Abstract

A digital phase-mapping method has been developed for application in real-time electronic speckle interferometry studies. Its principles and application to a continuously deforming object are described. An efficient digital image-processing algorithm has been developed that permits quantitative interpretation of the resulting phase maps.

© 1995 Optical Society of America

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References

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  1. B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
    [Crossref]
  2. P. Hariharan, B. F. Oreb, N. Brown, “Real-time holographic interferometry: a microcomputer system for the measurement of vector displacements,” Appl. Opt. 22, 876–880 (1983).
    [Crossref] [PubMed]
  3. D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,”; Opt. Commun. 57, 26–30 (1986).
    [Crossref]
  4. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [Crossref] [PubMed]
  5. S. Nakadate, H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
    [Crossref] [PubMed]
  6. D. Kerr, F. M. Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am.A 7, 820–826 (1990).
    [Crossref]
  7. E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
    [Crossref] [PubMed]
  8. R. Jones, C. Wykes, Holographic and Speckle Interferometry, (Cambridge U. Press, New York, 1983).
  9. I. Grant, J. Wang, Y. Tan, “Use of feedback fringe control in holographic nondestructive testing of debonding,” Appl. Opt. 28, 1744–1745 (1989).
    [Crossref] [PubMed]
  10. I. Grant, J. Wang, “Use of reference beam self-feedback phase modulation in the holographic detection of debonding,” Appl. Opt. 29, 1403–1405 (1990).
    [Crossref] [PubMed]
  11. J. Wang, “A study of optical and opto-electronic techniques for nondestructive testing” Ph.D. dissertation (Heriot-Watt University, Edinburgh, United Kingdom, 1992), pp. 100–102.
  12. T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
    [Crossref]
  13. W. Zheng, Y. Tan, “Phase-stepping technique in holography,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 278–285 (1991).

1990 (3)

1989 (1)

1986 (1)

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,”; Opt. Commun. 57, 26–30 (1986).
[Crossref]

1985 (3)

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

S. Nakadate, H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[Crossref] [PubMed]

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[Crossref] [PubMed]

1983 (1)

1979 (1)

T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
[Crossref]

Brown, N.

Button, B. L.

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

Creath, K.

Cutts, J.

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

Dobbins, B. N.

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

Grant, I.

Hariharan, P.

Huang, T. S.

T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
[Crossref]

Jones, R.

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

Kerr, D.

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am.A 7, 820–826 (1990).
[Crossref]

Moxon, C. J.

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

Nakadate, S.

Oreb, B. F.

Robinson, D. W.

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,”; Opt. Commun. 57, 26–30 (1986).
[Crossref]

Saito, H.

Santoyo, F. M.

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am.A 7, 820–826 (1990).
[Crossref]

Tan, Y.

I. Grant, J. Wang, Y. Tan, “Use of feedback fringe control in holographic nondestructive testing of debonding,” Appl. Opt. 28, 1744–1745 (1989).
[Crossref] [PubMed]

W. Zheng, Y. Tan, “Phase-stepping technique in holography,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 278–285 (1991).

Tang, G. Y.

T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
[Crossref]

Tyrer, J. R.

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am.A 7, 820–826 (1990).
[Crossref]

Vikhagen, E.

Wang, J.

Williams, D. C.

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,”; Opt. Commun. 57, 26–30 (1986).
[Crossref]

Wykes, C.

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

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

Yang, G. I.

T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
[Crossref]

Zheng, W.

W. Zheng, Y. Tan, “Phase-stepping technique in holography,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 278–285 (1991).

Appl. Opt. (6)

IEEE Trans. Acoust. Speech Signal Process. (1)

T. S. Huang, G. I. Yang, G. Y. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
[Crossref]

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

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am.A 7, 820–826 (1990).
[Crossref]

Opt. Commun. (1)

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,”; Opt. Commun. 57, 26–30 (1986).
[Crossref]

Opt. Laser Technol. (1)

B. L. Button, J. Cutts, B. N. Dobbins, C. J. Moxon, C. Wykes, “The identification of fringe positions in speckle patterns,” Opt. Laser Technol. 17, 189–192 (1985).
[Crossref]

Other (3)

W. Zheng, Y. Tan, “Phase-stepping technique in holography,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 278–285 (1991).

J. Wang, “A study of optical and opto-electronic techniques for nondestructive testing” Ph.D. dissertation (Heriot-Watt University, Edinburgh, United Kingdom, 1992), pp. 100–102.

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

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for the application of phase-mapping ESPI to a continuously deforming object: L's, lenses; M's, mirrors; BS's, beam splitters.

Fig. 2
Fig. 2

Flow diagram that shows the algorithm for obtaining Imax and Imin.

Fig. 3
Fig. 3

Graphical representation of the phase-angle calculation error.

Fig. 4
Fig. 4

Timing diagram for ESPI image capture.

Fig. 5
Fig. 5

Real-time ESPI interferograms: (a)–(d), main images A1–A4, respectively; (e)–(h), sign images A1′–A4′, respectively; (i)–(l), phase maps of main images B1–B4, respectively.

Fig. 6
Fig. 6

Quantitative three-dimensional representation of the detected debonded areas within the window shown in Fig. 5(l).

Equations (14)

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

I = I o + I r + 2 I o I r cos ( ϕ ) ,
I = I d + I e cos ( ϕ ) ,
I max = I d + I e ( ϕ = 2 π n , n = 0 , 1 , 2 , ) ,
I min = I d I e ( ϕ = ( 2 n + 1 ) π , n = 0 , 1 , 2 , ) .
ϕ = cos 1 ( 2 I I max I min I max I min ) .
Δ ϕ = ϕ 1 ϕ 2 = cos 1 ( 2 I 2 I max I min I max I min ) cos 1 ( 2 I 1 I max I min I max I min ) .
Δ ϕ = 2 π λ [ cos ( θ 1 ) + cos ( θ 2 ) ] Δ L ,
A B = { T ( A B ) 0 ( A B ) } ,
B + { T 0 } = { G A G B } .
A { T 0 } = { S A S B } .
I i I s = I e [ cos ( ϕ ) cos ( ϕ δ ϕ ) ] = 2 I e [ sin ( ϕ + δ ϕ 2 ) sin ( δ ϕ 2 ) ]
2 I e sin ( δ ϕ / 2 ) 0 ,
I i I s sin ( ϕ + δ ϕ / 2 ) .
I i I s sin ( ϕ ) .

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