Abstract

This paper presents a detailed investigation of the effect of speckle averaging in electronic speckle-pattern interferometric fringes. The theory states that the constrast of the resultant smoothed fringes increases as the number of frames is increased. It is shown that the contrast of the fringes is optimized with a limited number of superpositions, and further addition results in the reduction of speckle noise with the contrast remaining almost the same. The contrast of the fringes obtained with π and π/2 phase-stepping methods with speckle averaging is also discussed. Both theoretical and experimental results are presented in this paper.

© 1992 Optical Society of America

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References

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  1. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1983).
  2. O. J. Løkberg, “ESPI-The ultimate holographic tool for vibration analysis,” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
    [CrossRef]
  3. J. R. Tyrer, “Structural analysis using phase-stepped double pulsed ESPI,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 144–155 (1989).
  4. K. Creath, G. A. Slettemoen, “Vibration-observation techniques for digital speckle pattern interferometry,” J. Opt. Soc. Am. A 2, 1629–1636 (1985).
    [CrossRef]
  5. C. Joenathan, “Recent developments in electronic speckle pattern interferometry,” in Proceedings of the SEM Conference, Milwaukee, WI 1991 (Society for Experimental Mechanics, Inc., Bethel, Conn., 1991) pp. 198–204.
  6. J. C. Davies, C. H. Buchberry, “Application of a fiber optic TV holography system to the study of large automotive structures,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 279–292 (1989).
  7. B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
    [CrossRef]
  8. C. Joenathan, “Analysis of the vibration fringes by phase stepping in ESPI,” Appl. Opt. 30, 46–58 (1991).
    [CrossRef]
  9. E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
    [CrossRef]
  10. T. Bushman, “Development of a holographic computing system,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 66–77 (1989).
  11. B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
    [CrossRef]
  12. G. A. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
    [CrossRef] [PubMed]
  13. P. C. Montgomery, B. D. Berquist, “Contrast enhancement of ESPI vibration patterns by speckle averaging in a video frame store,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 201–206 (1985).
  14. C. Joenathan, B. M. Khorana, “Phase measuring fiber optic ESPI system: phase step calibration and phase drift minimization,” Opt. Eng. (to be published).
  15. G. A. Slettemoen, “First-order statistics of displayed speckle patterns in electronic speckle pattern interferometry,” J. Opt. Soc. Am. 71, 474–482 (1981).
    [CrossRef]

1991 (1)

C. Joenathan, “Analysis of the vibration fringes by phase stepping in ESPI,” Appl. Opt. 30, 46–58 (1991).
[CrossRef]

1990 (1)

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

1989 (2)

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

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

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)

Abendroth, H.

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Berquist, B. D.

P. C. Montgomery, B. D. Berquist, “Contrast enhancement of ESPI vibration patterns by speckle averaging in a video frame store,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 201–206 (1985).

Buchberry, C. H.

J. C. Davies, C. H. Buchberry, “Application of a fiber optic TV holography system to the study of large automotive structures,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 279–292 (1989).

Bushman, T.

T. Bushman, “Development of a holographic computing system,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 66–77 (1989).

Creath, K.

Davies, J. C.

J. C. Davies, C. H. Buchberry, “Application of a fiber optic TV holography system to the study of large automotive structures,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 279–292 (1989).

Eggers, H.

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Hu, Z.

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

Joenathan, C.

C. Joenathan, “Analysis of the vibration fringes by phase stepping in ESPI,” Appl. Opt. 30, 46–58 (1991).
[CrossRef]

C. Joenathan, B. M. Khorana, “Phase measuring fiber optic ESPI system: phase step calibration and phase drift minimization,” Opt. Eng. (to be published).

C. Joenathan, “Recent developments in electronic speckle pattern interferometry,” in Proceedings of the SEM Conference, Milwaukee, WI 1991 (Society for Experimental Mechanics, Inc., Bethel, Conn., 1991) pp. 198–204.

