossref] [PubMed]

O. Sasaki, K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
[Crossref] [PubMed]

Electron. Lett. (1)

A. Dandridge, R. O. Miles, T. G. Giallorenzi, “Diode laser sensor,” Electron. Lett. 16, 948–949 (1980).
[Crossref]

J. Appl. Phys. (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[Crossref]

Opt. Lett. (3)

Other (5)

K. Petermann, Laser Diode Modulation and Noise (Kluwer, Dordrecht, The Netherlands, 1991), Chap. 9, pp. 250–290.

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).

L. Wosinski, M. Breidne, “An in-situ fiber interferometer for measuring quasi-conical diamond-turned surfaces,” in In-Process Optical Measurements and Industrial Methods, P. Langenbeck, H. A. Macleod, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1266, 138–141 (1990).

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. De Paula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1990).

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, “An interferometer incorporating active optical feedback from a diode laser with application to vibrational measurement,” in Proceedings of the 8th Optical Fiber Sensors Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Paper 92CH3107, pp. 358–361.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic of a dual-diode laser-based self-mixing interferometer in a free-space configuration: LD1, LD2, diode lasers; λ1, λ2 laser wavelengths; BS, the beam splitter; M1, Mr, mirrors; T, the target reflector; I1 I2, the output intensities; D, the distance between the reference plane and the target surface.

Fig. 2
Fig. 2

Geometry of a four-mirror Fabry–Perot-type cavity laser and its two-mirror Fabry–Perot equivalent.

Fig. 3
Fig. 3

Experimental arrangement for the dual-diode laser-based fiber-optic self-mixing interferometer: A1, A2, ac amplifiers; DC, directional coupler of the optical fiber; DSA, digital storage adapter; D0, displacement to be measured; OS, oscilloscope.

Fig. 4
Fig. 4

Self-mixing interference pattern (upper trace) with target displacement (lower trace).

Fig. 5
Fig. 5

Interference patterns from two diode lasers. The time difference shown between these two outputs gives the phase difference Δϕ.

Fig. 6
Fig. 6

Displacement dependence on the phase difference between the two output signals of the lasers.

Equations (11)

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r 2 ( ν ) = r 2 + ( 1 | r 2 | 2 ) r 3 exp ( j 2 π ν 2 L c ) + ( 1 | r 2 | 2 ) × ( 1 | r 3 | 2 ) r 4 exp [ j 2 π ν 2 ( L + D ) c ] .
r 2 ( ν ) = | r 2 | exp ( j Φ 2 ) .
| r 2 | = r 2 { 1 + ξ 3 cos ( 2 π ν 2 L c ) + ξ 4 cos [ 2 π ν 2 ( L + D ) c ] } ,
ξ 3 = r 3 r 2 ( 1 | r 2 | 2 ) ,
ξ 4 = r 4 r 2 ( 1 | r 2 | 2 ) ( 1 | r 3 | 2 ) ,
Φ 2 = ξ 3 sin ( 2 π ν 2 L c ) + ξ 4 sin [ 2 π ν 2 ( L + D ) c ] .
r 1 r 2 ( ν ) exp [ ( g γ ) d j 2 π ν n d c ] + 1 ,
g th = g 0 ξ 3 d cos ( 4 π ν L c ) ξ 4 d cos ( 4 π ν L + D c ) ,
4 π ( ν ν 0 ) n e d c + ξ 3 1 + α 2 sin ( 4 π ν L c ) + ξ 4 1 + α 2 sin ( 4 π ν L + D c ) = 0 ,
Y i = A i [ 1 + μ i cos ( ϕ i ) + ρ i cos ( 4 π D 0 λ i + ϕ i ) ] ,
Δ ϕ = 4 π ( 1 λ 1 1 λ 2 ) D 0 = 4 π λ 2 λ 1 λ 1 λ 2 D 0 = 4 π 1 λ 12 D 0 ,

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