Abstract

An optical technique to detect the velocity of a moving object that has a brightness distribution is presented. We show theoretically and experimentally that the amplitude of the detected signal in transmission-grating velocimetry is proportional to the Fourier component of the object spectrum at the spatial frequency of the grating. This fact can be used advantageously to sense the velocities of moving objects of any shape in one pass through the detector’s field of view. Results of the application of this method to measure the velocities of some common outdoor moving objects are also presented.

© 1992 Optical Society of America

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References

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  1. B. M. Watrasiewicz, M. J. Rudd, Laser Doppler Measurements, (Butterworths, London, 1976).
  2. R. M. Munoz, H. W. Mocker, L. Koehler, “Airborne laser Doppler velocimeter,” Appl. Opt. 13, 2890–2898 (1974).
    [CrossRef]
  3. R. T. Menzies, “Doppler lidar atmospheric wind sensors: a comparative performance evaluation for global measurement applications from earth orbit,” Appl. Opt. 25, 2546–2553 (1986).
    [CrossRef] [PubMed]
  4. J. T. Ator, “Image-velocity sensing with parallel-slit reticles,” J. Opt. Soc. Am. 53, 1416–1422 (1963).
    [CrossRef]
  5. J. T. Ator, “Image velocity sensing by optical correlation,” Appl. Opt. 5, 1325–1331 (1966).
    [CrossRef] [PubMed]
  6. M. Gaster, “A new technique for the measurement of low fluid velocities,” J. Fluid Mech. 20, 183–192 (1964).
    [CrossRef]
  7. E. A. Ballik, J. H. C. Chan, “Fringe image technique for the measurement of flow velocities,” Appl. Opt. 12, 2607–2615 (1973).
    [CrossRef] [PubMed]
  8. T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating,” Appl. Opt. 22, 1870–1874 (1983).
    [CrossRef] [PubMed]
  9. Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating: A differential type,” Appl. Opt. 24, 627–635 (1985).
    [CrossRef] [PubMed]
  10. Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating: elimination of directional ambiguity,” Appl. Opt. 24, 636–640 (1985).
    [CrossRef] [PubMed]
  11. Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of the velocity gradient in a microscopic region using a transmission grating,” Appl. Opt. 24, 641–647 (1985).
    [CrossRef] [PubMed]
  12. Y. Aizu, T. Ushizaka, T. Asakura, T. Koyama, “Measurements of flow velocity in a microscopic region using a transmission grating: a practical velocimeter,” Appl. Opt. 25, 31–38 (1986).
    [CrossRef] [PubMed]
  13. Y. Itakura, A. Sugimura, S. Tsutsumi, “Amplitude-modulated reticle constructed by a liquid crystal cell array,” Appl. Opt. 20, 2819–2826 (1981).
    [CrossRef] [PubMed]
  14. A. Hayashi, Y. Kitagawa, “Image velocity sensing using an optical fiber array,” Appl. Opt. 21, 1394–1399 (1982).
    [CrossRef] [PubMed]
  15. T. Aruga, “A method for high-accuracy velocity measurement of objects using spatial frequency,” Japanese Patent2-69374, (19March1990).

1986

1985

1983

1982

1981

1974

1973

1966

1964

M. Gaster, “A new technique for the measurement of low fluid velocities,” J. Fluid Mech. 20, 183–192 (1964).
[CrossRef]

1963

Aizu, Y.

Aruga, T.

T. Aruga, “A method for high-accuracy velocity measurement of objects using spatial frequency,” Japanese Patent2-69374, (19March1990).

Asakura, T.

Ator, J. T.

Ballik, E. A.

Chan, J. H. C.

Gaster, M.

M. Gaster, “A new technique for the measurement of low fluid velocities,” J. Fluid Mech. 20, 183–192 (1964).
[CrossRef]

Hayashi, A.

Itakura, Y.

Kitagawa, Y.

Koehler, L.

Koyama, T.

Menzies, R. T.

Mocker, H. W.

Munoz, R. M.

Rudd, M. J.

B. M. Watrasiewicz, M. J. Rudd, Laser Doppler Measurements, (Butterworths, London, 1976).

Sugimura, A.

Tsutsumi, S.

Ushizaka, T.

Watrasiewicz, B. M.

B. M. Watrasiewicz, M. J. Rudd, Laser Doppler Measurements, (Butterworths, London, 1976).

Appl. Opt.

E. A. Ballik, J. H. C. Chan, “Fringe image technique for the measurement of flow velocities,” Appl. Opt. 12, 2607–2615 (1973).
[CrossRef] [PubMed]

T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating,” Appl. Opt. 22, 1870–1874 (1983).
[CrossRef] [PubMed]

Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating: A differential type,” Appl. Opt. 24, 627–635 (1985).
[CrossRef] [PubMed]

Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating: elimination of directional ambiguity,” Appl. Opt. 24, 636–640 (1985).
[CrossRef] [PubMed]

Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of the velocity gradient in a microscopic region using a transmission grating,” Appl. Opt. 24, 641–647 (1985).
[CrossRef] [PubMed]

Y. Aizu, T. Ushizaka, T. Asakura, T. Koyama, “Measurements of flow velocity in a microscopic region using a transmission grating: a practical velocimeter,” Appl. Opt. 25, 31–38 (1986).
[CrossRef] [PubMed]

