Abstract

Deformation study of curved engineering and technical surfaces, such as pipes and pressure vessels, has gained much importance in the recent past. Speckle interferometric techniques and their electronic and digital analogs, which are whole field techniques, have been effectively applied for practical nondestructive testing applications over the years. However, little work has been done that discusses the speckle fringe formation with a fruitful theoretical formulation to study deformation analysis of curved surfaces. We propose an extended theory for speckle fringe formation on curved surfaces, which can be applied to the study of curved engineering and technical specimens under various loading conditions such as in-plane, out-of-plane, and out-of-plane shear configurations. Simulated contours are generated by use of finite element models with similar loading conditions, and the data are analyzed and compared with the obtained experimental results.

© 2004 Optical Society of America

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References

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  1. R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
    [CrossRef]
  2. R. S. Sirohi, Speckle Methods in Experimental Mechanics (Marcel Dekker, New York, 1993), p. 99.
  3. C. M. Vest, Related Measurement Techniques (Wiley, New York, 1979), p. 387.
  4. V. M. Murukeshan, A. R. Ganesan, R. S. Sirohi, “Design and development of a compact fiber optic phase shifting ESPI system for engineering metrology,” Proceedings of the 14th World Conference on Non Destructive Testing (A. A. Balkema/Rotterdam, New Delhi, India, 1997), pp. 1525–1530.
  5. K. Krakhella, O. J. Lokberg, “Electronic speckle pattern interferometry using optical fibers,” Opt. Commun. 38, 155–158 (1981).
    [CrossRef]
  6. C. C. Kin, F. P. Chiang, “Objective laser speckle method for three dimensional displacement measurement on curved surface,” Opt. Eng. 22, 153–155 (1983).
    [CrossRef]
  7. M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
    [CrossRef]
  8. S. C. J. Parker, S. L. Salter, “A novel shearography system for aerospace nondestructive testing,” Proc. Inst. Mech. Eng. 213, 23–33 (1999).
    [CrossRef]
  9. R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
    [CrossRef]
  10. M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
    [CrossRef]
  11. K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
    [CrossRef]
  12. X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
    [CrossRef]
  13. J. B. Fraleigh, Plane Curves and Polar Co-ordinates (Addison-Wesley, Reading, Mass., 1990), p. 549.

2003

M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
[CrossRef]

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

2002

X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
[CrossRef]

1999

S. C. J. Parker, S. L. Salter, “A novel shearography system for aerospace nondestructive testing,” Proc. Inst. Mech. Eng. 213, 23–33 (1999).
[CrossRef]

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

1997

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

1992

M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
[CrossRef]

1983

C. C. Kin, F. P. Chiang, “Objective laser speckle method for three dimensional displacement measurement on curved surface,” Opt. Eng. 22, 153–155 (1983).
[CrossRef]

1981

K. Krakhella, O. J. Lokberg, “Electronic speckle pattern interferometry using optical fibers,” Opt. Commun. 38, 155–158 (1981).
[CrossRef]

Ananthan, A.

M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
[CrossRef]

Boo, W. P.

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

Breukmann, B.

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

Cheong, S. K.

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

Chiang, F. P.

C. C. Kin, F. P. Chiang, “Objective laser speckle method for three dimensional displacement measurement on curved surface,” Opt. Eng. 22, 153–155 (1983).
[CrossRef]

Evans, W. T.

M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
[CrossRef]

Fraleigh, J. B.

J. B. Fraleigh, Plane Curves and Polar Co-ordinates (Addison-Wesley, Reading, Mass., 1990), p. 549.

Galanulis, K.

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

Ganesan, A. R.

V. M. Murukeshan, A. R. Ganesan, R. S. Sirohi, “Design and development of a compact fiber optic phase shifting ESPI system for engineering metrology,” Proceedings of the 14th World Conference on Non Destructive Testing (A. A. Balkema/Rotterdam, New Delhi, India, 1997), pp. 1525–1530.

Kang, K. S.

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

Kang, Y. J.

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

Kim, K. S.

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

Kin, C. C.

C. C. Kin, F. P. Chiang, “Objective laser speckle method for three dimensional displacement measurement on curved surface,” Opt. Eng. 22, 153–155 (1983).
[CrossRef]

Krakhella, K.

K. Krakhella, O. J. Lokberg, “Electronic speckle pattern interferometry using optical fibers,” Opt. Commun. 38, 155–158 (1981).
[CrossRef]

Li, X.

X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
[CrossRef]

Liu, X.

X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
[CrossRef]

Lokberg, O. J.

K. Krakhella, O. J. Lokberg, “Electronic speckle pattern interferometry using optical fibers,” Opt. Commun. 38, 155–158 (1981).
[CrossRef]

Muller, E.

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

Murukeshan, V. M.

