Abstract

Holographic interferometry is employed to study deformations of a water surface by various disturbances. By using nondiffuse illumination and observing fringe patterns in the holographically reconstructed real image, high resolution even in the presence of large gradients in the surface deformation is achieved. Mathematical procedures for evaluating the fringe patterns are outlined. Several interesting applications (determination of surface tension, surface deformation by floating bodies) demonstrate the accuracy and versatility of the method.

© 1978 Optical Society of America

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References

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  1. F. P. Buff, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1960), Vol. 10, p. 281.
    [CrossRef]
  2. H. Moser, Ann. Phys. 82, 963 (1927).
    [CrossRef]
  3. G. Bakker, in Handbuch der Experimentalphysik, W. Wien, F. Harms, Eds. (Akad. Verlagsges., Leipzig, 1928), Vol. 6.
  4. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  5. G. Schulz, J. Schwider, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1976), Vol. 13, p. 94.
    [CrossRef]
  6. L. H. Tanner, J. Phys. E 1, 517 (1968).
    [CrossRef]
  7. L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), p. 230.
  8. M. Françon, Opt. Acta 11, 253 (1962).
    [CrossRef]

1968 (1)

L. H. Tanner, J. Phys. E 1, 517 (1968).
[CrossRef]

1962 (1)

M. Françon, Opt. Acta 11, 253 (1962).
[CrossRef]

1927 (1)

H. Moser, Ann. Phys. 82, 963 (1927).
[CrossRef]

Bakker, G.

G. Bakker, in Handbuch der Experimentalphysik, W. Wien, F. Harms, Eds. (Akad. Verlagsges., Leipzig, 1928), Vol. 6.

Buff, F. P.

F. P. Buff, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1960), Vol. 10, p. 281.
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Françon, M.

M. Françon, Opt. Acta 11, 253 (1962).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), p. 230.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), p. 230.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Moser, H.

H. Moser, Ann. Phys. 82, 963 (1927).
[CrossRef]

Schulz, G.

G. Schulz, J. Schwider, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1976), Vol. 13, p. 94.
[CrossRef]

Schwider, J.

G. Schulz, J. Schwider, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1976), Vol. 13, p. 94.
[CrossRef]

Tanner, L. H.

L. H. Tanner, J. Phys. E 1, 517 (1968).
[CrossRef]

Ann. Phys. (1)

H. Moser, Ann. Phys. 82, 963 (1927).
[CrossRef]

J. Phys. E (1)

L. H. Tanner, J. Phys. E 1, 517 (1968).
[CrossRef]

Opt. Acta (1)

M. Françon, Opt. Acta 11, 253 (1962).
[CrossRef]

Other (5)

F. P. Buff, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1960), Vol. 10, p. 281.
[CrossRef]

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), p. 230.

G. Bakker, in Handbuch der Experimentalphysik, W. Wien, F. Harms, Eds. (Akad. Verlagsges., Leipzig, 1928), Vol. 6.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

G. Schulz, J. Schwider, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1976), Vol. 13, p. 94.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Experimental setup for (a) recording of hologram and (b) reconstruction of real holographic image in double exposure interferometry of fluid surface deformations.

Fig. 2
Fig. 2

Deformation of a water surface when a vertical wall with angle of contact θ = 0° is introduced at x = 0 mm. The rays of a plane light wave entering from below are shown as they penetrate the deformed surface.

Fig. 3
Fig. 3

(a) Portion of the water surface deformation due to a vertical wall, (b) Error in phase in an observation plane a distance d above the free water surface when refraction at the deformed surface is disregarded. The parameter is the distance d.

Fig. 4
Fig. 4

Holographically obtained interference fringes indicating the deformation of a water surface by a plane vertical wall. The wall starts at the darker contour at the left. The original size of the scene is 22 mm.

Fig. 5
Fig. 5

Microscopic recordings of details of fringe pattern of Fig. 4 demonstrating resolution of the method. The vertical wall is located as indicated.

Fig. 6
Fig. 6

Comparison of fringe patterns obtained in (a) uniphase and (b) diffuse illumination of the water surface. For (b) a real image was reconstructed using the complete aperture of the hologram.

Fig. 7
Fig. 7

The experimentally obtained phase function in a plane of observation d = 1 mm above the free water surface. The deformation was produced by a vertical wall at x = 0 mm.

Fig. 8
Fig. 8

Holographically obtained interference fringes produced by a steel pin of 25-mm length floating on a water surface.

Fig. 9
Fig. 9

Surface deformations produced by small particles (brass filings) floating on a water surface. The diameter of the pictures corresponds to 3.8 mm in the original surface.

Fig. 10
Fig. 10

Surface deformation caused by an insect (family Gerridae) resting on the water surface. The length of the insect body is about 10 mm.

Equations (2)

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Δ h = [ 1 / ( n 1 n 0 ) ] λ 0 ,
x = a 2 cosh 1 2 a y a [ ( 2 y 2 a 2 ) ] 1 / 2 + x 0 ,

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