Abstract

Shearography is a noncontact optical technique used to measure surface displacement derivatives. Full surface strain characterization can be achieved using shearography configurations employing at least three measurement channels. Each measurement channel is sensitive to a single displacement gradient component defined by its sensitivity vector. A matrix transformation is then required to convert the measured components to the orthogonal displacement gradients required for quantitative strain measurement. This transformation, conventionally performed using three measurement channels, amplifies any errors present in the measurement. This paper investigates the use of additional measurement channels using the results of a computer model and an experimental shearography system. Results are presented showing that the addition of a fourth channel can reduce the errors in the computed orthogonal components by up to 33% and that, by using 10 channels, reductions of around 45% should be possible.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
    [CrossRef]
  2. Y. T. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 391–395 (1982).
  3. D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
    [CrossRef]
  4. M. Kalms and W. Osten, “Mobile shearography system for the inspection of aircraft and automotive components,” Opt. Eng. 42, 1188–1196 (2003).
    [CrossRef]
  5. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  6. M. A. Herráez, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Robust, fast, and effective two-dimensional automatic phase unwrapping algorithm based on image decomposition,” Appl. Opt. 41, 7445–7455 (2002).
    [CrossRef] [PubMed]
  7. S. Waldner and S. Brem, “Compact shearography system for the measurement of 3D deformation,” Proc. SPIE 3745, 141–148 (1999).
    [CrossRef]
  8. R. Kästle, E. Hack, and U. Sennhauser, “Multiwavelength shearography for quantitative measurements of two-dimensional strain distributions,” Appl. Opt. 38, 96–100(1999).
    [CrossRef]
  9. R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
    [CrossRef]
  10. D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
    [CrossRef]
  11. D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
    [CrossRef]
  12. D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
    [CrossRef]
  13. T. O. Charrett, D. S. Nobes, and R. Tatam, “Investigation into the selection of viewing configurations for three-component planar Doppler velocimetry measurements,” Appl. Opt. 46, 4102–4116 (2007).
    [CrossRef] [PubMed]
  14. K. Arbenz and A. Wohlhauser, Advanced Mathematics For Practicing Engineers (Artech House, 1986).
  15. P. Hariharan, B. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506(1987).
    [CrossRef] [PubMed]
  16. H. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
    [CrossRef]
  17. A. Dolinko and G. H. Kaufmann, “A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses,” Opt. Lasers Eng. 44, 1336–1347 (2006).
    [CrossRef]

2010

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[CrossRef]

2008

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
[CrossRef]

2007

T. O. Charrett, D. S. Nobes, and R. Tatam, “Investigation into the selection of viewing configurations for three-component planar Doppler velocimetry measurements,” Appl. Opt. 46, 4102–4116 (2007).
[CrossRef] [PubMed]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[CrossRef]

2006

A. Dolinko and G. H. Kaufmann, “A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses,” Opt. Lasers Eng. 44, 1336–1347 (2006).
[CrossRef]

2004

D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
[CrossRef]

2003

R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
[CrossRef]

M. Kalms and W. Osten, “Mobile shearography system for the inspection of aircraft and automotive components,” Opt. Eng. 42, 1188–1196 (2003).
[CrossRef]

2002

1999

S. Waldner and S. Brem, “Compact shearography system for the measurement of 3D deformation,” Proc. SPIE 3745, 141–148 (1999).
[CrossRef]

R. Kästle, E. Hack, and U. Sennhauser, “Multiwavelength shearography for quantitative measurements of two-dimensional strain distributions,” Appl. Opt. 38, 96–100(1999).
[CrossRef]

H. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

1987

1985

1982

Y. T. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 391–395 (1982).

1973

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Aebischer, H.

H. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Arbenz, K.

K. Arbenz and A. Wohlhauser, Advanced Mathematics For Practicing Engineers (Artech House, 1986).

Brem, S.

S. Waldner and S. Brem, “Compact shearography system for the measurement of 3D deformation,” Proc. SPIE 3745, 141–148 (1999).
[CrossRef]

Burton, D. R.

Butters, J.

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Charrett, T. O.

Creath, K.

Dolinko, A.

A. Dolinko and G. H. Kaufmann, “A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses,” Opt. Lasers Eng. 44, 1336–1347 (2006).
[CrossRef]

Eiju, T.

Ford, H. D.

D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
[CrossRef]

Francis, D.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[CrossRef]

Gdeisat, M. A.

Groves, R. M.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[CrossRef]

R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
[CrossRef]

Hack, E.

Hariharan, P.

Herráez, M. A.

Hung, Y. T.

Y. T. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 391–395 (1982).

James, S. W.