V. M. Murukeshan, A. R. Ganesan, R. S. Sirohi, “Design and development of a compact fiber optic phase shifting ESPI system for engineering metrology,” Proceedings of the 14th World Conference on Non Destructive Testing (A. A. Balkema/Rotterdam, New Delhi, India, 1997), pp. 1525–1530.

Parker, S. C. J.

S. C. J. Parker, S. L. Salter, “A novel shearography system for aerospace nondestructive testing,” Proc. Inst. Mech. Eng. 213, 23–33 (1999).
[CrossRef]

Rao, M. V.

M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
[CrossRef]

Ratnam, M. M.

M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
[CrossRef]

Ritter, R.

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

Salter, S. L.

S. C. J. Parker, S. L. Salter, “A novel shearography system for aerospace nondestructive testing,” Proc. Inst. Mech. Eng. 213, 23–33 (1999).
[CrossRef]

Samuel, R.

M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
[CrossRef]

Shang, H. M.

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

V. M. Murukeshan, A. R. Ganesan, R. S. Sirohi, “Design and development of a compact fiber optic phase shifting ESPI system for engineering metrology,” Proceedings of the 14th World Conference on Non Destructive Testing (A. A. Balkema/Rotterdam, New Delhi, India, 1997), pp. 1525–1530.

R. S. Sirohi, Speckle Methods in Experimental Mechanics (Marcel Dekker, New York, 1993), p. 99.

Tay, C. J.

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

Tyrer, J. R.

M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
[CrossRef]

Vest, C. M.

C. M. Vest, Related Measurement Techniques (Wiley, New York, 1979), p. 387.

Wang, K.

X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
[CrossRef]

Winter, D.

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

J. Nondestruct. Eval.

X. Li, X. Liu, K. Wang, “Quantitative detection of the defects in thin-walled pressure vessels with holography and shearing speckle interferometry,” J. Nondestruct. Eval. 21, 85–94 (2002).
[CrossRef]

Opt. Commun.

K. Krakhella, O. J. Lokberg, “Electronic speckle pattern interferometry using optical fibers,” Opt. Commun. 38, 155–158 (1981).
[CrossRef]

Opt. Eng.

C. C. Kin, F. P. Chiang, “Objective laser speckle method for three dimensional displacement measurement on curved surface,” Opt. Eng. 22, 153–155 (1983).
[CrossRef]

M. M. Ratnam, W. T. Evans, J. R. Tyrer, “Measurement of thermal expansion of a piston using holographic and electronic speckle pattern interferometry,” Opt. Eng. 31, 61–69 (1992).
[CrossRef]

R. S. Sirohi, C. J. Tay, H. M. Shang, W. P. Boo, “Nondestructive assessment of thinning of plates using electronic shearography,” Opt. Eng. 38, 1582–1585 (1999).
[CrossRef]

Opt. Laser Technol.

K. S. Kim, K. S. Kang, Y. J. Kang, S. K. Cheong, “Analysis of an internal crack of pressure pipeline using ESPI and shearography,” Opt. Laser Technol. 35, 639–643 (2003).
[CrossRef]

Opt. Lasers Eng.

M. V. Rao, R. Samuel, A. Ananthan, “Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components,” Opt. Lasers Eng. 40, 563–571 (2003).
[CrossRef]

R. Ritter, K. Galanulis, D. Winter, E. Muller, B. Breukmann, “Notes on the application of electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 283–299 (1997).
[CrossRef]

Proc. Inst. Mech. Eng.

S. C. J. Parker, S. L. Salter, “A novel shearography system for aerospace nondestructive testing,” Proc. Inst. Mech. Eng. 213, 23–33 (1999).
[CrossRef]

Other

R. S. Sirohi, Speckle Methods in Experimental Mechanics (Marcel Dekker, New York, 1993), p. 99.

C. M. Vest, Related Measurement Techniques (Wiley, New York, 1979), p. 387.

V. M. Murukeshan, A. R. Ganesan, R. S. Sirohi, “Design and development of a compact fiber optic phase shifting ESPI system for engineering metrology,” Proceedings of the 14th World Conference on Non Destructive Testing (A. A. Balkema/Rotterdam, New Delhi, India, 1997), pp. 1525–1530.

J. B. Fraleigh, Plane Curves and Polar Co-ordinates (Addison-Wesley, Reading, Mass., 1990), p. 549.

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Figures (9)

Fig. 1
Fig. 1

Vector diagrams for a curved object: (a) in-plane configuration, (b) out-of-plane configuration, (c) shearographic configuration, (d) representation of sheared points in the object plane.

Fig. 2
Fig. 2

(a) Different deformation components for a square specimen: u, in-plane-sensitive component of deformation in the X direction; v, in-plane-sensitive component of deformation in the Y direction; w, out-of-plane-sensitive component of deformation in the Z direction. (b) Different deformation components for a half-cylindrical specimen: ds, elemental deformation along the curved surface; dϕ, angle between the tangents at points P and Q; w r , deformation component along the radial direction; w θ, deformation component along the tangential direction; w a , deformation component along the axial direction.

