Abstract

We present a method based on color encoding for measurement of transient 3D deformation in diffuse objects. The object is illuminated by structured light that consists of a fringe pattern with cyan fringes embedded in a white background. Color images are registered and information on each color channel is then separated. Surface features appear on the blue channel while fringes on the red channel. The in-plane components of displacement are calculated via digital correlation of the texture images. Likewise, the resulting fringes serve for the measuring of the out-of-plane component. As crossing of information between signals is avoided, the accuracy of the method is high. This is confirmed by a series of displacement measurements of an aluminum plate.

©2011 Optical Society of America

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References

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  1. C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
    [Crossref]
  2. B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
    [Crossref]
  3. P. Siegmann, V. Álvarez-Fernández, F. Díaz-Garrido, and E. A. Patterson, “A simultaneous in- and out-of-plane displacement measurement method,” Opt. Lett. 36(1), 10–12 (2011).
    [Crossref] [PubMed]
  4. Z. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency Selection,” Opt. Express 14(14), 6444–6455 (2006).
    [Crossref] [PubMed]
  5. L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
    [Crossref]
  6. H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
    [Crossref]
  7. C. Brücker, “3-D PIV via spatial correlation in a color-coded light-sheet,” Exp. Fluids 21 (4), 312–314 (1996).
    [Crossref]
  8. P. Synnergren and M. Sjodahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31(6), 425–443 (1999).
    [Crossref]
  9. A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29(2), 103–116 (2000).
    [Crossref]
  10. M. Raffel, C. Willert, and J. Kompenhans, Particle image velocimetry, a practical guide, (Springer-Verlag, 1998).
  11. D. J. Chen, F. P. Chiang, Y. S. Tan, and H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32(11), 1839–1849 (1993).
    [Crossref] [PubMed]
  12. B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).
  13. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
    [Crossref]
  14. K. J. Gasvik, Optical Metrology, (3rd Ed. John Wiley and Sons, Sussex 2003).
  15. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3(6), 847–855 (1986).
    [Crossref]
  16. D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
    [Crossref]
  17. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
    [Crossref]
  18. S. Rosendahl, E. Hällstig, P. Gren, and M. Sjödahl, “Phase errors due to speckles in laser fringe projection,” Appl. Opt. 49(11), 2047–2053 (2010).
    [Crossref] [PubMed]
  19. J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997).
    [Crossref]

2011 (1)

2010 (2)

S. Rosendahl, E. Hällstig, P. Gren, and M. Sjödahl, “Phase errors due to speckles in laser fringe projection,” Appl. Opt. 49(11), 2047–2053 (2010).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

2008 (1)

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

2006 (2)

2004 (2)

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

2001 (1)

H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
[Crossref]

2000 (1)

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29(2), 103–116 (2000).
[Crossref]

1999 (1)

P. Synnergren and M. Sjodahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31(6), 425–443 (1999).
[Crossref]

1998 (1)

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
[Crossref]

1997 (1)

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997).
[Crossref]

1996 (1)

C. Brücker, “3-D PIV via spatial correlation in a color-coded light-sheet,” Exp. Fluids 21 (4), 312–314 (1996).
[Crossref]

1993 (1)

1986 (1)

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Álvarez-Fernández, V.

Barrientos, B.

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

Brücker, C.

C. Brücker, “3-D PIV via spatial correlation in a color-coded light-sheet,” Exp. Fluids 21 (4), 312–314 (1996).
[Crossref]

Bryanston-Cross, P.

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

Caspi, D.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
[Crossref]

Cerca, M.

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

Chen, D. J.

Chiang, F. P.

Cywiak, M.

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

Dabiri, D.

H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
[Crossref]

Díaz-Garrido, F.

Don, H. S.

Fu, L.

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Garcia-Marquez, J.

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

Gharib, M.

H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
[Crossref]

Gren, P.

Hällstig, E.

He, A.

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Hernandez-Bernal, C.

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

Huang, Y. H.

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Kiryati, N.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
[Crossref]

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Kreis, T.

Lee, W. K.

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

Li, Z.

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Park, H. G.

H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
[Crossref]

Patterson, E. A.

Prasad, A. K.

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29(2), 103–116 (2000).
[Crossref]

Quan, C.

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

Rosendahl, S.

Shamir, J.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
[Crossref]

Siegmann, P.

Sjodahl, M.

P. Synnergren and M. Sjodahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31(6), 425–443 (1999).
[Crossref]

Sjödahl, M.

Synnergren, P.

P. Synnergren and M. Sjodahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31(6), 425–443 (1999).
[Crossref]

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Tan, Y. S.

Tay, C. J.

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

Towers, C. E.

Towers, D. P.

Westerweel, J.

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997).
[Crossref]

Wu, T.

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

Yang, L.

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Yang, Q.

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Zhang, S.

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

Zhang, Z.