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[CrossRef]

R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
[CrossRef]

Kalms, M.

M. Kalms and W. Osten, “Mobile shearography system for the inspection of aircraft and automotive components,” Opt. Eng. 42, 1188–1196 (2003).
[CrossRef]

Kästle, R.

Kaufmann, G. H.

A. Dolinko and G. H. Kaufmann, “A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses,” Opt. Lasers Eng. 44, 1336–1347 (2006).
[CrossRef]

Lalor, M. J.

Leendertz, J.

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Nobes, D. S.

T. O. Charrett, D. S. Nobes, and R. Tatam, “Investigation into the selection of viewing configurations for three-component planar Doppler velocimetry measurements,” Appl. Opt. 46, 4102–4116 (2007).
[CrossRef] [PubMed]

D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
[CrossRef]

Oreb, B.

Osten, W.

M. Kalms and W. Osten, “Mobile shearography system for the inspection of aircraft and automotive components,” Opt. Eng. 42, 1188–1196 (2003).
[CrossRef]

Sennhauser, U.

Tatam, R.

T. O. Charrett, D. S. Nobes, and R. Tatam, “Investigation into the selection of viewing configurations for three-component planar Doppler velocimetry measurements,” Appl. Opt. 46, 4102–4116 (2007).
[CrossRef] [PubMed]

D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
[CrossRef]

Tatam, R. P.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[CrossRef]

R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
[CrossRef]

Waldner, S.

H. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

S. Waldner and S. Brem, “Compact shearography system for the measurement of 3D deformation,” Proc. SPIE 3745, 141–148 (1999).
[CrossRef]

Wohlhauser, A.

K. Arbenz and A. Wohlhauser, Advanced Mathematics For Practicing Engineers (Artech House, 1986).

Appl. Opt.

Exp. Fluids

D. S. Nobes, H. D. Ford, and R. Tatam, “Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles,” Exp. Fluids 36, 3–10 (2004).
[CrossRef]

J. Phys. E

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Meas. Sci. Technol.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[CrossRef]

D. Francis, S. W. James, and R. P. Tatam, “Surface strain measurement of rotating objects using pulsed laser shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 19, 105301 (2008).
[CrossRef]

Opt. Commun.

H. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Opt. Eng.

M. Kalms and W. Osten, “Mobile shearography system for the inspection of aircraft and automotive components,” Opt. Eng. 42, 1188–1196 (2003).
[CrossRef]

Y. T. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 391–395 (1982).

Opt. Lasers Eng.

A. Dolinko and G. H. Kaufmann, “A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses,” Opt. Lasers Eng. 44, 1336–1347 (2006).
[CrossRef]

Proc. SPIE

R. M. Groves, S. W. James, and R. P. Tatam, “Multi-component shearography employing four measurement channels,” Proc. SPIE , 4933135–140 (2003).
[CrossRef]

S. Waldner and S. Brem, “Compact shearography system for the measurement of 3D deformation,” Proc. SPIE 3745, 141–148 (1999).
[CrossRef]

Other

K. Arbenz and A. Wohlhauser, Advanced Mathematics For Practicing Engineers (Artech House, 1986).

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 (13)

Fig. 1
Fig. 1

Typical single-channel shearography arrangement based on a Michelson interferometer.

Fig. 2
Fig. 2

Relationship between the Cartesian x, y, and z directions and the displacement components u, v, and w. The component of displacement gradient that a shearography instrument measures is determined by the sensitivity vector, k ^ , which is the bisector of the observation, o ^ , and illumination, i ^ , unit vectors.

Fig. 3
Fig. 3

Schematic and photograph of the multicomponent shearography system used in this investigation. LM, laser module, shutter and beam expanding optics; MSI, Michelson shearing interferometer; CCD, charge-coupled device camera.

Fig. 4
Fig. 4

Simulated wrapped (top) and unwrapped (bottom) phase shifts for each of the four channels for a Gaussian out-of-plane displacement in the center of the field of view and including the noise sources.

Fig. 5
Fig. 5

Example results of the computer model for a Gaussian out-of-plane displacement in the center of the field of view. Top, theoretical displacement gradients; middle, displacement gradients calculated using three channels; and bottom, displacement gradients calculated using four channels.

Fig. 6
Fig. 6

Calculated orthogonal displacement gradients for shear in the x direction, calculated using the three (top row) and four (bottom row) channel methods for experimental results on a flat plate with zero deformation.

Fig. 7
Fig. 7

Calculated orthogonal displacement gradients for shear in the x direction, calculated using the three (top row) and four (bottom row) channel methods for modeled data with zero deformation.

