Abstract

A time-averaged recording of a sinusoidally vibrating object reconstructs a fringe function, which is determined by the ratio between the exposure time and the vibration period. For short exposures, compared with the vibration period, the fringe function is highly dependent on the number of vibration cycles recorded and on the starting point of the exposure in the vibration cycle. When several fringe functions that are recorded at different parts of the vibration cycle are added, the resulting averaged fringe function is similar to the normal J02 function, even at short exposures. The frequency ranges at which numerical analysis can be used in these two cases are defined, and the result of short exposures permitting digital fringe analysis, even under extremely unstable situations, is demonstrated. Extending the standard video exposure time permits recording vibrations at low frequencies as the normal J02 function and improves the light economy.

© 1993 Optical Society of America

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References

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  1. J. N. Butters, J. A. Leendertz, “Holographic and videotechniques applied to engineering measurements,” J. Meas. Control. 4, 349–354 (1971).
  2. O. J. Løkberg, “ESPI—the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am 75, 1783–1791 (1984).
    [CrossRef]
  3. G. Å. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
    [CrossRef] [PubMed]
  4. O. J. Løkberg, G. Å. Slettemoen, “Improved fringe definition by speckle averaging in ESPI,” in Optics in Modern Science and Technology, H. Ohzu, ed. (ICO-13 Organizing Committee, Sapporo, Japan, 1984), pp: 116–117.
  5. S. Nakadate, T. Yatagai, H. Saito, “Fringe scanning speckle pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
    [CrossRef] [PubMed]
  6. 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]
  7. O. J. Løkberg, “Use of chopped laser light in electronic speckle pattern interferometry,” Appl. Opt. 18, 2377–2384 (1979).
    [CrossRef] [PubMed]
  8. O. J. Løkberg, K. Høgmoen, O. M. Holje, “Vibration measurement on the human ear in vivo,” Appl. Opt. 18, 763–765 (1979):
    [CrossRef] [PubMed]
  9. K. Høgmoen, O. J. Løkberg, “Detection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
    [CrossRef] [PubMed]
  10. See, e.g. F. W. J. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions, M. A. Abramowitz, I. A. Stegun, eds. (Dover, New York, 1965), pp. 355–433.
  11. K. Stetson, “Theory and applications of electronic holography,” in Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 294–300.
  12. P. Neiswander, G. Å Slettemoen, “Electronic speckle pattern interferometric measurements of the basilar membrane in the inner ear,” Appl. Opt. 20, 4271–4276 (1981).
    [CrossRef] [PubMed]

1992 (1)

1985 (1)

1984 (1)

O. J. Løkberg, “ESPI—the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am 75, 1783–1791 (1984).
[CrossRef]

1981 (1)

1980 (1)

1979 (2)

1977 (1)

1971 (1)

J. N. Butters, J. A. Leendertz, “Holographic and videotechniques applied to engineering measurements,” J. Meas. Control. 4, 349–354 (1971).

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Holographic and videotechniques applied to engineering measurements,” J. Meas. Control. 4, 349–354 (1971).

Ellingsrud, S.

Høgmoen, K.

Holje, O. M.

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Holographic and videotechniques applied to engineering measurements,” J. Meas. Control. 4, 349–354 (1971).

Løkberg, O. J.

O. J. Løkberg, “ESPI—the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am 75, 1783–1791 (1984).
[CrossRef]

O. J. Løkberg, “Use of chopped laser light in electronic speckle pattern interferometry,” Appl. Opt. 18, 2377–2384 (1979).
[CrossRef] [PubMed]

O. J. Løkberg, K. Høgmoen, O. M. Holje, “Vibration measurement on the human ear in vivo,” Appl. Opt. 18, 763–765 (1979):
[CrossRef] [PubMed]

K. Høgmoen, O. J. Løkberg, “Detection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
[CrossRef] [PubMed]

O. J. Løkberg, G. Å. Slettemoen, “Improved fringe definition by speckle averaging in ESPI,” in Optics in Modern Science and Technology, H. Ohzu, ed. (ICO-13 Organizing Committee, Sapporo, Japan, 1984), pp: 116–117.

Nakadate, S.

Neiswander, P.

Olver, F. W. J.

See, e.g. F. W. J. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions, M. A. Abramowitz, I. A. Stegun, eds. (Dover, New York, 1965), pp. 355–433.

Rosvold, G. O.

Saito, H.

Slettemoen, G. Å

Slettemoen, G. Å.