Jones, R.

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

Khorana, B. M.

C. Joenathan, B. M. Khorana, “Phase measuring fiber optic ESPI system: phase step calibration and phase drift minimization,” Opt. Eng. (to be published).

Løkberg, O. J.

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

Lu, B.

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Montgomery, P. C.

P. C. Montgomery, B. D. Berquist, “Contrast enhancement of ESPI vibration patterns by speckle averaging in a video frame store,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 201–206 (1985).

Slettemoen, G. A.

Tyrer, J. R.

J. R. Tyrer, “Structural analysis using phase-stepped double pulsed ESPI,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 144–155 (1989).

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, 1983).

Yang, X.

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Ziolkowski, E.

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

Appl. Opt. (2)

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. Opt. Soc. Am. (1)

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

Opt. Commun. (3)

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

B. Lu, Z. Hu, H. Abendroth, H. Eggers, E. Ziolkowski, “Improvement of time-average subtraction technique applied to the vibration analysis with TV-holography,” Opt. Commun. 78, 217–221 (1990).
[CrossRef]

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

Other (7)

T. Bushman, “Development of a holographic computing system,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 66–77 (1989).

C. Joenathan, “Recent developments in electronic speckle pattern interferometry,” in Proceedings of the SEM Conference, Milwaukee, WI 1991 (Society for Experimental Mechanics, Inc., Bethel, Conn., 1991) pp. 198–204.

J. C. Davies, C. H. Buchberry, “Application of a fiber optic TV holography system to the study of large automotive structures,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum Eng.1162, 279–292 (1989).

J. R. Tyrer, “Structural analysis using phase-stepped double pulsed ESPI,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 144–155 (1989).

P. C. Montgomery, B. D. Berquist, “Contrast enhancement of ESPI vibration patterns by speckle averaging in a video frame store,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 201–206 (1985).

C. Joenathan, B. M. Khorana, “Phase measuring fiber optic ESPI system: phase step calibration and phase drift minimization,” Opt. Eng. (to be published).

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

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Figures (10)

Fig. 1
Fig. 1

Schematic of the ESPI arrangement that is used for observing vibrational mode.

Fig. 2
Fig. 2

Theoretical plot showing the increase in the contrast of the fringes versus the number of superposed fringe patterns. Three values of the phase shift δo (15°, 10°, and 5°) were used.

Fig. 3
Fig. 3

Theoretical plot of the increase in contrast for a π phase-step method. The increase in contrast for constant and variable phase differences is plotted.

Fig. 4
Fig. 4

This plot compares the increase in contrast for a π and a π/2 phase-step difference between two frames. The phase steps were maintained constant between any two frames.

Fig. 5
Fig. 5

Theoretical plot of the increase in contrast for a π/2 phase-step method. The increase in contrast for constant and variable phase differences is plotted.

Fig. 6
Fig. 6

Experimental plot of the contrast as a function of the number of incoherent addition. There is good agreement between theory and experiment.

Fig. 7
Fig. 7

Photographs of the vibration fringes of a loudspeaker vibrating at 3.4 kHz with phase step of 10° introduced between frames: (a) n = 1, (b) n = 3, (c) n = 6, (d) n = 12.

Fig. 8
Fig. 8

Photographs of the vibration fringe patterns of the speaker vibrating at 6.37 kHz with a π phase step: (a) single fringe pattern, (b) 12 fringe patterns.

Fig. 9
Fig. 9

Photographs of the vibration fringes for the speaker vibrating at 5.44 kHz with a π/2 phase step between frames: (a) single fringe pattern, (b) average of 12 fringe patterns with a constant phase step, (c) average of 12 fringe patterns with a variable phase step. The δo used was 10°.

Fig. 10
Fig. 10

Photographs of the loudspeaker vibrating at 3.64 kHz. Random phase steps were used to acquire the 12 fringes.