Fig. 8
Fig. 8

Calculated orthogonal displacement gradients for shear in the x direction, calculated using the three (top row) and four (bottom row) channel methods for experimental results on a flat plate with out-of-plane deformation.

Fig. 9
Fig. 9

Calculated orthogonal displacement gradients for shear in the x direction, calculated using the three (top row) and four (bottom row) channel methods for modeled data of a Gaussian out-of-plane deformation.

Fig. 10
Fig. 10

Photograph of the notch cut-out object used for the in-plane deformation test.

Fig. 11
Fig. 11

Orthogonal displacement gradients for shear in the y direction calculated using the three (top row) and four (bottom row) channel methods from experimental results from the Perspex notch test object.

Fig. 12
Fig. 12

Multiple channel shearography system geometries used showing the arrangement of illumination sources and observation vector for n channels ( n = 3 to 6).

Fig. 13
Fig. 13

Modeled standard deviations in the error and percentage reduction in comparison to a three channel system for n-channel configurations ( n = 3 to 10). The results for all three orthogonal displacement gradients ( · ) u s , ( × ) v s , and ( + ) w s are shown.

Tables (5)

Tables Icon

Table 1 Settings Used in Multichannel Shearography Model, Chosen to Match Values Used in the Experimental System

Tables Icon

Table 2 Results of the Zero Deformation Test for the Three-Channel and Four-Channel Methods

Tables Icon

Table 3 Results of the Out-of-Plane Deformation Test for Experimental Data for the Three-Channel and Four-Channel Methods a

Tables Icon

Table 4 Results of the Out-of-Plane Deformation Test for Modeled Data (Mean of 20 Runs) for the Three-Channel and Four-Channel Methods

Tables Icon

Table 5 Results of the In-Plane Deformation Test for Experimental Data, for the Three-channel and Four-Channel Methods a

Equations (19)

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

k ^ = o ^ i ^ .
Δ ϕ x = 2 π λ [ k x u x + k y v x + k z w x ] d x ,
Δ ϕ y = 2 π λ [ k x u y + k y v y + k z w y ] d y ,
[ Δ ϕ x 1 Δ ϕ x 2 Δ ϕ x 3 ] = 2 π λ [ k x 1 k y 1 k z 1 k x 2 k y 2 k z 2 k x 3 k y 3 k z 3 ] [ u / x v / x w / x ] d x ,
[ Δ ϕ y 1 Δ ϕ y 2 Δ ϕ y 3 ] = 2 π λ [ k x 1 k y 1 k z 1 k x 2 k y 2 k z 2 k x 3 k y 3 k z 3 ] [ u / y v / y w / y ] d y .
Φ = ( 2 π d s λ ) J M ,
M = ( λ 2 π d s ) J 1 Φ .
M = ( λ 2 π d s ) ( J T W J ) 1 J T W Φ .
W = [ W 1 0 0 0 W 2 0 0 0 W 3 W n ] .
u s = ( λ 2 π d s ) [ g ( d f e e ) + h ( c e b f ) + j ( b e c d ) ] [ a ( d f e e ) b ( b f c e ) + c ( b e d c ) ] ,
v s = ( λ 2 π d s ) [ g ( c e b f ) + h ( a f c c ) + j ( b c a e ) ] [ a ( d f e e ) b ( b f c e ) + c ( b e d c ) ] ,
w s = ( λ 2 π d s ) [ g ( b e c d ) + h ( b c a e ) + j ( a d b b ) ] [ a ( d f e e ) b ( b f c e ) + c ( b e d c ) ] ,
a = i n k x i W 2 i , b = i n k x i k y i W i , c = i n k x i k z i W i , d = i n k y i W 2 i , e = i n k y i k z i W i , f = i n k z i W 2 i , g = i n k x i Δ ϕ i W i , h = i n k y i Δ ϕ i W i , j = i n k z i Δ ϕ i W i .
ϕ = tan 1 { 2 ( I 2 I 4 ) 2 I 3 I 5 I 1 } .
S 1 ( x , y ) = exp { i [ ϕ 0 ( x , y ) + ϕ U ( x , y ) + ϕ step ] } ,
ϕ U ( x , y ) = 2 π λ ( k ^ ( x , y ) · U ^ ( x , y ) ) .
S 2 ( x , y ) = exp { i [ ϕ 0 ( x , y ) + ϕ U ( x , y ) ] } .
I ( x , y ) = | F 1 { F [ S 1 ( x , y ) ] H } + F 1 { F [ S 2 ( x , y ) ] H } | 2 ,
w ( x , y ) = w 0 exp { ( x x 0 s x ) 2 ( y y 0 s y ) 2 } ,

Metrics