G. Å. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
[CrossRef] [PubMed]

O. J. Løkberg, G. Å. Slettemoen, “Improved fringe definition by speckle averaging in ESPI,” in Optics in Modern Science and Technology, H. Ohzu, ed. (ICO-13 Organizing Committee, Sapporo, Japan, 1984), pp: 116–117.

Stetson, K.

K. Stetson, “Theory and applications of electronic holography,” in Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 294–300.

Yatagai, T.

Appl. Opt. (6)

J. Acoust. Soc. Am (1)

O. J. Løkberg, “ESPI—the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am 75, 1783–1791 (1984).
[CrossRef]

J. Meas. Control. (1)

J. N. Butters, J. A. Leendertz, “Holographic and videotechniques applied to engineering measurements,” J. Meas. Control. 4, 349–354 (1971).

J. Opt. Soc. Am. A (1)

Other (3)

O. J. Løkberg, G. Å. Slettemoen, “Improved fringe definition by speckle averaging in ESPI,” in Optics in Modern Science and Technology, H. Ohzu, ed. (ICO-13 Organizing Committee, Sapporo, Japan, 1984), pp: 116–117.

See, e.g. F. W. J. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions, M. A. Abramowitz, I. A. Stegun, eds. (Dover, New York, 1965), pp. 355–433.

K. Stetson, “Theory and applications of electronic holography,” in Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 294–300.

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Figures (8)

Fig. 1
Fig. 1

Single-frame fringe functions for exposure-time-to-vibration-period ratios (a) 0.8 and (b) 1.2. Midphase settings θ are as indicated.

Fig. 2
Fig. 2

Semilog plots of average fringe functions for exposure-time-to-vibration-period ratios 1.0, 1.25, 1.5, 1.75, and 2.25. At the second fringe minimum in which the curves are clearly separated, the curves, from bottom to top, are 1, 2.25, 1.75, 1.25, and 1.5.

Fig. 3
Fig. 3

Linear plots of the averaged fringe functions for the exposure-time-to-vibration-period ratios 1.0, 0.8, 0.4, 0.2, and 0.1, as indicated.

Fig. 4
Fig. 4

Instrumentation layout of the TV holographic system used for shortened and prolonged exposure times: Exp. Contr., exposure control; Integr. Contr., integration control; PM, phase modulation; GPIB, general-purpose instrument bus.

Fig. 5
Fig. 5

Vibration patterns recorded of an object held freely in the hand: vibration frequency is 5250 Hz with exposure times (a) 1/254 s and (b) 1/5250 s. The pictures consist of 15 consecutive averaged frames.

Fig. 6
Fig. 6

Calculated amplitude and phase distributions for an object mounted on a motor; the vibration frequency is 5250 Hz, and the exposure time is 1/5250 s: (a) motor off, (b) motor running, (c) 3-D graphs of the amplitude (top) and the phase distribution (bottom) in case (b).

Fig. 7
Fig. 7

Amplitude and phase distributions of an unstable object recorded at exposure time 1/5250 s: vibration frequencies are (a) 2100 Hz and (b) 1050 Hz; (c) 3-D graphs of the distributions in case (a).

Fig. 8
Fig. 8

Time-averaged recordings (∼J02 fringe function) at low frequencies recorded by extended exposure time: (a) vibration frequency 5 Hz and exposure time 1/2.5 s, (b) frequency 1 Hz and exposure time 1 s.

Equations (4)

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U 0 ( x , y , t ) = U 0 ( x , y ) exp { [ 4 π i a 0 ( x , y ) λ ] sin [ 2 π f 0 t + φ 0 ( x , y ) ] } ,
I ( x , y ) = I 0 ( x , y ) | 1 ( T T 2 ) T 1 T 2 exp { 4 π i λ a 0 ( x , y ) × sin [ 2 π f 0 t + φ 0 ( x , y ) ] d t | 2 ,
I ( x , y ) = I 0 ( x , y ) | q = J q [ u ( x , y ) ] × exp { i q [ θ ¯ + φ 0 ( x , y ) ] } sinc ( q T c T 0 ) | 2 = I 0 ( x , y ) Z { u ( x , y ) , φ 0 ( x , y ) + θ ¯ , T c } ,
I ( x , y ) = I 0 ( x , y ) q = J q 2 [ u ( x , y ) ] sinc 2 ( q T c T 0 ) = I 0 ( x , y ) Z av { u ( x , y ) , T c } ,

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