Abstract

A new, to the best of our knowledge, method for the measurement of the absolute distance of a remote target based on the laser diode self-mixing interferometry is presented. A double-modulation technique is introduced to improve the measurement resolution. Wavelength modulation of the laser beam is obtained by modulating the injection current of the laser diode. Phase modulation of the laser beam is obtained by an electro-optic crystal in the external cavity. Absolute distance of the external target is determined by the Fourier analysis method. Theoretical analysis and numerical simulations are given. Experimental results show that a resolution of ±0.3  mm can be achieved for absolute distance ranging from 277 to 477  mm.

© 2007 Optical Society of America

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References

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  1. M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
    [CrossRef]
  2. J. A. Stone, A. Stejskal, and L. Howard, "Absolute interferometry with a 670 nm external cavity diode laser," Appl. Opt. 38, 5981-5994 (1999).
    [CrossRef]
  3. T. Kinder and K.-D. Salewski, "Absolute distance interferometer with grating-stabilized tunable laser at 633 nm," J. Opt. A , Pure Appl. Opt. 4, S364-S368 (2002).
    [CrossRef]
  4. G. Beheim and K. Fritch, "Range finding using frequency-modulated laser diode," Appl. Opt. 25, 1439-1442 (1986).
    [CrossRef] [PubMed]
  5. F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
    [CrossRef]
  6. M. Wang and G. Lai, "Displacement measurement based on Fourier transform method with external cavity modulation," Rev. Sci. Instrum. 72, 3440-3445 (2001).
    [CrossRef]
  7. S. Donati and M. Sorel, "A phase-modulated feedback method for testing optical isolators assembled into the laser diode package," IEEE. Photon. Technol. Lett. 8, 405-407 (1996).
    [CrossRef]
  8. T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
    [CrossRef]

2002 (1)

T. Kinder and K.-D. Salewski, "Absolute distance interferometer with grating-stabilized tunable laser at 633 nm," J. Opt. A , Pure Appl. Opt. 4, S364-S368 (2002).
[CrossRef]

2001 (2)

M. Wang and G. Lai, "Displacement measurement based on Fourier transform method with external cavity modulation," Rev. Sci. Instrum. 72, 3440-3445 (2001).
[CrossRef]

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

1999 (1)

1998 (2)

F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
[CrossRef]

T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
[CrossRef]

1996 (1)

S. Donati and M. Sorel, "A phase-modulated feedback method for testing optical isolators assembled into the laser diode package," IEEE. Photon. Technol. Lett. 8, 405-407 (1996).
[CrossRef]

1986 (1)

Allgeier, T.

T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
[CrossRef]

Amann, M. C.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

Beheim, G.

Bosch, T.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
[CrossRef]

Donati, S.

S. Donati and M. Sorel, "A phase-modulated feedback method for testing optical isolators assembled into the laser diode package," IEEE. Photon. Technol. Lett. 8, 405-407 (1996).
[CrossRef]

Fritch, K.

Gouaux, F.

Hofler, H.

T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
[CrossRef]

Howard, L.

Kinder, T.

T. Kinder and K.-D. Salewski, "Absolute distance interferometer with grating-stabilized tunable laser at 633 nm," J. Opt. A , Pure Appl. Opt. 4, S364-S368 (2002).
[CrossRef]

Lai, G.

M. Wang and G. Lai, "Displacement measurement based on Fourier transform method with external cavity modulation," Rev. Sci. Instrum. 72, 3440-3445 (2001).
[CrossRef]

Lescure, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

Myllyla, R.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

Rioux, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

Salewski, K.-D.

T. Kinder and K.-D. Salewski, "Absolute distance interferometer with grating-stabilized tunable laser at 633 nm," J. Opt. A , Pure Appl. Opt. 4, S364-S368 (2002).
[CrossRef]

Servagent, N.

Sorel, M.

S. Donati and M. Sorel, "A phase-modulated feedback method for testing optical isolators assembled into the laser diode package," IEEE. Photon. Technol. Lett. 8, 405-407 (1996).
[CrossRef]

Stejskal, A.

Stone, J. A.

Wagner, E.

T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
[CrossRef]

Wang, M.

