Abstract

Three different image-processing methods based on the time-averaged technique were compared by the electronic speckle pattern interferometry (ESPI) technique for vibration measurement. The three methods are the video-signal-addition method, the video-signal-subtraction method, and the amplitude-fluctuation method. Also, errors introduced by using the zero-order Bessel function directly into the analysis of the fringe pattern were investigated. The video-signal-addition method has been the most generally used ESPI technique for vibration measurement. However, without additional image and/or signal-processing procedures, the fringe pattern obtained directly by the video-signal-addition method is rather difficult to observe. The reason for poor visibility of the experimentally obtained fringe pattern with this method is explained. To increase the fringe pattern’s visibility without additional image and/or signal processes, we tried two video-signal-subtraction methods. One of the two methods is the video-signal-subtraction method that has normally been used in the static applications. The other method, called the amplitude-fluctuation method, and its associated theory are reported here.

© 1996 Optical Society of America

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References

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  1. J. N. Butters, J. A. Leendertz, “Holographic and video techniques applied to engineering measurement,” J. Meas. Control 4, 349–354 (1971).
  2. O. J. Løkberg, K. Høgmoen, “Vibration phase mapping using electronic speckle pattern interferometry,” Appl. Opt. 15, 2701–2704 (1976).
    [CrossRef] [PubMed]
  3. K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–576 (1975).
    [CrossRef]
  4. M. C. Shellabear, J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Lasers Eng. 15, 43–56 (1991).
    [CrossRef]
  5. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, U.K., 1983).
  6. K. Høgmoen, O. J. Løkberg, “Objection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
    [CrossRef] [PubMed]
  7. S. Nakadate, T. Yatagai, H. Saito, “Electronic speckle pattern interferometry using digital image processing techniques,” Appl. Opt. 19, 1879–1883 (1980).
    [CrossRef] [PubMed]
  8. E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
    [CrossRef]
  9. C. Joenathan, “Vibration fringes by phase stepping on an electronic speckle pattern interferometer: an analysis,” Appl. Opt. 30, 4658–4665 (1991).
    [CrossRef] [PubMed]
  10. F. M. Santoyo, M. C. Shellabear, J. R. Tyrer, “Whole field in-plane vibration analysis using pulsed phase-stepped ESPI,” Appl. Opt. 30, 717–721 (1991).
    [CrossRef] [PubMed]
  11. R. S. Sirohi, Speckle Metrology (Dekker, New York, 1993).

1991 (3)

1989 (1)

E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
[CrossRef]

1980 (1)

1977 (1)

1976 (1)

1975 (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–576 (1975).
[CrossRef]

1971 (1)

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

Biedermann, K.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–576 (1975).
[CrossRef]

Butters, J. N.

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

Ek, L.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–576 (1975).
[CrossRef]

Høgmoen, K.

Joenathan, C.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, U.K., 1983).

Leendertz, J. A.

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

Løkberg, O. J.

Nakadate, S.

Saito, H.

Santoyo, F. M.

Shellabear, M. C.

F. M. Santoyo, M. C. Shellabear, J. R. Tyrer, “Whole field in-plane vibration analysis using pulsed phase-stepped ESPI,” Appl. Opt. 30, 717–721 (1991).
[CrossRef] [PubMed]

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Lasers Eng. 15, 43–56 (1991).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Dekker, New York, 1993).

Tyrer, J. R.

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Lasers Eng. 15, 43–56 (1991).
[CrossRef]

F. M. Santoyo, M. C. Shellabear, J. R. Tyrer, “Whole field in-plane vibration analysis using pulsed phase-stepped ESPI,” Appl. Opt. 30, 717–721 (1991).
[CrossRef] [PubMed]

Vikhagen, E.

E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, U.K., 1983).

Yatagai, T.

Appl. Opt. (5)

J. Meas. Control (1)

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

J. Phys. E (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–576 (1975).
[CrossRef]

Opt. Commun. (1)

E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
[CrossRef]

Opt. Lasers Eng. (1)

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Lasers Eng. 15, 43–56 (1991).
[CrossRef]

Other (2)

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, U.K., 1983).

R. S. Sirohi, Speckle Metrology (Dekker, New York, 1993).

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Figures (6)

Fig. 1
Fig. 1

Out-of-plane ESPI optical setup.

Fig. 2
Fig. 2

Mismatch effect of the shutter opening and the vibration period for different frequencies: (a) 100 Hz, (b) 1000 Hz.

Fig. 3
Fig. 3

Typical time history record of the exciting force.

Fig. 4
Fig. 4

Test specimen.

Fig. 5
Fig. 5

Images of the [0]16 composite plate obtained by the three time-averaged ESPI methods (second mode; frequency, 215 Hz; force, 0.017 N): (a) video-signal-addition method, (b) video-subtraction method, (c) amplitude-fluctuation method.

Fig. 6
Fig. 6

Theoretical brightness distribution of the three different methods.

