Abstract

A compact self-aligning laser radar has been constructed for coherent ranging and velocimetry using a laser diode modulated by feedback from light scattered from a diffusing target. The phenomenology of beat-signal generation in the device is discussed from both experimental and theoretical points of view. The ac-coupled modulation waveform is asymmetric (similar to a sawtooth) and different for the two propagation directions of the light leaving the diode. A theoretical model, based on the mode structure of a three-mirror Fabry-Perot cavity, describes signal generation in these experiments and accounts for the asymmetric waveform.

© 1988 Optical Society of America

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References

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  1. K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
    [CrossRef]
  2. J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
    [CrossRef]
  3. C. P. Wang, “Laser Doppler Displacement Measurement,” Lasers Optron. 6, 69 (1987).
  4. M. J. Rudd, “A Laser Doppler Velocimeter Employing the Laser as a Mixer-Oscillator,” J. Phys. E 1, 723, (1968).
    [CrossRef]
  5. J. H. Churnside, “Laser Doppler Velocimetry by Modulating a CO2 Laser with Backscattered Light,” Appl. Opt. 23, 61 (1984).
    [CrossRef] [PubMed]
  6. J. H. Churnside, “Signal-to-Noise in a Backscatter-Modulated Doppler Velocimeter,” Appl. Opt. 23, 2097 (1984).
    [CrossRef] [PubMed]
  7. G. Beheim, K. Fritsch, “Range Finding using Frequency-Modulated Laser Diode,” Appl. Opt. 25, 1439 (1986).
    [CrossRef] [PubMed]
  8. E. T. Shimizu, “Directional Discrimination in the Self-Mixing Type Laser Doppler Velocimeter,” Appl. Opt. 26, 4541 (1987).
    [CrossRef] [PubMed]
  9. T. Kubota, M. Hara, T. Yoshino, “Interferometer for Measuring Displacement and Distance,” Opt. Lett. 12, 310 (1987).
    [CrossRef] [PubMed]
  10. H. W. Jentink, F. F. M. de Mul, H. E. Suichies, J. G. Aarnoudse, J. Greve, “Small Laser Doppler Velocimeter Based on the Self-Mixing Effect in a Diode Laser,” Appl. Opt. 27, 379 (1988).
    [CrossRef] [PubMed]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  12. P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
    [CrossRef]
  13. G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
    [CrossRef]
  14. R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]

1988 (1)

1987 (4)

E. T. Shimizu, “Directional Discrimination in the Self-Mixing Type Laser Doppler Velocimeter,” Appl. Opt. 26, 4541 (1987).
[CrossRef] [PubMed]

C. P. Wang, “Laser Doppler Displacement Measurement,” Lasers Optron. 6, 69 (1987).

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
[CrossRef]

T. Kubota, M. Hara, T. Yoshino, “Interferometer for Measuring Displacement and Distance,” Opt. Lett. 12, 310 (1987).
[CrossRef] [PubMed]

1986 (1)

1984 (4)

J. H. Churnside, “Laser Doppler Velocimetry by Modulating a CO2 Laser with Backscattered Light,” Appl. Opt. 23, 61 (1984).
[CrossRef] [PubMed]

J. H. Churnside, “Signal-to-Noise in a Backscatter-Modulated Doppler Velocimeter,” Appl. Opt. 23, 2097 (1984).
[CrossRef] [PubMed]

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

1982 (1)

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

1980 (1)

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

1968 (1)

M. J. Rudd, “A Laser Doppler Velocimeter Employing the Laser as a Mixer-Oscillator,” J. Phys. E 1, 723, (1968).
[CrossRef]

Aarnoudse, J. G.

Acket, G. A.

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

Beheim, G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Churnside, J. H.

Corke, M.

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

Cutler, L. S.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
[CrossRef]

de Mul, F. F. M.

den Boef, A. J.

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

Fritsch, K.

Greve, J.

Hakayama, T.

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

Hara, M.

Jackson, D. A.

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

Jentink, H. W.

Jones, J. D. C.

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

Kersey, A. D.

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

Kobayashi, K.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Kubota, T.

Kyuma, K.

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lenstra, D.

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

Numoshita, M.

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

Rudd, M. J.

M. J. Rudd, “A Laser Doppler Velocimeter Employing the Laser as a Mixer-Oscillator,” J. Phys. E 1, 723, (1968).
[CrossRef]

Shimizu, E. T.

Suichies, H. E.

Tai, S.

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

Trutna, W. R.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
[CrossRef]

Verbeek, B. H.

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

Wang, C. P.

C. P. Wang, “Laser Doppler Displacement Measurement,” Lasers Optron. 6, 69 (1987).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Yoshino, T.

