Abstract

We separately measure the higher harmonics vibration patterns of a periodic vibrating object by using time-average TV holography and phase modulation. During measurements the frequency of the phase modulation is adjusted to each harmonic component while the excitation of the object is set low enough to record all components on the linear part of the fringe function. Using acoustical phase stepping and calibration of the fringe function, we compute the amplitude and phase distributions of the frequency component. We measure components up to the 65th harmonic by using square-wave excitation.

© 1994 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. J. Politsch, “Spectroscopic holography: a new method for mode analysis of randomly excited structures,” J. Opt. Soc. Am. A 7, 1355–1361 (1990).
    [CrossRef]
  3. H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
    [CrossRef]
  4. N. E. Molin, K. A. Stetson, “Measuring combination mode vibration patterns by holographic interferometry,” J. Phys. E 2, 609–612 (1969).
    [CrossRef]
  5. S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
    [CrossRef]
  6. S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV-holography and digital image processing,” J. Sound. Vibr. 168, 193–208 (1993).
    [CrossRef]
  7. G. O. Rosvold, “Fast measurements of phase using a PC-based frame grabber and phase stepping technique,” Appl. Opt. 29, 237–241 (1990).
    [CrossRef] [PubMed]
  8. G. Å. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
    [CrossRef] [PubMed]
  9. G. O. Rosvold, “Video based vibration analysis using projected fringes,” Appl. Opt. 33, 775–786 (1994).
    [CrossRef] [PubMed]

1994 (2)

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

G. O. Rosvold, “Video based vibration analysis using projected fringes,” Appl. Opt. 33, 775–786 (1994).
[CrossRef] [PubMed]

1993 (1)

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV-holography and digital image processing,” J. Sound. Vibr. 168, 193–208 (1993).
[CrossRef]

1992 (1)

1990 (2)

1980 (1)

1969 (1)

N. E. Molin, K. A. Stetson, “Measuring combination mode vibration patterns by holographic interferometry,” J. Phys. E 2, 609–612 (1969).
[CrossRef]

Ellingsrud, S.

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV-holography and digital image processing,” J. Sound. Vibr. 168, 193–208 (1993).
[CrossRef]

S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
[CrossRef]

Løkberg, O. J.

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV-holography and digital image processing,” J. Sound. Vibr. 168, 193–208 (1993).
[CrossRef]

Molin, N. E.

N. E. Molin, K. A. Stetson, “Measuring combination mode vibration patterns by holographic interferometry,” J. Phys. E 2, 609–612 (1969).
[CrossRef]

Pedersen, H. M.

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Politsch, J.

Rosvold, G. O.

Slettemoen, G. Å.

Stetson, K. A.

N. E. Molin, K. A. Stetson, “Measuring combination mode vibration patterns by holographic interferometry,” J. Phys. E 2, 609–612 (1969).
[CrossRef]

Valø, H.

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Wang, G.

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. A (2)

J. Phys. E (1)

N. E. Molin, K. A. Stetson, “Measuring combination mode vibration patterns by holographic interferometry,” J. Phys. E 2, 609–612 (1969).
[CrossRef]

J. Sound. Vibr. (1)

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV-holography and digital image processing,” J. Sound. Vibr. 168, 193–208 (1993).
[CrossRef]

Opt. Commun. (1)

H. M. Pedersen, O. J. Løkberg, H. Valø, G. Wang, “Detection of nonsinusoidal periodic vibrations using phase modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Other (1)

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

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Figures (6)

Fig. 1
Fig. 1

Time-average fringe function at low vibration levels with PM at working point a b .

Fig. 2
Fig. 2

Flow chart that shows recording and analysis of higher harmonics vibration with TV holography: SA, speckle-averaging mechanism; PM, phase-modulation mirror. For object excitation, the square wave is at frequency, f. Sinusoidal PM is at higher harmonic frequency nf.

Fig. 3
Fig. 3

Time-average vibration pattern of a box wall excited by a square-wave signal at 146 Hz and with a high excitation level.

Fig. 4
Fig. 4

Box wall excited by a square wave at 146 Hz and with a low vibration level. Higher harmonics of vibration recorded by PM TV holography. (a)–(f) Computed values of amplitude and phase distributions at the 3rd, 5th, 7th, 9th, 11th, and 13th, harmonics respectively.

Fig. 5
Fig. 5

Sinusoidal excitation of object. Amplitude and phase values recorded at (a) 730 Hz, (b) 1314 Hz, corresponding to the 5th and 9th harmonics of square-wave excitation in Fig. 4.

Fig. 6
Fig. 6

As in Fig. 4 but showing only amplitude distribution of (a) the 25th and (b) the 41st harmonics of square-wave vibration.

Equations (11)

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J 0 2 ( a 0 ) = { 1 T 0 T cos [ a 0 sin ( ω 0 t + ϕ r ) ] d t } 2 .
x ( t ) = k a k sin ( k ω t + ϕ k ) .
X ( a k ) = { 1 T 0 T cos [ x ( t ) ] d t } 2 = k J 0 2 ( a k ) .
X mod ( a ) = 1 J 0 2 ( a m ) ( J 0 2 { [ a m 2 + a r 2 - 2 a m a r × cos ( ϕ m - ϕ r ) ] 1 / 2 } k J 0 2 ( a k ) ) .
I m I 0 = J 0 2 [ a m 2 + a r 2 - 2 a m a r cos ( ϕ m - ϕ r ) ] 1 / 2 J 0 2 ( a m ) .
I 0 ( x , y ) = I b ( x , y ) - k ( x , y ) a 0 ( x , y ) cos φ 0 ( x , y ) ,
I 90 ( x , y ) = I b ( x , y ) + k ( x , y ) a 0 ( x , y ) sin φ 0 ( x , y ) ,
I 180 ( x , y ) = I b ( x , y ) + k ( x , y ) a 0 ( x , y ) cos φ 0 ( x , y ) ,
I 270 ( x , y ) = I b ( x , y ) - k ( x , y ) a 0 ( x , y ) sin φ 0 ( x , y ) ,
φ 0 ( x , y ) = arctan [ I 90 ( x , y ) - I 270 ( x , y ) I 180 ( x , y ) - I 0 ( x , y ) ] .
a 0 ( x , y ) = { [ I 180 ( x , y ) - I 0 ( x , y ) ] 2 + [ I 90 ( x , y ) - I 270 ( x , y ) ] 2 } 1 / 2 2 k ( x , y ) .

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