Equations (24)

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I 1 ( x , y , t ) = I o + I r + 2 I o I r cos × [ 2 π λ ( 1 + cos θ ) W ( x , y , t ) + ϕ ] + N 1 ,
I 1 a ( x , y , t ) = I o + I r + 2 I o I r J 0 ( P ) cos ( ϕ ) + N 1 ,
Δ V 1 = 4 K sin ( ϕ + δ / 2 ) sin ( δ / 2 ) + N 1 - N 2 ,
Δ V 2 = 4 K sin ( ϕ + δ o + δ / 2 ) sin ( δ / 2 ) + N 3 - N 4 .
Δ V 1 + Δ V 2 = 4 K sin ( δ / 2 ) [ cos ( ϕ + δ / 2 ) ( 1 + sin δ o ) + sin ( ϕ + δ / 2 ) cos δ o ] + N 1 - N 2 + N 3 - N 4 .
Δ = i = 1 n Δ V i = 4 K sin ( δ / 2 ) { cos ( ϕ + δ / 2 ) [ 1 + i > 1 n sin ( n - 1 ) δ o ] + sin ( ϕ + δ / 2 ) i > 1 n cos ( n - 1 ) δ o } + N 1 - N 2 + N 3 - N 4 N 2 n + 1 - N 2 ( n + 1 ) ,
B Δ 2 = + 2 n σ e 2 ,
C = S N S N + 2 .
S N = Δ 2 ( information ) electronic noise
S N = 4 K 2 sin 2 ( δ / 2 ) { [ 1 + i > 1 n sin ( n - 1 ) δ o ] 2 + [ i > 1 n cos ( n - 1 ) δ o ] 2 } n σ e 2 .
S N ( 1 ) = 4 K 2 sin 2 ( δ / 2 ) σ e 2 ,
S N ( 2 ) = 2 K 2 sin 2 ( δ / 2 ) [ ( 1 + sin δ o ) 2 + ( cos δ o ) 2 ] σ e 2 ,
S N ( 3 ) = 2 K 2 sin 2 ( δ / 2 ) [ ( 1 + sin δ o + sin 2 δ o ) 2 + ( cos δ o + cos 2 δ o ) 2 ] 3 σ e 2 ,
S N = 4 K 2 sin 2 ( δ / 2 ) { [ 1 + i > 1 n sin δ ( n - 1 ) ] 2 + [ i > 1 n c o s δ ( n - 1 ) ] 2 } n σ e 2 .
Δ V 1 a = 2 K J 0 ( P ) [ cos ( ϕ ) ( 1 - cos δ o ) + sin ( ϕ ) sin δ a ] + N 1 - N 2 ,
Δ V = 2 K J 0 [ cos ( ϕ ) ( n - i = 1 n cos n δ o ) + sin ( ϕ ) i = 1 n sin n δ o ] + N 1 - N 2 + N 3 - N 4 N 2 n + 1 - N 2 ( n + 1 ) .
B Δ V 2 = 1 + 2 n σ e 2 ,
S N = K 2 J 0 2 [ ( n - i = 1 n cos n δ o ) 2 + ( i = 1 n sin n δ o ) 2 ] n σ e 2 .
S N = K 2 J 0 2 [ ( n - i = 1 n cos δ n ) 2 + ( i = 1 n sin δ n ) 2 ] n σ e 2 .
Δ V 1 , 2 2 ( π ) = 1 , 2 ( π ) + 2 n σ e 2 ,
Δ V 2 2 ( π ) = 2 ( π ) + 2 n σ e 2 ,
Δ V 1 = 2 K J 0 ( P ) [ cos ( ϕ ) + sin ( ϕ ) ] + N 1 - N 2 .
Δ V 1 , 2 2 ( π / 2 ) = 1 , 2 ( π / 2 ) + 2 n σ e 2 ,
Δ V 2 2 ( π / 2 ) = 2 ( π / 2 ) + 2 n σ e 2 ,

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