Y. Itakura, A. Sugimura, S. Tsutsumi, “Amplitude-modulated reticle constructed by a liquid crystal cell array,” Appl. Opt. 20, 2819–2826 (1981).
[CrossRef] [PubMed]

A. Hayashi, Y. Kitagawa, “Image velocity sensing using an optical fiber array,” Appl. Opt. 21, 1394–1399 (1982).
[CrossRef] [PubMed]

R. M. Munoz, H. W. Mocker, L. Koehler, “Airborne laser Doppler velocimeter,” Appl. Opt. 13, 2890–2898 (1974).
[CrossRef]

R. T. Menzies, “Doppler lidar atmospheric wind sensors: a comparative performance evaluation for global measurement applications from earth orbit,” Appl. Opt. 25, 2546–2553 (1986).
[CrossRef] [PubMed]

J. T. Ator, “Image velocity sensing by optical correlation,” Appl. Opt. 5, 1325–1331 (1966).
[CrossRef] [PubMed]

J. Fluid Mech.

M. Gaster, “A new technique for the measurement of low fluid velocities,” J. Fluid Mech. 20, 183–192 (1964).
[CrossRef]

J. Opt. Soc. Am.

Other

B. M. Watrasiewicz, M. J. Rudd, Laser Doppler Measurements, (Butterworths, London, 1976).

T. Aruga, “A method for high-accuracy velocity measurement of objects using spatial frequency,” Japanese Patent2-69374, (19March1990).

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Figures (11)

Fig. 1
Fig. 1

Object O moving with velocity υ0 perpendicularly to the optical axis of a lens L. Image I will move with a corresponding velocity υ. A transmission grating G is placed in the image plane. Light transmitted through the grating is detected by a photon detector.

Fig. 2
Fig. 2

Schematic of the indoor experimental setup: D, rotating disk; L, zoom lens; BS, beam splitter; G, transmission grating.

Fig. 3
Fig. 3

(a) Example of the picture used as the object for the indoor experiment. (b) Relative brightness distribution of (a) along its horizontal axis, which is divided into 768 pixels.

Fig. 4
Fig. 4

The signal detected by the PMT as observed on (a) an oscilloscope and (b) a spectrum analyzer.

Fig. 5
Fig. 5

(a) Plot of the relative signal amplitude from the spectrum analyzer versus the spatial frequency of the grating used, with Fig. 3(a) serving as the object. A set of 64 gratings of different frequencies is used. (b) The Fourier spectrum of the object, obtained by a FFT of the brightness distribution shown in Fig. 3(b). The +’s represent the actual values obtained by the FFT.

Fig. 6
Fig. 6

(a) Picture used as the second object for the indoor experiment. (b) The relative brightness distribution of (a) along the horizontal direction

Fig. 7
Fig. 7

Same plots as in Fig. 5: (a) with the picture shown in Fig. 6(a) as the object and (b) the object spectrum obtained from Fig. 6(b).

Fig. 8
Fig. 8

Same plots as in Fig. 5: (a) with alternating white and black stripes serving as the object and (b) the object spectrum obtained from its brightness distribution.

Fig. 9
Fig. 9

Frequency signals generated by (a) a pedestrian, (b) a jogger, and (c) a cyclist.

Fig. 10
Fig. 10

The frequency signals generated by moving cars obtained from (a) a distance of 52 m with a 1-line/mm grating, (b) a distance of 17 m with a 5-line/mm grating.

Fig. 11
Fig. 11

Effect of a square wave transmission grating. In addition to the fundamental component, the harmonics are also present.

Equations (14)

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

I ( t ) = f ( x υ t ) T ( x ) d x ,
T ( x ) = a 0 + a cos ( 2 π u x ) .
T ( x ) = a 0 + a exp ( i 2 π u x ) ,
I ( t ) = a f ( x υ t ) exp ( i 2 π u x ) d x .
x = x υ t .
I ( t ) = a exp ( i 2 π u υ t ) f ( x ) exp ( i 2 π u x ) d x = a exp ( i 2 π u υ t ) F ( u ) ,
F ( u ) = f ( x ) exp ( i 2 π u x ) d x .
f = u υ .
T ( x ) = 1 2 + 2 π u odd cos 2 π u x u .
I ( t ) = a f ( x υ t ) cos ( 2 π u x ) d x .
x = x υ t ,
I ( t ) = a f ( x ) cos ( 2 π u x + 2 π u υ t ) d x .
I ( t ) = a f ( x ) [ cos ( 2 π u x ) cos ( 2 π u υ t ) sin ( 2 π u x ) sin ( 2 π u υ t ) ] d x = a cos 2 π u υ t f ( x ) cos 2 π u x d x a sin 2 π u υ t f ( x ) sin 2 π u x d x = a cos 2 π u υ t F 1 ( u ) a sin 2 π u υ t F 2 ( u ) ,
I ( t ) = a F ( u ) cos ( 2 π u υ t + ϕ ) , F ( u ) = { [ F 1 ( u ) ] 2 + [ F 2 ( u ) ] 2 } 1 / 2 , tan ϕ = F 2 ( u ) F 1 ( u ) .

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