Tables (2)

Tables Icon

Table 1 Values of ζ i for the Video-Signal-Subtraction Method

Tables Icon

Table 2 Values of ζ i * for the Amplitude-Fluctuation Method

Equations (35)

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I ( x , y , t ) = I o + I r + 2 I o I r cos [ φ ( x , y ) + Δ ( x , y , t ) ] ,
V CCD = α t 1 t 1 + τ [ I o + I r + 2 I o I r cos ( φ + Δ ) ] d t ,
τ = δ + 2 N π / ω ,
V CCD = 2 α N π ω [ I o + I r + 2 I o I r J 0 ( k ) cos φ ] + αδ { I o + I r + 2 I o I r [ cos φ k sin ωδ δω sin φ ( k ) 2 sin 2 ωδ δω cos φ cos φ 4 + ] } ,
V CCD = 2 N απ ω [ I o + I r + 2 I o I r J 0 ( k ) cos φ ] .
V CCD = 4 N απ [ 1 + J 0 ( k ) ] / ω .
V = V CCD / α
( V CCD ) REF = 2 N απ ω ( I o + I r + 2 I o I r cos φ ) .
V IM = 4 N απ ω I o I r [ J 0 ( k ) 1 ] cos φ .
V IM = 4 N απ ω I o I r { [ J 0 ( k ) 1 ] 2 cos 2 φ } 1 / 2 .
B IM = 4 N αβπ ω I o I r { [ J 0 ( k ) 1 ] 2 cos 2 φ } 1 / 2 ,
A = λζ i * / [ 2 π ( 1 + cos θ ) ] ,
( V CCD ) REF = 2 N απ ω { I o + I r + 2 I o I r J 0 [ 2 π λ A ( 1 + cos θ ) ] cos φ } .
( V CCD ) SEC = 2 N απ ω ( I o + I r + 2 I o I r J 0 × { [ 2 π λ ( A + Δ A ) ( 1 + cos θ ) ] } cos φ ) .
( V CCD ) DIFF = 2 N απ ω ( 2 I o I r { J 0 [ η ( A + Δ A ) ] J o ( η A ) } cos φ ) ,
lim Δ A 0 ( Δ V / Δ A ) = lim Δ A 0 2 N απ ω ( 2 I o I r { J 0 [ η ( A + Δ A ) ] J 0 ( η A ) Δ A } cos φ ) ,
d V d A = 2 N απ ω [ 2 I o I r J 1 ( η A ) cos φ ] .
V rec . = 4 N απ I o I r ω [ J 1 2 ( η A ) cos 2 φ ] 1 / 2 .
B IM = 4 N αβπ I o I r ω [ J 1 2 ( η A ) cos 2 φ ] 1 / 2 = 4 N αβπ I o I r ω [ J 1 2 ( k ) cos 2 φ ] 1 / 2 .
A = λζ i 2 π ( 1 + cos θ ) ,
Δ V CCD = 2 αβ I o I r J 0 ( k ) [ cos ( φ ) cos ( φ + Δ ) ] + N 1 N 2 ,
visibility = ( B IM ) max ( B IM ) min ( B IM ) max + ( B IM ) min .
Φ ( modified visibility ) = 1 k 0 k | B IM ( ζ ) B ¯ IM | B ¯ IM ,
B ¯ IM = 1 k 0 k B IM ( ζ )
Φ = 2 I o I r | J 0 ( K ) | ( I o + I r ) , K ( 0 , k ) ,
k | J o ( K ) | = 0 k | J 0 ( ζ ) | .
Φ = [ J 0 2 ( K b ) J 0 2 ( K a ) ] 1 / 2 [ 1 J 0 ( K a ) ] , K a , K b ( 0 , k ) , K a K b ,
k | J 0 ( K a ) | = 0 k | J 0 ( ζ ) | dζ, k | J 0 ( K b ) | = 0 k | J 0 ( ζ ) | 1/2 .
Φ = [ J 1 2 ( K b ) J 1 2 ( K a ) ] 1 / 2 | J 1 ( K a ) | , K a , K b ( 0 , k ) , K a K b ,
k | J 1 ( K a ) | = 0 k | J 1 ( ζ ) | dζ, k | J 1 ( K b ) | = 0 k | J 1 ( ζ ) | 1 / 2 .
B IM = 2 N αβπ ω [ I o + I r + 2 I o I r J 0 ( k ) cos φ ] .
B ¯ IM = 2 N αβπ ω k 0 k [ I o + I r + 2 I o I r J 0 ( ξ ) cos φ ] = 2 N αβπ ω k [ k ( I o + I r ) + 2 I o I r cos φ 0 k J 0 ( ξ ) ] .
B ¯ IM 2 N παβ ω ( I o + I r ) .
B var = 1 k 0 k | B IM ( ξ ) B ¯ IM | = 2 N αβπ I o I r cos φ k ω 0 k | J 0 ( ξ ) | .
( B var ) max = 2 N αβπ I o I r ω | J 0 ( K ) | , K ( 0 , k ) .

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