Abstract

A sequence of image processing algorithms for the analysis of interference patterns generated by a phase-shifting speckle interferometer is discussed. The goal is the accurate determination of displacement and strain components at the surface of an object. The phase change related to the displacement is accurately calculated from eight digitized interference patterns using a phase-shifting algorithm. Digital image processing algorithms have been developed for phase unwrapping, phase restoration, and phase fitting. During the processing steps a binary mask is used to solve the problem of invalid areas. Experimental results for the strain components at the surface of a simple object demonstrate a repeatability of 0.3-μstrain rms.

© 1991 Optical Society of America

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References

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  1. K. Creath, “Phase-Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  2. S. Nakadate, H. Saito, “Fringe Scanning Speckle-Pattern Interferometry,” Appl. Opt. 24, 2172–2180 (1985).
    [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-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–369 (1988).
    [CrossRef]
  5. R. Jones, C. Wykes, “De-Correlation Effects in Speckle-Pattern Interferometry/2. Displacement Dependent Decorrelation and Applications to the Observation of Machine Induced Strain,” Opt. Acta 24, 533–550 (1977).
    [CrossRef]
  6. A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975).
    [CrossRef]
  7. H. A. Vrooman, A. A. M. Maas, “New Image Processing Algorithms for the Analysis of Speckle Interference Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).
  8. L. J. van Vliet, B. J. H. Verwer, “A Contour Processing Method for Fast Binary Neighbourhood Operations,” Pattern Recognition Lett. 7, 27–36 (1988).
    [CrossRef]
  9. B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
    [CrossRef]
  10. A. Rosenfeld, A. Kak, Digital Picture Processing, Vol. 2 (Academic, Orlando, FL, 1982).
  11. A. A. M. Maas, H. A. Vrooman, “Strain Measurement by Digital Speckle Interferometry,” in Proceedings, Twelfth World Conference on Non Destructive Testing, J. Boogaard, G. M. van Dijk, Eds. (Elsevier, Amsterdam, 1989), pp. 594–600.
  12. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  13. K. A. Stetson, “Use of Sensitivity Vector Variations to Determine Absolute Displacements in Double Exposure Hologram Interferometry,” Appl. Opt. 29, 502–504 (1990).
    [CrossRef] [PubMed]

1990 (1)

1989 (2)

B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
[CrossRef]

H. A. Vrooman, A. A. M. Maas, “New Image Processing Algorithms for the Analysis of Speckle Interference Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

1988 (2)

L. J. van Vliet, B. J. H. Verwer, “A Contour Processing Method for Fast Binary Neighbourhood Operations,” Pattern Recognition Lett. 7, 27–36 (1988).
[CrossRef]

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–369 (1988).
[CrossRef]

1986 (1)

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

1985 (2)

1977 (1)

R. Jones, C. Wykes, “De-Correlation Effects in Speckle-Pattern Interferometry/2. Displacement Dependent Decorrelation and Applications to the Observation of Machine Induced Strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–369 (1988).
[CrossRef]

K. Creath, “Phase-Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef] [PubMed]

Dekker, S. T.

B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
[CrossRef]

Ennos, A. E.

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, “De-Correlation Effects in Speckle-Pattern Interferometry/2. Displacement Dependent Decorrelation and Applications to the Observation of Machine Induced Strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

Kak, A.

A. Rosenfeld, A. Kak, Digital Picture Processing, Vol. 2 (Academic, Orlando, FL, 1982).

Maas, A. A. M.

H. A. Vrooman, A. A. M. Maas, “New Image Processing Algorithms for the Analysis of Speckle Interference Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

A. A. M. Maas, H. A. Vrooman, “Strain Measurement by Digital Speckle Interferometry,” in Proceedings, Twelfth World Conference on Non Destructive Testing, J. Boogaard, G. M. van Dijk, Eds. (Elsevier, Amsterdam, 1989), pp. 594–600.

Nakadate, S.

Robinson, D. W.

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Rosenfeld, A.

A. Rosenfeld, A. Kak, Digital Picture Processing, Vol. 2 (Academic, Orlando, FL, 1982).

Saito, H.

Stetson, K. A.

van Vliet, L. J.

L. J. van Vliet, B. J. H. Verwer, “A Contour Processing Method for Fast Binary Neighbourhood Operations,” Pattern Recognition Lett. 7, 27–36 (1988).
[CrossRef]

Verbeek, P. W.

B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
[CrossRef]

Verwer, B. J. H.