Appl. Opt. (2)

Exp. Fluids (3)

H. G. Park, D. Dabiri, and M. Gharib, “Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder,” Exp. Fluids 30(3), 327–338 (2001).
[Crossref]

C. Brücker, “3-D PIV via spatial correlation in a color-coded light-sheet,” Exp. Fluids 21 (4), 312–314 (1996).
[Crossref]

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29(2), 103–116 (2000).
[Crossref]

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

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

B. Barrientos, M. Cerca, J. Garcia-Marquez, and C. Hernandez-Bernal, “Three-dimensional displacement fields measured in a deforming granular-media surface by combined fringe projection and speckle photography,” J. Opt. A, Pure Appl. Opt. 10(10), 104027 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3(6), 847–855 (1986).
[Crossref]

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Meas. Sci. Technol. (1)

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997).
[Crossref]

Opt. Eng. (2)

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, “Integrated method for 3-D rigid-body displacement measurement using fringe projection,” Opt. Eng. 43(5), 1152–1159 (2004).
[Crossref]

L. Fu, Z. Li, L. Yang, Q. Yang, and A. He, “New phase measurement profilometry by grating projection,” Opt. Eng. 45(7), 073601 (2006).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (2)

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

P. Synnergren and M. Sjodahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31(6), 425–443 (1999).
[Crossref]

Opt. Lett. (1)

Rev. Mex. Fis. (1)

B. Barrientos, M. Cywiak, W. K. Lee, and P. Bryanston-Cross, “Measurement of dynamic deformation using a superimposed grating,” Rev. Mex. Fis. 50(1), 12–18 (2004).

Other (2)

K. J. Gasvik, Optical Metrology, (3rd Ed. John Wiley and Sons, Sussex 2003).

M. Raffel, C. Willert, and J. Kompenhans, Particle image velocimetry, a practical guide, (Springer-Verlag, 1998).

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Figures (8)

Fig. 1
Fig. 1 Schematic layout of DIC. Here P and L stand for projector and imaging lens, respectively. Other variables are described in the text.

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Fig. 2
Fig. 2 a) Computer-generated image (subimage of the original image of 3264x2448 pixels). b) Recorded image (subimage of the recorded image of 3264x2448 pixels). c) and d) Cross sections of the two previous images (RGB components) along x-direction (center row). After color separation, detected signals on e) red channel and f) blue channel. g) Cross sections of the Fourier transform of the last two images (full versions). Colors indicate the corresponding channel. An equivalent period of 1.93 mm was used. Dimensions: abscissae and ordinates in pixels, except ordinates in c) and d) (in gray levels) and g) (arbitrary units).

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Fig. 3
Fig. 3 Equivalent period of 9.90 mm. Titles of figures are as the corresponding ones in Fig. 2.

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Fig. 4
Fig. 4 Equivalent period of 2.83 mm. Titles of figures (a)-(g) are as the corresponding ones in Fig. 2. (h) Object illuminated by white light.

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Fig. 5
Fig. 5 Synthetic images used to show the influence of residual speckle on the accuracy of the FP method: (a) Speckle-free fringe image, (b) and (c) fringe images with different level of speckle disturbance. Experimental images: (d) and (e), images with similar speckle influence to (b) and (c), respectively. Dimensions are pixels.

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Fig. 6
Fig. 6 Optical layout. (a) Photograph. (b) Schematic drawing. Dimensions are mm. (c) Typical image obtained when illuminating the object with black-and-white structured light. Dimensions are pixels. Symbols are as in Fig. 1.

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Fig. 7
Fig. 7 Relative error for measured displacements, (a) out-of-plane, and (b) in-plane, for various projected grating periods (in mm), T. The size of subimages is 64x64 pix. For displaying purposes, the graphs are clipped at 15% and 5%, respectively. The thicker curves correspond to results obtained by standard methods of FP and DIC.

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Fig. 8
Fig. 8 In-plane residual error. (a) In obtaining this vector field, the signal on the blue channel (speckle image) is used. The aluminum plate undergoes an out-of-plane displacement of 1.5 mm. The maximum residual in-plane displacement is 0.26 mm, and is located at the corners. (b) To obtain this graph, the signal on the red channel (image of fringes) is used. An in-plane displacement of 1.5 mm is given to the plate. The absolute residual average in-plane displacement is 19.5 μm. Dimensions of coordinate axes are pixels.

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Equations (9)

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

h( Δx,Δy )= ∫ −∞ ∞ ∫ −∞ ∞ I 1 (x,y) I 1 (x−Δx,y−Δy)dxdy ,
h(Δx,Δy)= ℑ −1 { F 1 ( f x , f y ) F 2 * ( f x , f y ) },
I 1 (x,y)=a(x,y)+b(x,y)cos( 2π f 0 x+ ϕ ref ),
I 2 (x,y)=a(x,y)+b(x,y)cos( 2π f 0 x+ ϕ ref +Δϕ ).
I F ( f x , f y )=A( f x , f y )+B( f x − f 0 , f y )+ B * (− f x − f 0 , f y ),
ℑ −1 { B( f x − f 0 , f y ) }= ℑ −1 { ℑ { 1 2 b(x,y)exp(i2π f 0 x)exp( i ϕ ref ) } f x − f 0 , f y }      =Re(x,y)+i Im(x,y),
2π f 0 x+ ϕ ref = tan −1 [ Im(x,y) Re(x,y) ].
Δϕ( x,y )= tan −1 ( Im 2 Re 1 − Im 1 Re 2 Re 1 Re 2 + Im 1 Im 2 ),
I 2 (x,y)=r(x,y)[ a(x,y)+b(x,y)cos( 2π f 0 x+ ϕ ref +Δϕ ) ].

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