Abstract

This paper presents a simple spatial phase shift shearography based on the Michelson interferometer. The Michelson interferometer based shearographic system has been widely utilized in industry as a practical nondestructive test tool. In the system, the Michelson interferometer is used as a shearing device to generate a shearing distance by tilting a small angle in one of the two mirrors. In fact, tilting the mirror in the Michelson interferometer also generates spatial frequency shift. Based on this feature, we introduce a simple Michelson interferometer based spatial phase shift shearography. The Fourier transform (FT) method is applied to separate the spectrum on the spatial frequency domain. The phase change due to the loading can be evaluated using a properly selected windowed inverse-FT. This system can generate a phase map of shearography by using only a single image. The effects of shearing angle, spatial resolution of couple charge device camera, and filter methods are discussed in detail. The theory and the experimental results are presented.

© 2013 Optical Society of America

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  1. L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
    [CrossRef]
  2. Y. Y. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 213391 (1982).
    [CrossRef]
  3. W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003), pp. 116–122.
  4. W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).
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    [CrossRef]
  6. G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
    [CrossRef]
  7. B. Bhaduri, N. K. Mohan, M. P. Kothiyal, and R. S. Sirohi, “Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS),” Opt. Express 14, 11598–11607 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. Dantec Dynamics, “Shearography—non destructive testing,” http://www.dantecdynamics.com/Default.aspx?ID=665 .
  11. Laser Technology Inc., “Laser shearography technology,” http://www.laserndt.com/technology/shearography.htm .
  12. Steinbichler Inspiring Innovation, “Shearography NDT,” http://www.steinbichler.com/products/surface-scanning/shearography-ndt.html .
  13. S. Wu, X. He, and L. Yang, “Enlarging the angle of view in Michelson interferometer-based shearography by embedding a 4f system,” Appl. Opt. 50, 3789–3794 (2011).
    [CrossRef]
  14. Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
    [CrossRef]
  15. L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
    [CrossRef]
  16. G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456–3462 (2006).
    [CrossRef]
  17. Y. Fu, H. Shi, and H. Miao, “Vibration measurement of a miniature component by high-speed image-plane digital holographic microscopy,” Appl. Opt. 48, 1990–1997 (2009).
    [CrossRef]

2013 (1)

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

2011 (1)

2009 (1)

2007 (1)

2006 (2)

2004 (2)

M. Schuth, F. Voessing, and L. X. Yang, “A shearographic endoscope for nondestructive test,” J. Holography Speckle 1, 46–52 (2004).
[CrossRef]

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

2003 (1)

Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
[CrossRef]

1998 (2)

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

1996 (1)

G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

1982 (1)

Y. Y. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 213391 (1982).
[CrossRef]

Bhaduri, B.

Chen, F.

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

Fu, Y.

Gusev, M. E.

He, X.

Hung, Y. Y.

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
[CrossRef]

Y. Y. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 213391 (1982).
[CrossRef]

Kothiyal, M. P.

Kupfer, G.

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

Maeckel, P.

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

Miao, H.

Mohan, N. K.

Osten, W.

Pedrini, G.

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456–3462 (2006).
[CrossRef]

G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Schuth, M.

M. Schuth, F. Voessing, and L. X. Yang, “A shearographic endoscope for nondestructive test,” J. Holography Speckle 1, 46–52 (2004).
[CrossRef]

Shang, H. M.

Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
[CrossRef]

Shi, H.

Sirohi, R. S.

Steinchen, W.

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003), pp. 116–122.

Sun, J.

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

Tiziani, H. J.

G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Voessing, F.

M. Schuth, F. Voessing, and L. X. Yang, “A shearographic endoscope for nondestructive test,” J. Holography Speckle 1, 46–52 (2004).
[CrossRef]

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

Wang, Y.

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

Wu, S.

Xie, X.

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

Xu, N.

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

Yang, L.

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

S. Wu, X. He, and L. Yang, “Enlarging the angle of view in Michelson interferometer-based shearography by embedding a 4f system,” Appl. Opt. 50, 3789–3794 (2011).
[CrossRef]

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003), pp. 116–122.

Yang, L. X.

M. Schuth, F. Voessing, and L. X. Yang, “A shearographic endoscope for nondestructive test,” J. Holography Speckle 1, 46–52 (2004).
[CrossRef]

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
[CrossRef]

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

Zou, Y.-L.

G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Appl. Opt. (4)

J. Aerosp. Eng. (1)

W. Steinchen, L. X. Yang, G. Kupfer, and P. Maeckel, “Nondestructive testing of aerospace composite materials using digital shearography,” J. Aerosp. Eng. 212, 21–30 (1998).