Zorabedian, P.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

K. Kyuma, S. Tai, M. Numoshita, T. Hakayama, “Fiberoptic Laser Doppler Velocimeter Using and External Cavity Semiconductor Laser,” Appl. Phys. Lett. 45, 1005 (1984).
[CrossRef]

Electron. Lett. (1)

J. D. C. Jones, M. Corke, A. D. Kersey, D. A. Jackson, “Miniature Solid-State Directional Laser Doppler Velocimeter,” Electron. Lett. 22, 967 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in Grating-Tuned External-Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-23, 1855 (1987).
[CrossRef]

G. A. Acket, D. Lenstra, A. J. den Boef, B. H. Verbeek, “The influence of Feedback Intensity on Longitudinal Mode Properties and Optical Noise in Index-Guided Semiconductor Lasers,” IEEE J. Quantum Electron. QE-20, 1163 (1984).
[CrossRef]

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

J. Phys. E (1)

M. J. Rudd, “A Laser Doppler Velocimeter Employing the Laser as a Mixer-Oscillator,” J. Phys. E 1, 723, (1968).
[CrossRef]

Lasers Optron. (1)

C. P. Wang, “Laser Doppler Displacement Measurement,” Lasers Optron. 6, 69 (1987).

Opt. Lett. (1)

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

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Figures (5)

Fig. 1
Fig. 1

Block diagram of the experimental setup used to demonstrate the ranging capability of a backscatter-modulated laser diode. The power supply and the function generator provide the pump current for the laser. The detector is a photodiode. A spectrum analyzer is sometimes used in place of the oscilloscope.

Fig. 2
Fig. 2

Ranging signal frequency as a function of target distance for the setup shown in Fig. 1. The function generator superimposed a 500-Hz 1.25-mA triangle wave modulation on the 78-mA drive current from the dc power supply. The solid line is the theoretical plot for a diode frequency dependence of 2.6 GHz/mA of drive current. The frequencies were measured with a spectrum analyzer.

Fig. 3
Fig. 3

Oscilloscope trace of the ranging signal obtained with a backscatter-modulated laser diode. The laser drive current was modulated with a 2-kHz 1.25-mA triangle wave. The target was an ordinary piece of paper placed 25 cm from the laser’s front facet.

Fig. 4
Fig. 4

Theoretical model of the laser system including the diode cavity and a weak external reflector. The lasing properties of this system can be determined by taking the front facet and the target together as an effective mirror with a complex reflection coefficient Z.

Fig. 5
Fig. 5

Theoretical power output from the system shown in Fig. 4 as a function of the phase parameter Θ. This plot may be compared directly with the experimental data in Fig. 3.

Equations (35)

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

f b = τ d f / d t .
E = E 0 R exp ( i n c k L D ) ,
n C = n - i g .
R = n C - 1 n C + 1 = R exp ( i Ψ ) .
1 = R 2 exp ( 2 i n C k L D ) .
ω M = c k M = M π n L D , G T = k M g = - 1 2 L D ln ( R 2 ) ,
Z = R + r exp ( 2 i k L E ) 1 + R r exp ( 2 i k L E ) ,
1 = R Z exp ( 2 i n C k L D ) = R R + r exp ( 2 i k L E ) 1 + r R exp ( 2 i k L E ) exp ( 2 i n C k L D ) .
Θ ( t ) = ( L 0 + V t ) k .
Θ ( t ) = L E k 0 + 2 π ( τ d f d t ) t .
1 = R 2 [ 1 + a exp ( 2 i k L E ) ] exp ( 2 i n C k L D ) ,
a = ( 1 - R 2 R ) r .
1 = R 2 [ 1 + a cos ( 2 k L E ) ] × exp [ i a sin ( 2 k L E ) ] exp ( 2 i n C k L D ) ,
G T = k M g = - 1 2 L D [ ln ( R 2 ) + a cos ( 2 k L D ) ] .
2 n k L D + a sin ( 2 k L E ) = 2 π M .
n ( N 0 + Δ N ) = n 0 + ( d n / d N ) 0 Δ N = n 0 + χ Δ N ; g ( N 0 + Δ N ) = g 0 + ( d g / d N ) 0 Δ N = g 0 + ρ Δ N .
Δ ω = c Δ k = - γ cos ( ϕ ) sin [ 2 Θ ( t ) + 2 Δ k L E - ϕ ] ,
Δ N = - n 0 γ c k ρ cos [ 2 Θ ( t ) + 2 Δ k L E ] ,
ϕ = tan - 1 ( χ / ρ ) , γ = c 2 n 0 L D a .
d N ( t ) d t = 0 = - N T S - 2 v k g ( N ) Q + J / q d ,
J / q d = N 0 T S + 2 v k g 0 Q 0 .
Δ Q = - ρ g 0 ( κ + Q 0 ) Δ N ,
κ = 1 2 v k ρ T S .
W = [ 1 - R 2 ( 2 k L D g 0 ) R ] ( 1 + κ Q 0 ) r .
Q 0 κ = ( J J th - 1 ) ,
W ( J / J th J / J th - 1 ) r ξ ,
E OUT = S * E IN ,
E OUT ( p OUT ) = d 2 p IN S ( p OUT , p IN ) E IN ( p IN ) ,
0 = S - 1 * E OUT .
S 2 = - R + R exp ( 2 i n C k L D ) 1 - R 2 exp ( 2 i n C k L D ) exp ( - 2 i k L D ) ,
1 = R 2 exp ( 2 i n C k L D ) ,
S 3 = - R + S 2 exp ( 2 i n C k L ) 1 - R S 2 exp ( 2 i n C k L ) exp ( - 2 i k L ) ,
S 2 = R + r exp ( 2 i k L E ) 1 - R r exp ( 2 i k L E ) exp ( - 2 i k n C L E ) ,
S 2 = Z exp ( - 2 i n C k L E ) .
1 = R Z exp ( 2 i n C k L D ) ,

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