Abstract

The interpretation of time-averaged holographic fringes recorded with a vibrating object presents problems when the direction of the motion is not known or when points on the object are moving in two or three dimensions. Measurements on additional holograms with properly chosen directions of the sensitivity vector are then required to evaluate the vibration amplitude. However, reduction of the data, even along a single line, is laborious and subject to errors. This paper describes a computerized system which uses stroboscopic illumination in conjunction with digital phase-shifting techniques to evaluate the magnitude and direction of the surface displacements at a uniformly spaced array of points covering the vibrating object. These values are used along with data on the shape of the object to calculate the in-plane and out-of-plane components of the vibration at these points. The operation of the system is illustrated with some results obtained with a compressor blade from a jet engine. Measurements of the surface displacements at different epochs of the vibration cycle permit a detailed analysis of complex vibrations.

© 1987 Optical Society of America

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References

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  1. R. L. Powell, K. A. Stetson, “Interferometric Vibration Analysis by Wavefront Reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
    [CrossRef]
  2. P. Hariharan, Optical Holography (Cambridge U.P., London, 1984), p. 232.
  3. R. Tonin, D. A. Bies, “Time-Averaged Holography for the Study of Three-Dimensional Vibrations,” J. Sound Vib. 52, 315 (1977).
    [CrossRef]
  4. R. Tonin, D. A. Bies, “General Theory of Time-Averaged Holography for the Study of Three-Dimensional Vibrations at a Single Frequency,” J. Opt. Soc. Am. 68, 924 (1978).
    [CrossRef]
  5. B. F. Oreb, P. Hariharan, “A Simple Stroboscopic Pulse Generator for Holographic Interferometry of Vibrating Objects,” J. Phys. E (in press) 20, 660 (1987).
    [CrossRef]
  6. P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: A Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876 (1983).
    [CrossRef] [PubMed]
  7. P. Hariharan, B. F. Oreb, “Stroboscopic Holographic Interferometry: Application of Digital Techniques,” Opt. Commun. 59, 83 (1986).
    [CrossRef]

1986 (1)

P. Hariharan, B. F. Oreb, “Stroboscopic Holographic Interferometry: Application of Digital Techniques,” Opt. Commun. 59, 83 (1986).
[CrossRef]

1983 (1)

1978 (1)

1977 (1)

R. Tonin, D. A. Bies, “Time-Averaged Holography for the Study of Three-Dimensional Vibrations,” J. Sound Vib. 52, 315 (1977).
[CrossRef]

1965 (1)

Bies, D. A.

R. Tonin, D. A. Bies, “General Theory of Time-Averaged Holography for the Study of Three-Dimensional Vibrations at a Single Frequency,” J. Opt. Soc. Am. 68, 924 (1978).
[CrossRef]

R. Tonin, D. A. Bies, “Time-Averaged Holography for the Study of Three-Dimensional Vibrations,” J. Sound Vib. 52, 315 (1977).
[CrossRef]

Brown, N.

Hariharan, P.

P. Hariharan, B. F. Oreb, “Stroboscopic Holographic Interferometry: Application of Digital Techniques,” Opt. Commun. 59, 83 (1986).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: A Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876 (1983).
[CrossRef] [PubMed]

B. F. Oreb, P. Hariharan, “A Simple Stroboscopic Pulse Generator for Holographic Interferometry of Vibrating Objects,” J. Phys. E (in press) 20, 660 (1987).
[CrossRef]

P. Hariharan, Optical Holography (Cambridge U.P., London, 1984), p. 232.

Oreb, B. F.

P. Hariharan, B. F. Oreb, “Stroboscopic Holographic Interferometry: Application of Digital Techniques,” Opt. Commun. 59, 83 (1986).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: A Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876 (1983).
[CrossRef] [PubMed]

B. F. Oreb, P. Hariharan, “A Simple Stroboscopic Pulse Generator for Holographic Interferometry of Vibrating Objects,” J. Phys. E (in press) 20, 660 (1987).
[CrossRef]

Powell, R. L.

Stetson, K. A.

Tonin, R.

R. Tonin, D. A. Bies, “General Theory of Time-Averaged Holography for the Study of Three-Dimensional Vibrations at a Single Frequency,” J. Opt. Soc. Am. 68, 924 (1978).
[CrossRef]

R. Tonin, D. A. Bies, “Time-Averaged Holography for the Study of Three-Dimensional Vibrations,” J. Sound Vib. 52, 315 (1977).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Sound Vib. (1)

R. Tonin, D. A. Bies, “Time-Averaged Holography for the Study of Three-Dimensional Vibrations,” J. Sound Vib. 52, 315 (1977).
[CrossRef]

Opt. Commun. (1)

P. Hariharan, B. F. Oreb, “Stroboscopic Holographic Interferometry: Application of Digital Techniques,” Opt. Commun. 59, 83 (1986).
[CrossRef]

Other (2)

B. F. Oreb, P. Hariharan, “A Simple Stroboscopic Pulse Generator for Holographic Interferometry of Vibrating Objects,” J. Phys. E (in press) 20, 660 (1987).
[CrossRef]

P. Hariharan, Optical Holography (Cambridge U.P., London, 1984), p. 232.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the experimental arrangement.

Fig. 2
Fig. 2

Schematic of the illumination geometry.

Fig. 3
Fig. 3

Time-averaged holograms obtained for the two directions of illumination with the blade vibrating in its fundamental mode at a frequency of 310 Hz.

Fig. 4
Fig. 4

Phase maps obtained for the two directions of illumination at 310 Hz.

Fig. 5
Fig. 5

Evaluation of the in-plane component Ly and out-of-plane component Lz of the surface displacement from data recorded with two different directions of illumination.

Fig. 6
Fig. 6

Three-dimensional plot of the out-of-plane component of the vibration amplitude at 310 Hz.

Fig. 7
Fig. 7

Time-averaged holograms obtained for the two directions of illumination with the blade vibrating in a higher-order mode at a frequency of 1100 Hz.

Fig. 8
Fig. 8

Phase maps obtained for the two directions of illumination at 1100 Hz.

Fig. 9
Fig. 9

Three-dimensional plot of the out-of-plane component of the vibration at 1100 Hz.

Fig. 10
Fig. 10

Three-dimensional plot of the in-plane component of the vibration at 1100 Hz.

Equations (8)

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φ = ( 2 π / λ ) ( k ̂ 2 k ̂ 1 ) L = K L ,
L l = L y cos [ ψ + ( π θ H ) / 2 ] + L z cos [ ( θ H / 2 ) ψ ] ,
L r = L y cos [ ψ + ( π + θ H ) / 2 ] + L z cos [ ψ + ( θ H / 2 ) ] .
L y = { L l cos [ ψ + ( θ H / 2 ) ] L r cos [ ψ ( θ H / 2 ) ] } / sin θ H .
L z = { L l sin [ ψ + ( θ H / 2 ) ] L r sin [ ψ ( θ H / 2 ) ] } / sin θ H .
ψ = ψ L + ( ψ L ψ B ) ( x x 1 ) / ( x 2 x 1 ) + ( ψ R ψ L ) ( y 1 y ) / ( y 2 y 1 ) ,
δ L y δ ψ [ L l sin ( ψ + θ H / 2 ) + L r sin ( ψ θ H / 2 ) ] / sin θ H ,
δ L z δ ψ [ L l cos ( ψ + θ H / 2 ) L r cos ( ψ θ H / 2 ) ] / sin θ H .

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