B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
[CrossRef]

L. J. van Vliet, B. J. H. Verwer, “A Contour Processing Method for Fast Binary Neighbourhood Operations,” Pattern Recognition Lett. 7, 27–36 (1988).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Vrooman, H. A.

H. A. Vrooman, A. A. M. Maas, “New Image Processing Algorithms for the Analysis of Speckle Interference Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

A. A. M. Maas, H. A. Vrooman, “Strain Measurement by Digital Speckle Interferometry,” in Proceedings, Twelfth World Conference on Non Destructive Testing, J. Boogaard, G. M. van Dijk, Eds. (Elsevier, Amsterdam, 1989), pp. 594–600.

Williams, D. C.

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, “De-Correlation Effects in Speckle-Pattern Interferometry/2. Displacement Dependent Decorrelation and Applications to the Observation of Machine Induced Strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

B. J. H. Verwer, P. W. Verbeek, S. T. Dekker, “An Efficient Uniform Cost Algorithm Applied to Distance Transforms,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11, 425–429 (1989).
[CrossRef]

Opt. Acta (1)

R. Jones, C. Wykes, “De-Correlation Effects in Speckle-Pattern Interferometry/2. Displacement Dependent Decorrelation and Applications to the Observation of Machine Induced Strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

Opt. Commun. (1)

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Pattern Recognition Lett. (1)

L. J. van Vliet, B. J. H. Verwer, “A Contour Processing Method for Fast Binary Neighbourhood Operations,” Pattern Recognition Lett. 7, 27–36 (1988).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. A. Vrooman, A. A. M. Maas, “New Image Processing Algorithms for the Analysis of Speckle Interference Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

Prog. Opt. (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–369 (1988).
[CrossRef]

Other (4)

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975).
[CrossRef]

A. Rosenfeld, A. Kak, Digital Picture Processing, Vol. 2 (Academic, Orlando, FL, 1982).

A. A. M. Maas, H. A. Vrooman, “Strain Measurement by Digital Speckle Interferometry,” in Proceedings, Twelfth World Conference on Non Destructive Testing, J. Boogaard, G. M. van Dijk, Eds. (Elsevier, Amsterdam, 1989), pp. 594–600.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

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Figures (8)

Fig. 1
Fig. 1

Two-dimensional lookup table used to calculate the phase modulo 2π.

Fig. 2
Fig. 2

Phase unwrapping algorithm scans the data using a pixel queue. The selection of a start position and different stages of the scanning are shown.

Fig. 3
Fig. 3

Flow chart of the phase unwrapping algorithm.

Fig. 4
Fig. 4

Processing of the original mask to separate objects from the background.

Fig. 5
Fig. 5

Fitting a plane in a rectangular neighborhood of (x,y) to estimate the first spatial derivatives of the data.

Fig. 6
Fig. 6

A 10-mm thick T-shaped aluminum object.

Fig. 7
Fig. 7

One out of eight phase-shifted speckle interference patterns (left-hand side), the in-plane displacement Lx (middle), and Lx after a 25 × 25 smoothing filter (right-hand side). Both continuous displacement maps are coded in grey values; the total grey value range (black to white) corresponds to a displacement of 250 nm.

Fig. 8
Fig. 8

In-plane displacement Ly after a 25 × 25 smoothing filter (left-hand side; the total grey value range corresponds to a displacement of 250 nm), a vector plot representing the in-plane displacement (middle; a vector length of 1 mm corresponds to a displacement of 125 nm), and the shear strain exy (right-hand side; the isostrain lines have a spacing of 3 μstrain).

Equations (8)

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I k ( x , y ) = A ( x , y ) + B ( x , y ) cos [ ϕ o ( x , y ) + ϕ s ( x , y ) + k δ ] ,
ϕ o ( x , y ) + ϕ s ( x , y ) = arctan [ I 4 ( x , y ) I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y ) ] .
Δ ϕ o ( x , y ) = ϕ o ( x , y ) ϕ o , ref ( x , y ) .
B ( x , y ) = 1 2 [ I 4 ( x , y ) I 2 ( x , y ) ] 2 + [ I 1 ( x , y ) I 3 ( x , y ) ] 2 .
S ( x , y ) = [ a m + b n + c g ( m , n ) ] 2 ,
Δ { ( m 2 ) } = N 2 ( m ) , Δ { ( m n ) } = ( n ) , Δ { ( m g ) } = ( g ) , Δ { ( m ) } = N .
Δ ϕ o = K · L = ( 2 π / λ ) ( i i + i υ ) · L ,
e x x = L x x , e y y = L y y , e x y = e y x = 1 2 ( L x y + L y x ) .

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