J. Holography Speckle (2)

M. Schuth, F. Voessing, and L. X. Yang, “A shearographic endoscope for nondestructive test,” J. Holography Speckle 1, 46–52 (2004).
[CrossRef]

L. X. Yang, F. Chen, W. Steinchen, and Y. Y. Hung, “Digital shearography for nondestructive testing: potentials, limitations, and applications,” J. Holography Speckle 1, 69–79 (2004).
[CrossRef]

Opt. Commun. (1)

X. Xie, N. Xu, J. Sun, Y. Wang, and L. Yang, “Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography,” Opt. Commun. 286, 277–281 (2013).
[CrossRef]

Opt. Eng. (2)

Y. Y. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 213391 (1982).
[CrossRef]

Y. Y. Hung, H. M. Shang, and L. X. Yang, “Unified approach for holography and shearography in surface deformation measurement and nondestructive testing,” Opt. Eng. 42, 1197–1207 (2003).
[CrossRef]

Opt. Express (1)

Opt. Laser Eng. (1)

L. Yang, W. Steinchen, G. Kupfer, P. Maeckel, and F. Voessing, “Vibration analysis by means of digital shearography,” Opt. Laser Eng. 30, 199–212 (1998).
[CrossRef]

Pure Appl. Opt. (1)

G. Pedrini, Y.-L. Zou, and H. J. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Other (4)

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003), pp. 116–122.

Dantec Dynamics, “Shearography—non destructive testing,” http://www.dantecdynamics.com/Default.aspx?ID=665 .

Laser Technology Inc., “Laser shearography technology,” http://www.laserndt.com/technology/shearography.htm .

Steinbichler Inspiring Innovation, “Shearography NDT,” http://www.steinbichler.com/products/surface-scanning/shearography-ndt.html .

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of 4f system embedded shearography setup.

Fig. 2.
Fig. 2.

Spectrum after FT.

Fig. 3.
Fig. 3.

Wrapped phase map of a shearogram calculated by WIFT.

Fig. 4.
Fig. 4.

3D plot of out-of-plane deformation gradient.

Fig. 5.
Fig. 5.

Comparison of measurement quality (a) phase map measured by 4+4 temporal phase-shift shearography system, (b) phase map measured by mentioned spatial phase-shift shearography system, (c) 2D plot of out-of-plane deformation gradient through center line calculated from (a), and (d) 2D plot of out-of-plane deformation gradient through center line calculated from (b). (e) The 2D plot of out-of plane deformation gradient through the center line calculated from (a). (f) The 2D plot of out-of-plane deformation gradient through the center line calculated from (b).

Fig. 6.
Fig. 6.

Schematic of unfolded 4f system.

Fig. 7.
Fig. 7.

Schematic of digital shearography setup for CCD camera comparison.

Fig. 8.
Fig. 8.

(a) Phase map evaluated from 1.5 M pixel camera and (b) phase map evaluated from 5 M pixel camera.

Fig. 9.
Fig. 9.

Ideal spectrum on Fourier domain.

Fig. 10.
Fig. 10.

(a) Cross section plot of a 2D gate function window and (b) 2D plot of inverse Fourier transformed gate function.

Fig. 11.
Fig. 11.

(a) Phase map calculated from WIFT using gate function filter window and (b) phase map calculated from WIFT using normal function filter window.

Fig. 12.
Fig. 12.

NDT results for a honeycomb structure under dynamic loading.

Equations (18)

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

u1(x,y)=|u1(x,y)|exp[iφ(x,y)],
u2(x,y)=|u2(x+Δx,y)|exp{iφ(x+Δx,y)+2πif0·x},
f0=(sinβ/λ),
I=(u1+u2)(u1*+u2*)=u1u1*+u2u2*+u1u2*+u2u1*.
FT(I)=U1(fx,fy)U1*(fx,fy)+U2(fx+f0,fy)U2*(fx+f0,fy)+U1(fx,fy)U2*(fx+f0,fy)+U2(fx+f0,fy)U1*(fx,fy).
[θ+2πxf0]=arctanIm[u2u1*]Re[u2u1*].
[θ+2πxf0]=arctanIm[u2u1*]Re[u2u1*].
Δθ=θθ.
Δθ=2π·Δxλd·s.
Δs=λf/D.
fc=D/2λf,
2fcf0=sinβλ.
arcsin(Df)β.
f0=sinβλ2fmax3=(13Δ).
βarcsin(λ3Δ).
β[arcsin(Df),arcsin(λ3Δ)].
Dfsinβλf3Δ.
φ(x,y)=12πσxσye12[(xμx)2σx2+(yμy)2σy2].

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