Abstract

The contours of constant phases across sinusoidally vibrating objects have been mapped using reference wave phase modulation in time-average electronic speckle pattern interferometry.

© 1976 Optical Society of America

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References

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  1. C. C. Aleksoff, in Holographic Nondestructive Testing, R. K. Erf, Ed. (Academic, New York, 1974), Chap. 8.3, p. 247.
    [CrossRef]
  2. D. B. Neumann, C. F. Jacobson, G. M. Brown, Appl. Opt. 9, 1357 (1970).
    [CrossRef] [PubMed]
  3. J. A. Levitt, K. A. Stetson, Appl. Opt. 15, 195 (1976).
    [CrossRef] [PubMed]
  4. N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
    [CrossRef]
  5. O. J. L⊘kberg, K. H⊘gmoen, J. Phys. E 9, 847 (1976).
    [CrossRef]
  6. H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
    [CrossRef]

1976 (3)

J. A. Levitt, K. A. Stetson, Appl. Opt. 15, 195 (1976).
[CrossRef] [PubMed]

N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
[CrossRef]

O. J. L⊘kberg, K. H⊘gmoen, J. Phys. E 9, 847 (1976).
[CrossRef]

1974 (1)

H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
[CrossRef]

1970 (1)

Aleksoff, C. C.

C. C. Aleksoff, in Holographic Nondestructive Testing, R. K. Erf, Ed. (Academic, New York, 1974), Chap. 8.3, p. 247.
[CrossRef]

Brown, G. M.

F?rre, B. M.

H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
[CrossRef]

H?gmoen, K.

O. J. L⊘kberg, K. H⊘gmoen, J. Phys. E 9, 847 (1976).
[CrossRef]

Idogawa, T.

N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
[CrossRef]

Jacobson, C. F.

L?kberg, O. J.

O. J. L⊘kberg, K. H⊘gmoen, J. Phys. E 9, 847 (1976).
[CrossRef]

H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
[CrossRef]

Levitt, J. A.

Neumann, D. B.

Pedersen, H. M.

H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
[CrossRef]

Stetson, K. A.

Takai, N.

N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
[CrossRef]

Yamada, M.

N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
[CrossRef]

Appl. Opt. (2)

J. Phys. E (1)

O. J. L⊘kberg, K. H⊘gmoen, J. Phys. E 9, 847 (1976).
[CrossRef]

Opt. Commun. (1)

H. M. Pedersen, O. J. L⊘kberg, B. M. F⊘rre, Opt. Commun. 12, 421 (1974).
[CrossRef]

Opt. Laser Technol. (1)

N. Takai, M. Yamada, T. Idogawa, Opt. Laser Technol. 8, 21 (1976).
[CrossRef]

Other (1)

C. C. Aleksoff, in Holographic Nondestructive Testing, R. K. Erf, Ed. (Academic, New York, 1974), Chap. 8.3, p. 247.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Phase shift required to reduce the intensity of the zero order fringe by 20%, 50%, and 100% as function of vibration amplitude (assuming equal object and reference mirror amplitude).

Fig. 2
Fig. 2

Experimental setup for ESPI with phase modulated reference wave.

Fig. 3
Fig. 3

(a) Ordinary time-average ESPI recording of plate vibrating in resonance at 1755 Hz. (b) Areas of constant phase φ0. (c) Areas of constant phase φ0 + π.

Fig. 4
Fig. 4

(a) Time-average recording of plate vibrating in composite mode at 1805 Hz. (b) Areas of phase φ0. (c) Areas of phase φ0 + π.

Fig. 5
Fig. 5

Map showing phase and amplitude distribution across the plate. The lines of constant phase are fully drawn, and iso-amplitude lines are shown dotted.

Fig. 6
Fig. 6

Map showing phase (fully drawn) and amplitude (dotted) distribution across a loudspeaker vibrating at 1000 Hz. N.P.—Nodal point located at the voice coil.

Equations (2)

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I ( x , y ) = I 0 ( x , y ) J 0 2 ( 4 π λ { a 0 2 ( x , y ) + a r 2 - 2 a 0 ( x , y ) a r cos [ φ 0 ( x , y ) - φ r ] } 1 / 2 ) ,
a 0 ( x , y ) = a r             and            φ 0 ( x , y ) = φ r .

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