Abstract

Double exposure holograms of a moving particle field having a 1-D velocity distribution are produced. The Fraunhofer plane is observed on reconstruction, and it is shown that for a Gaussian velocity distribution, the fringes which modulate the diffraction pattern have spacings characteristic of the peak velocity. Known and measured peak velocities are compared, and the effect of the velocity distribution width on the fringe contrast is demonstrated

© 1979 Optical Society of America

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References

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  1. M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
    [CrossRef]
  2. B. J. Thompson, J. Phys. E 7, 781 (1974).
    [CrossRef]
  3. D. J. Stigliani, R. G. Simonin, J. Opt. Soc. Am. 60, 1059 (1970).
    [CrossRef]
  4. R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
    [CrossRef]
  5. J. D. Trolinger, R. A. Belz, W. M. Farmer, Appl. Opt. 8, 957 (1969).
    [CrossRef] [PubMed]
  6. R. Menzel, F. M. Shofner, Appl. Opt. 9, 2073 (1970).
    [CrossRef] [PubMed]
  7. J. D. Redman, J. Sci. Instrum. 44, 1032 (1967).
    [CrossRef]
  8. W. T. Mayo, J. B. Allen, Appl. Opt. 10, 2119 (1971).
    [CrossRef] [PubMed]
  9. A. J. Decker, Appl. Opt. 14, 1061 (1975).
    [CrossRef] [PubMed]
  10. K. Iwata, T. Hakoshima, R. Nagata, J. Opt. Soc. Am. 67, 1117 (1977).
    [CrossRef]
  11. J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
    [CrossRef]
  12. P. M. Boone, L. C. De Backer, Optik 37, 61 (1973).
  13. C. Roychoudhuri, R. Machorro, Appl. Opt. 17, 848 (1978).
    [CrossRef] [PubMed]
  14. J. Cornillault, Appl. Opt. 11, 265 (1971).
    [CrossRef]
  15. J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

1978 (1)

1977 (2)

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

K. Iwata, T. Hakoshima, R. Nagata, J. Opt. Soc. Am. 67, 1117 (1977).
[CrossRef]

1976 (1)

R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
[CrossRef]

1975 (1)

1974 (1)

B. J. Thompson, J. Phys. E 7, 781 (1974).
[CrossRef]

1973 (1)

P. M. Boone, L. C. De Backer, Optik 37, 61 (1973).

1971 (2)

1970 (2)

1969 (3)

J. D. Trolinger, R. A. Belz, W. M. Farmer, Appl. Opt. 8, 957 (1969).
[CrossRef] [PubMed]

M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
[CrossRef]

J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

1967 (1)

J. D. Redman, J. Sci. Instrum. 44, 1032 (1967).
[CrossRef]

Abbot, D.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Allen, J. B.

Beer, J. M.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Belz, R. A.

Bexon, R.

R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
[CrossRef]

Bishop, G. D.

R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
[CrossRef]

Boone, P. M.

P. M. Boone, L. C. De Backer, Optik 37, 61 (1973).

Cornillault, J.

De Backer, L. C.

P. M. Boone, L. C. De Backer, Optik 37, 61 (1973).

Decker, A. J.

Farmer, W. M.

Fourney, M. E.

M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
[CrossRef]

Gibbs, J.

R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
[CrossRef]

Hakoshima, T.

Iwata, K.

Machorro, R.

Matkin, J. H.

M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
[CrossRef]

Matsuda, K.

J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

Mayo, W. T.

McCreath, G. C.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Menzel, R.

Nagata, R.

Redman, J. D.

J. D. Redman, J. Sci. Instrum. 44, 1032 (1967).
[CrossRef]

Roychoudhuri, C.

Shofner, F. M.

Simonin, R. G.

Stigliani, D. J.

Swithenbank, J.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Takeya, N.

J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

Taylor, D. S.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Thompson, B. J.

B. J. Thompson, J. Phys. E 7, 781 (1974).
[CrossRef]

Trolinger, J. D.

Tsujiuchi, J.

J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

Waggoner, A. P.

M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
[CrossRef]

Appl. Opt. (6)

J. Aerosol Sci. (1)

R. Bexon, J. Gibbs, G. D. Bishop, J. Aerosol Sci. 7, 397 (1976).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. E (1)

B. J. Thompson, J. Phys. E 7, 781 (1974).
[CrossRef]

J. Sci. Instrum. (1)

J. D. Redman, J. Sci. Instrum. 44, 1032 (1967).
[CrossRef]

Opt. Acta (1)

J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

Optik (1)

P. M. Boone, L. C. De Backer, Optik 37, 61 (1973).

Prog. Astronaut. Aeronaut. (1)

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, G. C. McCreath, Prog. Astronaut. Aeronaut. 53, 421 (1977).

Rev. Sci. Instrum. (1)

M. E. Fourney, J. H. Matkin, A. P. Waggoner, Rev. Sci. Instrum. 40, 205 (1969).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Formation and reconstruction of particle holograms: P–particles (X1 plane); F–spatial filter; H–hologram (X2 plane); R–observation plane (X4).

Figs. 2–5
Figs. 2–5

Influence of velocity distribution width on fringe patterns in Fraunhofer plane: (2) σ/A < 0.01; (3) σ/A–0.04; (4) σ/A–0.08; (5) σ/A–0.14.

Fig. 6
Fig. 6

Increase in size of speckle due to reduction of particle field from 5–1-cm diam.

Tables (1)

Tables Icon

Table I Comparison of Known and Measured Peak Velocities over a Range of the Distribution Width Parameter σ/A

Equations (15)

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A ( X 4 ) = G exp ( i S X 4 2 ) exp ( - i C Q · X 4 ) × - T ( X 1 ) exp ( i C X 1 · X 4 ) d X 1 ,
A ( X 4 ) = A ( X 4 ) exp ( - i C p · X 4 ) .
I ( X 4 ) = 2 G G * F ( X 4 ) F * ( X 4 ) [ 1 + cos ( C p · X 4 ) ] ,
F ( X 4 ) = - T ( X 1 ) exp ( i C X 1 · X 4 ) d X 1
I ( X 4 ) j F j ( X 4 ) F j * ( X 4 ) [ 1 + cos ( C p j · X 4 ) ] .
I ( X 4 ) B ( R ) [ 1 + 0 P ( p ) cos ( C p · X 4 ) d p ] ,
I ( X 4 ) B ( R ) [ 1 + 0 P ( V ) cos ( D V · X 4 ) d V ] ,
I ( X 4 ) B ( R ) [ 1 + cos ( D A · X 4 ) exp ( - D 2 σ 2 X 4 2 2 ) ] ,
P ( V ) = 1 σ 2 π exp [ - ( V - A ) 2 2 σ 2 ] .
X 4 = 2 π n D A             and             X 4 = ( 2 n + 1 ) π D A ,
R n = 1 + exp [ - 2 n 2 π 2 ( σ 2 / A 2 ) ] 1 - exp { - ( 2 n + 1 ) 2 π 2 [ σ 2 / ( 2 A 2 ) ] } .
A ( X 4 ) = G F ( X 4 ) j exp ( - i C Q j · X 4 ) .
A ( X 4 ) = G F ( X 4 ) - P ( Q ) exp ( - i C Q · X 4 ) d Q ,
I ( X 4 ) = [ G F ( X 4 ) - P ( Q ) exp ( - i C Q · X 4 ) d Q ] × c.c.
G G * F ( X 4 ) F * ( X 4 ) - - × P * ( Q ) P ( Q - p ) d Q · exp ( - i C p · X 4 ) d ρ ,

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