Abstract

A detailed analysis of the vibration fringes obtained by phase stepping on a time-averaged electronic speckle pattern interferometer is presented. It is shown that the contrast of the fringes remains relatively high for any phase step between 30° and 180° for low electronic noise and fringe density. Also, for the four-phase-stepped method, the vibration fringes have the same contrast as that of the π-phase-shift method except that the high-frequency speckles are smoothed. The contrast of the fringes obtained with extra phase steps along with incoherent superimposition is shown to be higher than the single- or four-phase-step method. Both theory and experimental results are presented.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
    [Crossref]
  2. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).
  3. O. J. Lokberg, “ESPI—The ultimate holographic tool for vibration analysis,” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
    [Crossref]
  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. 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, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 279–292 (1989).
  6. B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time average subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
    [Crossref]
  7. E. Vikhagen, “Vibration measurement using phase shifting TV-holography and digital image processing,” Opt. Commun. 69, 214–218 (1989).
    [Crossref]
  8. T. Bushman, “Development of a holographic computing system,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 66–77 (1989).
  9. 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]
  10. C. Joenathan, B. M. Khorana, “Phase measuring fiber optic ESPI system: phase step calibration and phase drift minimization,” Opt. Eng. (to be published).
  11. G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
    [Crossref]
  12. O. J. Lokberg, G. A. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), Vol. 9, pp 455–504.
  13. C. Wykes, “A theoretical approach to the optimization of electronic speckle interferometry with limited laser power,” J. Mod. Opt. 34, 539–554 (1987).
    [Crossref]
  14. C. Joenathan, “Effect of non-linearity of the TV camera in electronic speckle pattern interferometry,” Optik 85, 33–37 (1990).
  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]

1990 (2)

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]

C. Joenathan, “Effect of non-linearity of the TV camera in electronic speckle pattern interferometry,” Optik 85, 33–37 (1990).

1989 (2)

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

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

1987 (1)

C. Wykes, “A theoretical approach to the optimization of electronic speckle interferometry with limited laser power,” J. Mod. Opt. 34, 539–554 (1987).
[Crossref]

1985 (1)

1984 (1)

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

1981 (1)

1979 (1)

G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
[Crossref]

1971 (1)

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[Crossref]

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]

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, 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, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 66–77 (1989).

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[Crossref]

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, 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, “Effect of non-linearity of the TV camera in electronic speckle pattern interferometry,” Optik 85, 33–37 (1990).

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

Jones, R.

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

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[Crossref]

Lokberg, O. J.

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

O. J. Lokberg, G. A. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), Vol. 9, pp 455–504.

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]

Slettemoen, G. A.

K. Creath, G. A. Slettemoen, “Vibration observation techniques for digital speckle pattern interferometry,” J. Opt. Soc. Am. A 2, 1629–1636 (1985).
[Crossref]

G. A. Slettemoen, “First-order statistics of displayed speckle patterns in electronic speckle pattern interferometry,” J. Opt. Soc. Am. 71, 474–482 (1981).
[Crossref]

G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
[Crossref]

O. J. Lokberg, G. A. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), Vol. 9, pp 455–504.

Vikhagen, E.

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

Wykes, C.

C. Wykes, “A theoretical approach to the optimization of electronic speckle interferometry with limited laser power,” J. Mod. Opt. 34, 539–554 (1987).
[Crossref]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, London, 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]

J. Acoust. Soc. Am. (1)

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

J. Mod. Opt. (1)

C. Wykes, “A theoretical approach to the optimization of electronic speckle interferometry with limited laser power,” J. Mod. Opt. 34, 539–554 (1987).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Acta (1)

G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
[Crossref]

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]

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

Opt. Laser Technol. (1)

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[Crossref]

Optik (1)

C. Joenathan, “Effect of non-linearity of the TV camera in electronic speckle pattern interferometry,” Optik 85, 33–37 (1990).

Other (5)

O. J. Lokberg, G. A. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), Vol. 9, pp 455–504.

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

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, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 279–292 (1989).

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

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the fiber-optic ESPI arrangement used for conducting the experiments.

Fig. 2
Fig. 2

(a) Plot of the contrast with varying phase-step values. The three curves are for three values of the electronic noise, σe2 = 0.002, 0.02, 0.04. (b) Contrast for the three values, P = 10, P = 20, and P = 29.

Fig. 3
Fig. 3

Variation of contrast with P for the single phase step and the additional phase step with an incoherent superimposition. The contrast in the single phase step (PS) of 90° and 180° and the additional phase step (ADD) with 90° and 180° between pairs is plotted. The electronic noise for this plot is σe2 = 0.02.

Fig. 4
Fig. 4

Fringes for the loudspeaker vibrating with 1.992 kHz obtained by the following three methods: (a) four-phase step; (b) single-phase step of π; and (c) single-phase step of π/2.

