Abstract

A very small and simple velocimeter is presented consisting of a diode laser with a gradient-index lens in front of it. The basis of the velocity measurement is the mixing that occurs when light, scattered back by the moving object into the laser cavity, interferes with light inside the laser. This mixing induces large fluctuations of the laser intensity with the Doppler frequency. These fluctuations can be detected either with a photodiode or by measuring the voltage across the diode laser. As an illustration of the performance of the velocimeter, velocity measurements of a rotating disk covered with white paper are described. The differences arising because of using a single-mode or a multilongitudinal mode laser were calculated and verified in experiments. The advantage of the use of a multimode laser is that differential measurements of the distance between laser and moving object are also possible.

© 1988 Optical Society of America

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References

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  1. 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 (1986).
    [CrossRef] [PubMed]
  2. M. J. Rudd, “A Laser Doppler Velocimeter Employing the Laser as a Mixer-Oscillator,” J. Phys. E 1, 723 (1968).
    [CrossRef]
  3. J. H. Churnside, “Laser Doppler Velocimetry by Modulating a CO2 Laser with Backscattered Light,” Appl. Opt. 23, 61 (1984).
    [CrossRef] [PubMed]
  4. M. W. Fleming, A. Mooradian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 44 (1981).
    [CrossRef]
  5. R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  6. A. Olsson, C. L. Tang, “Coherent Optical Interference Effects in External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 1320 (1981).
    [CrossRef]
  7. J. H. Churnside, “Signal-to-Noise in a Backscatter-Modulated Doppler Velocimeter,” Appl. Opt. 23, 2079 (1984).
    [CrossRef]
  8. J. H. Churnside, “Speckle from a Rotating Diffuse Object,” J. Opt. Soc. Am. 72, 1464 (1982).
    [CrossRef]
  9. J. C. Dainty, Ed, Laser Speckle and Related Phenomena (Springer-Verlag, New York, 1975).
  10. R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
    [CrossRef]

1986 (1)

1984 (2)

J. H. Churnside, “Signal-to-Noise in a Backscatter-Modulated Doppler Velocimeter,” Appl. Opt. 23, 2079 (1984).
[CrossRef]

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

1982 (1)

1981 (3)

A. Olsson, C. L. Tang, “Coherent Optical Interference Effects in External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 1320 (1981).
[CrossRef]

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

M. W. Fleming, A. Mooradian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 44 (1981).
[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]

Churnside, J. H.

Dandridge, A.

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

Fleming, M. W.

M. W. Fleming, A. Mooradian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 44 (1981).
[CrossRef]

Giallorenzi, T. G.

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[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]

Lang, R.

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

Miles, R. O.

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

Mochizuki, A.

Mooradian, A.

M. W. Fleming, A. Mooradian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 44 (1981).
[CrossRef]

Olsson, A.

A. Olsson, C. L. Tang, “Coherent Optical Interference Effects in External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 1320 (1981).
[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]

Shinohara, S.

Sumi, M.

Tang, C. L.

A. Olsson, C. L. Tang, “Coherent Optical Interference Effects in External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 1320 (1981).
[CrossRef]

Taylor, H. F.

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

Tveten, A. B.

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

Yoshida, H.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. O. Miles, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, H. F. Taylor, “Low-Frequency Noise Characteristics of Channel Substrate Planar GaAlAs Laser Diodes,” Appl. Phys. Lett. 38, 848 (1981).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. W. Fleming, A. Mooradian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 44 (1981).
[CrossRef]

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

A. Olsson, C. L. Tang, “Coherent Optical Interference Effects in External Cavity Semiconductor Lasers,” IEEE J. Quantum Electron. QE-17, 1320 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

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]

Other (1)

J. C. Dainty, Ed, Laser Speckle and Related Phenomena (Springer-Verlag, New York, 1975).

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Figures (9)

Fig. 1
Fig. 1

Setup for measuring the self-mixing effect.

Fig. 2
Fig. 2

Spectra of the light (1 mW) of (a) a Matsushita diode laser operating at 1.11 times the threshold current and (b) a Hitachi diode laser operating well above threshold (output 3 mW at 1.22 times threshold current). The spectra were recorded with a spectroscope, consisting of a monochromator (Spex triplemate 1877) and an optical multichannel analyzer (EG&G model 1460).

Fig. 3
Fig. 3

Setup for measuring the magnitude of the self-mixing effect as a function of the distance l between laser and paper.

