Abstract

A laser Doppler velocimeter that consists of a semiconductor laser coupled to a fiber and that uses the self-mixing effect is presented. The velocimeter can be used for solids and fluids. A theoretical model is developed to describe the self-mixing signals as a function of the amount of feedback into the laser and the distance from the laser to the moving object. Good agreement is found between this theory and measurements.

© 1992 Optical Society of America

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References

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  1. M. J. Rudd, “A laser Doppler velocimeter employing the laser as a mixer-oscillator,” J. Phys. E 1, 723–726 (1968).
    [CrossRef]
  2. S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1417–1419 (1986).
    [CrossRef] [PubMed]
  3. P. J. de Groot, G. M. Gallatin, S. H. Macomber, “Ranging and velocity generation in a backscatter-modulated laser diode,” Appl. Opt. 27, 4475–4480 (1988).
    [CrossRef] [PubMed]
  4. P. J. de Groot, G. M. Gallatin, “Backscatter-modulation velocimetry with external-cavity laser diode,” Opt. Lett. 14, 165–167 (1989).
    [CrossRef] [PubMed]
  5. K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988).
    [CrossRef]
  6. 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, 1163–1169 (1984).
    [CrossRef]
  7. E. T. Shimizu, “Directional discrimination in the self-mixing type laser Doppler velocimeter,” Appl. Opt. 26, 4541–4544 (1987).
    [CrossRef] [PubMed]
  8. 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, 379–385 (1988).
    [CrossRef] [PubMed]
  9. H. Sato, J. Ohya, “Theory of Spectral Linewidth of External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-22, 1060–1063 (1986).
    [CrossRef]

1989 (1)

1988 (2)

1987 (1)

1986 (2)

H. Sato, J. Ohya, “Theory of Spectral Linewidth of External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-22, 1060–1063 (1986).
[CrossRef]

S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1417–1419 (1986).
[CrossRef] [PubMed]

1984 (1)

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, 1163–1169 (1984).
[CrossRef]

1968 (1)

M. J. Rudd, “A laser Doppler velocimeter employing the laser as a mixer-oscillator,” J. Phys. E 1, 723–726 (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, 1163–1169 (1984).
[CrossRef]

de Groot, P. J.

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, 1163–1169 (1984).
[CrossRef]

Gallatin, G. M.

Greve, J.

Jentink, H. W.

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, 1163–1169 (1984).
[CrossRef]

Macomber, S. H.

Mochizuki, A.

Ohya, J.

H. Sato, J. Ohya, “Theory of Spectral Linewidth of External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-22, 1060–1063 (1986).
[CrossRef]

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

Rudd, M. J.

M. J. Rudd, “A laser Doppler velocimeter employing the laser as a mixer-oscillator,” J. Phys. E 1, 723–726 (1968).
[CrossRef]

Sato, H.

H. Sato, J. Ohya, “Theory of Spectral Linewidth of External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-22, 1060–1063 (1986).
[CrossRef]

Shimizu, E. T.

Shinohara, S.

Suichies, H. E.

Sumi, M.

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, 1163–1169 (1984).
[CrossRef]

Yoshida, H.

Appl. Opt. (4)

IEEE J. Quantum Electron. (2)

H. Sato, J. Ohya, “Theory of Spectral Linewidth of External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-22, 1060–1063 (1986).
[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, 1163–1169 (1984).
[CrossRef]

J. Phys. E (1)

M. J. Rudd, “A laser Doppler velocimeter employing the laser as a mixer-oscillator,” J. Phys. E 1, 723–726 (1968).
[CrossRef]

Opt. Lett. (1)

Other (1)

K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Model for a semiconductor laser with external optical feedback. A typical value for L is ~ 300 μm with Lext ranging from a few centimeters up to a maximum of several meters (depending on the coherence length of the laser).

Fig. 2
Fig. 2

(a) Self-mixing signal gain as a function of the C parameter. With increasing C parameter the self-mixing signal changes from sinusoidal toward sawtoothlike. Parameters: v = 1.4 mm/s, Lext = 1.5 m, L = 300 μm, λ = 780 nm; α = 5, and μ ¯ e = 5; (b) deformation parameter (= 2nd–1st harmonic signal strength) as a function of κ. Parameters: as in (a), except v = 1.0 mm/s. Right curve gives the κ values × 5.

Fig. 3
Fig. 3

Directional discrimination in the self-mixing signal: (a) velocity to and (b) velocity from the laser.