Fig. 5
Fig. 5

Experimental plot of the variation of contrast (shown by error bars) for different phase-step angles. For the theoretical plot the value of σe2 = 0.005 and P = 13.4 was used.

Fig. 6
Fig. 6

Vibration fringes obtained with additional phase steps of 0, π/6, and π/3 and incoherent superimposition: (a) the π phase step between pairs, (b) the π/2 phase step between pairs, and (c) the four-phase-step method. A frequency of 3.9 kHz was used for vibrating the speaker.

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

I 1 ( x , y , t ) = I o + I r + 2 Re { A r * A o } ,
I 1 a ( x , y , t ) = f ( t ) I ( x , y , t ) d t , I 1 a ( x , y , t ) = I o + I r + 2 Re [ A r * A o M ( x , y ) ] ,
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 = 2 g 1 γ I o I r J 0 ( P ) [ cos ( ϕ ) cos ( ϕ + δ ) ] + N 1 N 2 ,
Δ V 1 2 = 4 I o I r g 1 2 γ 2 J 0 2 ( P ) × [ cos ( ϕ ) ( 1 cos δ ) + sin ( ϕ ) sin δ ] 2 + 2 σ e 2 ,
SNR = | Δ V 2 ( information ) | electronic noise ,
C = SNR SNR + 2 .
SNR = 4 I o I r g 1 2 γ 2 J 0 2 ( P ) sin 2 δ / 2 σ e 2 ,
I 1 a ( x , y , t ) = I o + I r + 2 I o I r J 0 ( P ) cos ( ϕ ) ,
I 2 a ( x , y , t ) = I o + I r 2 I o I r J 0 ( P ) sin ( ϕ ) ,
I 3 a ( x , y , t ) = I o + I r 2 I o I r J 0 ( P ) cos ( ϕ ) ,
I 4 a ( x , y , t ) = I o + I r + 2 I o I r J 0 ( P ) sin ( ϕ ) .
Δ V 1 I 1 a I 3 a , Δ V 1 = 4 g 1 γ I o I r J 0 ( P 0 ) cos ( ϕ ) + N 1 N 3 ,
Δ V 2 I 4 a I 2 a , Δ V 2 = 4 g 1 γ I o I r J 0 ( P 0 ) sin ( ϕ ) + N 4 N 2 ,
Δ V 2 = Δ V 1 2 + Δ V 2 2 , Δ V 2 = 16 γ 2 g 1 2 I o I r J 0 2 ( P ) + 4 σ e 2 ,
SNR = 4 γ 2 g 1 2 I o I r J 0 2 ( P ) σ e 2 .
Δ V = 4 K g 1 γ I o I r J 0 ( P ) ,
Δ V 1 = 2 γ g 1 I o I r J 0 ( P ) × [ cos ( ϕ ) cos ( ϕ + π / 2 ) ] + N 1 N 2 ,
Δ V 2 = 2 γ g 1 I o I r J 0 ( P ) × [ cos ( ϕ + π / 6 ) cos ( ϕ + π / 6 + π / 2 ) ] + N 3 N 4 ,
Δ V 3 = 2 γ g 1 I o I r J 0 ( P ) × [ cos ( ϕ + π / 3 ) cos ( ϕ + π / 3 + π / 2 ) ] + N 5 N 6 .
Δ V 2 = | Δ V 1 + Δ V 2 + Δ V 3 | 2 ,
Δ V 2 30 γ 2 g 1 2 I o I r J 0 2 ( P ) + 6 σ e 2 ,
SNR 5 γ 2 g 1 2 I o I r J 0 2 ( P ) σ e 2 .
SNR 10 γ 2 g 1 2 I o I r J 0 2 ( P ) σ e 2 .
σ 2 = Δ V out 2 ( x , y ) + σ e 2 ,
Δ V out ( x , y ) = Δ V in ( x , y ) h ( x x , y y ) d x d y ,
σ 2 = Δ V in ( x , y ) Δ V in ( x , y ) h ( x x , y y ) × h ( x x , y × y ) d x d x d y d y + σ e 2 ,
Δ V in ( x , y ) = 4 g 1 Re { A r * A o M } ,
ρ in ( Δ x , Δ y ) = 4 g 1 | M | 2 Re { J R * J O b } ,
ρ in ( Δ x , Δ y ) = S in ( f x , f y ) exp [ 2 π ( Δ x f x + Δ y f y ) ] d f x d f y ,
h ( τ ) = H ( f x , f y ) exp [ 2 π τ ( f x + f y ) ] d f x d f y ,
ρ 2 = S in ( f x , f y ) | H ( f x , f y ) | 2 d f x d f y ,
σ 2 = 4 g 1 2 γ 2 | M | 2 I r I o + σ e 2 ,
γ = 1 I r I o F [ Re { J R * J O b } ] | H ( f x , f y ) | 2 d f x d f y ,
γ = | P A | 2 | H | 2 d f x d f y | P A | 2 d f x d f y ,

Metrics