Fig. 3
Fig. 3

(a) Experimental setup for in-plane sensitive configuration, (b) out-of-plane sensitive configuration, (c) shearographic configuration. F, optical fiber; FH, fiber holder; CL, collimator lens; BC, beam combiner.

Fig. 4
Fig. 4

(a) Fringe pattern for in-plane displacement (5 μm) for the square plate; (b) fringe pattern for in-plane displacement (10 μm) for the square plate. (c) Numerically simulated displacement contours of an aluminum square plate with a uniform load at the top surface and a fixed bottom surface.

Fig. 5
Fig. 5

(a) Fringe pattern for in-plane displacement (5 μm) for the half-cylindrical plate; (b) fringe pattern for in-plane displacement (10 μm) for the half-cylindrical plate. (c) Numerically simulated displacement contours of an aluminium half-cylindrical plate with a uniform load at the top surface and a fixed bottom surface.

Fig. 6
Fig. 6

(a) Fringe pattern for out-of-plane displacement (5 μm) for the square plate; (b) fringe pattern for out-of-plane displacement (10 μm) for the square plate. (c) Numerically simulated displacement contours of a centrally loaded aluminium square plate with clamped edges.

Fig. 7
Fig. 7

(a) Fringe pattern for out-of-plane displacement (5 μm) for the half-cylindrical plate; (b) fringe pattern for out-of-plane displacement (10 μm) for the half-cylindrical plate. (c) Numerically simulated displacement contours of a centrally loaded aluminium half-cylindrical plate with clamped edges.

Fig. 8
Fig. 8

(a) Fringe pattern for out-of-plane displacement derivative (displacement 5 μm) for the square plate; (b) fringe pattern for out-of-plane displacement derivative (displacement 10 μm) for the square plate. (c) Numerically simulated displacement derivative contours of a centrally loaded aluminium square plate with clamped edges.

Fig. 9
Fig. 9

(a) Fringe pattern for out-of-plane displacement derivative (displacement 5 μm) for the half-cylindrical plate; (b) fringe pattern for out-of-plane displacement derivative (displacement 10 μm) for the half-cylindrical plate. (c) Numerically simulated displacement derivative contours of a centrally loaded aluminium half-cylindrical plate with clamped edges.

Equations (39)

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

I=I12+I22+2I1I21/2 cos ϕ,
I=I12+I22+2I1I21/2 cosϕ+Δϕ,
4I1I21/2|sinϕ+Δϕ/2sinΔϕ/2|.
Δϕ=2mπ,
Δϕ=2m+1π.
L=ui+vj-wk,
L=wθeθ+waea-wrer.
WT=wθ2+wr2+wa21/2.
wr=W sindϕ/2,
wθ=W cosdϕ/2,
W=wr2+wθ21/2.
dϕ=dsK,
K=1/r,
 dϕ=ds/r.
L=W cosds/2reθ+waea-W sinds/2rer.
k1=-ea sin θi+er cos θi,
k2=-er,
k3=ea sin θi+er cos θi.
Δϕ=2π/λk2-k1·L,
Δϕ=2π/λk2-k3·L,
Δϕ-Δϕ=2π/λk3-k1·L
=2π/λ2ea sin θi·L,
Δϕ=2π/λ2ea sin θi·W cosds/2reθ+waea-W sinds/2rer,
Δϕ=2π/λ2wa sin θi.
Δϕ=2π/λwasin θi2+sin θi1-wrcos θi2-cos θi1.
Δϕ=2π/λwasin θi1+sin θi2, where θi1θi2.
Δϕ=2π/λvsin θi2+sin θi1, where θi1θi2,
Δϕ=2π/λ2v sin θi, where θi1=θi2=θi.
k1=-ea sin θi+er cos θi,
k2=-er,
Δϕ=2π/λk2-k1·L=2π/λ-er--ea sin θi+er cos θi·L=2π/λea sin θi-er1+cos θi·L,
Δϕ=2π/λea sin θi-er1+cos θi·W cosds/2reθ+waea-W sinds/2rer=2π/λwa sin θi+W sinds/2r×1+cos θi.
Δϕ=2π/λ1+cos θiw.
Δϕ1=2π/λk2-k1·L,
Δϕ2=2π/λk2-k1·L,
Δϕ=Δϕ1-Δϕ2=2π/λk2-k1·L-L,
Δϕ=2π/λ-er--ea sin θi+er cos θi·dW/dθcosds/2reθ+dwa/dθea-dW/dθsinds/2rer·Δθ0,
Δϕ=2π/λdwadθsin θi+dWdθ1+cos θisinds/2r·Δθ0,
Δϕ=2π/λdwdx1+cos θi · Δx0

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