Abstract

The spatial structure of the optical field on the detector of a laser Doppler velocimeter is examined. It is shown that for sufficiently small scatterers, the optical field is a traveling wave of shape determined by the detector optics alone. The direction of travel of the optical field reflects that of the scattering particle. Thus, the direction of motion of the particle is determined by temporal correlation of photocurrents from two spatially offset detector arrays. The arrays also eliminate the Doppler pedestal as shown by Ogiwara (1979). In this paper, the theory of the new method is described; experimental implementation will be described in a complementary paper.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. S. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  2. L. E. Drain, J. Phys. D: 5, 481 (1972).
    [CrossRef]
  3. F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).
  4. H. Ogiwara, Appl. Opt. 18, 1533 (1979).
    [CrossRef] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  6. M. J. Rudd, J. Phys. E: 2, 723 (1969).
    [CrossRef]
  7. A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1979).
  8. C. C. Goodyear, Signals and Information (Wiley-Interscience, New York, 1971).

1979 (1)

1972 (1)

L. E. Drain, J. Phys. D: 5, 481 (1972).
[CrossRef]

1969 (1)

M. J. Rudd, J. Phys. E: 2, 723 (1969).
[CrossRef]

1964 (1)

C. S. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Cummins, H. Z.

C. S. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Drain, L. E.

L. E. Drain, J. Phys. D: 5, 481 (1972).
[CrossRef]

Durst, F.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

Ghatak, A. K.

A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1979).

Goodyear, C. C.

C. C. Goodyear, Signals and Information (Wiley-Interscience, New York, 1971).

Melling, A.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

Ogiwara, H.

Rudd, M. J.

M. J. Rudd, J. Phys. E: 2, 723 (1969).
[CrossRef]

Thyagarajan, K.

A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1979).

Whitelaw, J. H.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yeh, C. S.

C. S. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. S. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

J. Phys. D (1)

L. E. Drain, J. Phys. D: 5, 481 (1972).
[CrossRef]

J. Phys. E (1)

M. J. Rudd, J. Phys. E: 2, 723 (1969).
[CrossRef]

Other (4)

A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1979).

C. C. Goodyear, Signals and Information (Wiley-Interscience, New York, 1971).

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Schematic of the two-slit directional velocimeter. The intensity distribution in the detector plane, E 3 E * 3 is the same as that in Young’s experiment, centered at the geometrical image point of the scatterer.

Fig. 2
Fig. 2

Schematic of directional LDV with large aperture. The use of a wider aperture improves SNR. A square aperture allows two-axis velocity measurement.

Equations (24)

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

E 1 t = A ( x ) [ 1 G ( x l ) ] ,
E 2 = F { A ( x ) · [ 1 G ( x l ) ] }
= [ a ( y ) a ( y ) * g ( y l ) ] ,
E 2 t = C 1 [ a ( y ) a ( y ) * g ( y l ) ] · h ( y ) ,
h ( y ) = 1 } Δ δ y Δ + δ , Δ δ y Δ + δ , = 0 otherwise .
E 3 = C 2 F [ a ( y ) a ( y ) * g ( y l ) ] * H ( z ) ,
= C 2 [ A ( z ) A ( z ) G ( z + l f 2 / f 1 ) ] * H ( z ) ,
E 3 = C 2 [ A ( z ) G ( z M l ) ] * H ( z ) .
E 3 = C 2 A ( z ) G ( z M l ) · H ( z z ) d z .
E 3 ( z ) = C 3 A ( l ) H ( z M l ) .
H ( z ) = 4 f 2 i k z sin ( k δ z / f 2 ) sin ( k Δ z / f 2 ) ,
E 3 ( Z ) = C 4 A ( l ) k ( z M l ) sin k Δ ( z M l ) f 2 sin k δ ( z M l ) f 2 .
f 1 / k Δ and f 1 / k δ ,
I 3 ( z ) = E 3 E * 3 = C 5 A 2 ( l ) ( z M l ) 2 sin 2 k δ f 2 ( z M l ) sin 2 k Δ f 2 ( z M l ) .
I 3 ( z ) = C 5 A 2 ( l ) 4 ( z M l ) 2 [ cos k ( Δ + δ ) f 2 ( z M l ) cos k ( Δ δ ) f 2 ( z M l ) ] 2 ,
I 3 ( z ) = C 6 A 2 ( l ) ( z M l ) 2 [ 1 1 2 cos 2 k ( Δ + δ ) f 2 ( z M l ) 1 2 cos 2 k ( Δ δ ) f 2 ( z M l ) cos 2 Δ k f 2 ( z M l ) cos 2 δ k f 2 ( z M l ) ]
f c = 2 v · n Δ / λ f 1
B = 2 v · n · δ / λ f 1 .
f c = 2 v · n Δ λ f 1 2 + Δ 2 .
I ( t ) = C 6 A 2 ( l ) | H ( z M l ) | 2 n = 1 B n cos ( n K z + ϕ n ) d z ,
I 1 ( t ) = C 7 A 2 ( l ) | H ( z M l ) | 2 B 1 cos ( K z + ϕ 1 ) d z , I 2 ( t ) = C 7 A 2 ( l ) | H ( z M l ) | 2 B 1 cos ( K z + ϕ 1 + π / 2 ) d z .
ϕ n ( 1 4 f ) = σ 2 sin c ( π f m 2 f c ) .
ϕ n ( τ ) ϕ ( τ ) = ξ f m sin c ( π 2 f m f c ) or = ξ sin ( π f m 2 f c ) ,
h ( y ) = 1 Δ < y < Δ = 0 otherwise .

Metrics