Fig. 4
Fig. 4

Experimental setup for measurements of the signal amplitude and the signal shape of the self-mixing signals as a function of the optical feedback and the distance from the laser to the moving object. The distance from the laser to the nearest lens (~ 3 mm) and the distance from the second lens to the rotating wheel (40 mm) were kept constant, while the distance from the nearest lens to the second lens was varied. The radius of the wheel was 50 mm, laser power was 3 mW, and overall transmissions were 27% and 20%, with focusing of the beam from the fiber onto the moving target absent or present, respectively.

Fig. 5
Fig. 5

Signal amplitude of the self-mixing signal as a function of the amplitude transmission coefficient of the neutral density filter placed in the beam.

Fig. 6
Fig. 6

Signal deformation parameter of the self-mixing signal as a function of the signal amplitude times the distance from the laser to the moving object (proportional to the feedback parameter).

Fig. 7
Fig. 7

Experimental setup for the measurements of self-mixing signals in a fiber-coupled semiconductor laser. The distance from the laser to the nearest lens was 4 mm, the distance from the nearest lens to the second lens was ~ 8 cm, and the distance from the second lens to the nearest fiber facet was ~ 8 mm. The second fiber facet was positioned at a distance of ~ 2 mm for the rotating wheel with a viewing angle of 35°. SM, single mode; PPSM, polarization-preserving; MM, multimode.

Fig. 8
Fig. 8

Self-mixing signal measured on a paper-covered rotating wheel by using a glass fiber (length 1.5 m): (a) time domain, (b) frequency domain. Parameters: λ = 780 nm; v = 1.0 mm/s; ϑ = 35°; and n = 1. Bold curve, high feedback; thin curve, low feedback × 4; (signal strength ratio is 4:1). In the high-feedback curve the second harmonic is present, according to Figs. 2(b) and 6.

Fig. 9
Fig. 9

Signal amplitude of the self-mixing signal as a function of the amplitude transmission coefficient of neutral density filters placed in the beam, as in Fig. 5, with use of a fiber (length 1.5 m) and normal-to-the-signal amplitude with no filter.

Equations (27)

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r 2 ( ν ) = r 2 s + ( 1 - r 2 s 2 ) r 2 ext exp ( - i 2 π ν τ ext ) ,
r 2 ( ν ) = r 2 exp ( - i φ r ) .
2 β L + φ r = 2 π m ,
4 π μ e ν L / c + φ r = 2 π m .
r 1 r 2 exp [ ( g c - α s ) L ] = 1 ,
r 2 = r 2 s [ 1 + κ cos ( 2 π ν τ ext ) ] ,
κ = r 2 ext r 2 s ( 1 - r 2 s 2 ) ,             ( 0 < κ < 1 ) ,
φ r = κ sin ( 2 π ν τ ext ) ,
g e - g th = - κ L cos ( 2 π ν τ ext ) ,
Δ φ 1 = 2 π τ L ( ν - ν th ) + κ ( 1 + α 2 ) 1 / 2 × sin ( 2 π ν τ ext + arctan α ) ,
C = τ ext τ L κ ( 1 + α 2 ) 1 / 2 .
g th = a ( n - n 0 ) ,
Δ I th = e V ( 1 / T s ) Δ n th ,
Δ g = a Γ Δ n th ,
Δ g = T s a Γ e V Δ I th
P = Q ( I - I th ) ,
τ ext = 2 ( L 0 + v t ) / c ,
Δ P ~ g c - g th = - κ L cos ( 4 π ν τ v t / c + 4 π L 0 ν / c ) .
Δ t 1 / f d = λ / 2 v
ω n = ω n S ( ω ) d ω ,
E ( z , t ) = E 0 exp { - i [ k z + 2 π ν t + ψ ( t ) ] } ,
E r ( t ) = r 2 s E ( t ) + ( 1 - r 2 s 2 ) r 2 ext E ( t - τ ext ) .
E ( t - τ ext ) = E ( t ) exp ( - i 2 π ν τ ext ) exp { - i [ ψ ( t ) - ψ ( t - τ ext ) ] } .
exp { - i [ ψ ( t ) - ψ ( t - τ ext ) ] } = exp ( - τ ext / τ c ) ,
r 2 ( ν ) = r 2 s + ( 1 - r 2 s 2 ) r 2 ext exp ( - i 2 π ν τ ext ) exp ( - τ ext / τ c ) .
L ext < c / ( 2 π Δ ν ) .
Δ f = 2 v n cos ( ϑ ) / λ ,

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