Fig. 4
Fig. 4

Intensity fluctuation of light on the photodiode inside the diode laser house due to self-mixing, (a) The intensity was linearly converted into voltage and the dc part of −2.68 V was filtered out. The Hitachi laser chip produced 3-mW light and was placed 8.9 mm from the paper. The gradient-index lens was just in front of the protective window of the laser, which is 1.2 mm from the laser chip. (b) Spectrum of the fluctuation measured with the setup drawn in Fig. 3 using a Matsushita laser producing 3-mW light at 156 mm from the paper.

Fig. 5
Fig. 5

Spectrum of the (a) current fluctuations through the photo-diode in the diode laser house and (b) voltage fluctuations over the laser diode. The experimental setup was as described in the legend of Fig. 4(a).

Fig. 6
Fig. 6

Spectrum of the current through the photodiode in the Hitachi diode laser house in such conditions that the peak at twice the Doppler frequency is larger than the peak at the Doppler frequency. The diode laser was operating just above the threshold current (I = 39.5 mA, which is 1.09 times the threshold current), producing 1-mW light. The distance between laser chip and paper is 9.7 mm. This kind of spectrum was observed only for distances close to this value and for small currents through the diode.

Fig. 7
Fig. 7

Measured Doppler frequency as a function of the paper velocity component in the light beam direction with θ = 60°. The line in the figure shows the expected relation [Eq. (1)].

Fig. 8
Fig. 8

Measured Doppler frequency as a function of the angle between the light beam direction and the paper velocity. The line was calculated from Eq. (1).

Fig. 9
Fig. 9

Dependence of the height of the Doppler peak in spectra on the distance l between multimode diode laser and paper. The line was drawn to guide the eye.

Equations (14)

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ω d = 4 π υ cos ( θ ) / λ ,
E ( z , t ) = E o l exp i [ k 0 z ω 0 t + ϕ ( t z / c ) ] + c . c .,
E s ( z , t ) = E o s exp i { ( k 0 + k d ) ( l z ) + k 0 l ( ω 0 + ω d ) t + ϕ [ t ( 2 l z ) / c ] } S [ t ( l z ) / c ] × exp i { ϕ s [ t ( l z ) / c ] } + c . c .,
E L ( z , t ) = ( 1 / T ) E o l × exp i [ k 0 z ω 0 t + ϕ ( t + z / c ) + π ] + c . c .,
I ( z , t ) = ε c [ E L ( z , t ) + T E s ( z , t ) ] * [ E L ( z , t ) + T E s ( z , t ) ] = ε c | E o l / T | 2 + ε c | E o s S [ t ( l z ) / c ] T | 2 + ε c E o l E o s exp i [ 2 k 0 l + k d ( l z ) ω d t + ϕ ( t + z / c 2 l / c ) ϕ ( t + z / c ) π ] × S [ t ( l z ) / c ] exp i { ϕ s [ t ( l z ) / c ] } + c . c . ,
I l ( t ) = I 0 + I f exp i [ 2 k 0 l + k d l ω d t + ϕ ( t 2 l / c ) ϕ ( t ) π ] × S ( t l / c ) exp i [ ϕ s ( t l / c ) ] + c . c . ,
E l ( z , t ) = j = 1 p E l j exp i [ k j z ω j t + ϕ j ( t z / c ) ] + c . c . ,
E s ( z , t ) = j = 1 p E s j exp i { ( k j + k d j ) ( l z ) + k j l ( ω j + ω d j ) t + ϕ j [ t ( 2 l z ) / c ] } S j [ t ( l z ) / c ] × exp i { ϕ s j [ t ( l z ) / c ] } + c . c .,
E L ( z , t ) = j = 1 p ( 1 / T ) E l j exp i [ k j z ω j t + ϕ j ( t + z / c ) + π ] ,
I L ( z , t ) = ε c [ E L ( z , t ) + T E s ( z , t ) ] * [ E L ( z , t ) + T E s ( z , t ) ] = ε c j = 1 p [ | E l j / T | 2 + | E s j S [ t ( l z ) / c ] T | 2 + E l j E s j exp i { 2 k j l + k d j ( l z ) ω d j t + ϕ j [ t ( 2 l z ) / c ] ϕ j ( t + z / c ) + π } × S j [ t ( l z ) / c ] × exp i { ϕ s j [ t ( l z ) / c ] } + c . c . ] .
I l ( z , t ) = I 0 + j = 1 p S j ( t l / c ) I f j exp i [ 2 k j l + k d j ( l z ) + ω d j t + ϕ s j ( t l / c ) π ] + c . c .
I l ( t ) = I o l + [ j = 1 p I f j exp i ( 2 k j l ) ] exp i ( ω d t ) S ( t l / c ) × exp i [ ϕ s ( t l / c ) ] + c . c .,
2 k j l = 2 ( ω 0 + 2 π j c / 2 n L ) l / c .
l c = λ 2 / δ λ = 0 . 14 mm .

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