M. Wang and G. Lai, "Displacement measurement based on Fourier transform method with external cavity modulation," Rev. Sci. Instrum. 72, 3440-3445 (2001).
[CrossRef]

Appl. Opt. (3)

IEEE. Photon. Technol. Lett. (1)

S. Donati and M. Sorel, "A phase-modulated feedback method for testing optical isolators assembled into the laser diode package," IEEE. Photon. Technol. Lett. 8, 405-407 (1996).
[CrossRef]

J. Opt. A (1)

T. Kinder and K.-D. Salewski, "Absolute distance interferometer with grating-stabilized tunable laser at 633 nm," J. Opt. A , Pure Appl. Opt. 4, S364-S368 (2002).
[CrossRef]

Opt. Eng. (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, "Laser ranging: a critical review of usual technique for distance measurement," Opt. Eng. 40, 10-19 (2001).
[CrossRef]

Proc. SPIE (1)

T. Allgeier, H. Hofler, and E. Wagner, "High precision length measurement by means of multisensory laser feedback interferometry," in Third International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE 3411, 85-91 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Wang and G. Lai, "Displacement measurement based on Fourier transform method with external cavity modulation," Rev. Sci. Instrum. 72, 3440-3445 (2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) LD with an external cavity. (b) Equivalent model.

Fig. 2
Fig. 2

Plots of the Bessel functions J 1 ( 2 b ) (solid curve) and J 2 ( 2 b ) (dashed curve) with respect to b.

Fig. 3
Fig. 3

(a) Double sinusoidal modulating SMI signal. (b) Fourier spectra of the SMI signal. (c) Calculated phase (wrapping). (d) Extracted phase (unwrapped).

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

(a) Detected d SMI signal with double modulation. (b) Fourier spectra of the detected signal. (c) Demodulated phase (wrapping). (d) Reconstructed phase (unwrapping).

Fig. 6
Fig. 6

Distance measurements result.

Fig. 7
Fig. 7

Measurement error.

Fig. 8
Fig. 8

Relationship between δ ϕ / δ b and b.

Equations (18)

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υ 0 υ = C 2 π t L   sin ( 2 π υ t + arctan   α ) ,
I = I 0 [ 1 + m F ( ϕ ) ] = I 0 [ 1 + m   cos ( 4 π υ L / c ) ] ,
m = 2 l / K ζ ,
C = t L t l ζ 1 + α 2 .
h ( t ) = h 0 + p a   sin ( ω a t + θ ) ,
λ ( t ) = λ 0 + Δ λ ( t ) = λ 0 + q a   sin ( ω a t + θ ) ,
S ( t ) = h ( t ) [ 1 + m   cos   ϕ ( t ) ] ,
ϕ ( t ) = 4 π L λ 0 + Δ λ 4 π L λ 0 Δ λ ( t ) 4 π L λ 0 2 ϕ 0 H   sin ( ω a t + θ ) ,
H = λ 0 2 / 4 π L q a .
ψ ( t ) = b   sin ( ω m t + β ) ,
S ( t ) = h ( t ) + h ( t ) m   cos [ ϕ ( t ) + 2 b   sin ( ω m t + β ) ] .
S ( ω m , t ) = 2 m h ( t ) J 1 ( 2 b ) sin   ϕ ( t ) sin ( ω m t + β ) = A 1 ( t ) sin ( ω m t + β ) ,
S ( 2 ω m , t ) = 2 m h ( t ) J 2 ( 2 b ) cos   ϕ ( t ) cos ( 2 ω m t + 2 β ) = A 2 ( t ) cos ( 2 ω m t + 2 β ) ,
ϕ ( t ) = arctan [ A 1 ( t ) J 2 ( 2 b ) A 2 ( t ) J 1 ( 2 b ) ] .
A 1 ( t ) = Im [ I f m ( t ) / e j ( ω m t + β ) ] ,
A 2 ( t ) = Re [ I 2 f m ( t ) / e j ( 2 ω m + 2 β ) ] .
ϕ = arctan [ A J ] .
δ ϕ / δ b = 1 ( 1 + A 2 J 2 ) δ J / δ b .

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