Abstract

We present a novel neural network signal calibration technique to improve the performance of triangulation-based structured light profilometers based on digital projection. The performance of such profilometers is often hindered by the capture of aberrated pattern intensity distributions, and hence we address this problem by employing neural networks in a signal mapping approach. We exploit the generalization and interpolation capabilities of a feed-forward backpropagation neural network to map from distorted fringe data to nondistorted data. The performance of the calibration technique is gauged both through simulation and experimentation, with simulation results indicating that accuracy can be improved by more than 80%. The technique requires just one image cross section for calibration and hence is ideal for rapid profiling applications.

© 2007 Optical Society of America

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  1. V. Srinivasan, H. C. Lui, and M. Halioua, "Automated phase-measuring profilometry of 3D diffuse objects," Appl. Opt. 23, 3105-3108 (1984).
    [CrossRef] [PubMed]
  2. X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
    [CrossRef]
  3. J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
    [CrossRef]
  4. J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
    [CrossRef]
  5. H. Zhi and R. B. Johansson, "Adaptive filter for enhancement of fringe patterns," Opt. Lasers Eng. 15, 241-251 (1991).
    [CrossRef]
  6. S. Ryoo and T. Choi, "3D profilometry by analysis of noisy white-light interferograms," in Three-dimensional and Multidimensional Microscopy: Image Acquisition Processing VII,Proc. SPIE 3919, 152-160 (2000).
    [CrossRef]
  7. L. Kinell, "Multichannel method for absolute shape measurement using projected fringes," Opt. Lasers Eng. 41, 57-71 (2004).
    [CrossRef]
  8. C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Optical Engineering 38, 1573-1581 (1999).
    [CrossRef]
  9. S. Kakunai, T. Sakamoto, and K. Iwata, "Profile measurement taken with liquid-crystal grating," Appl. Opt. 38, 2824-2828 (1999).
    [CrossRef]
  10. H. Guo, H. He, and M. Chen, "Gamma correction for digital fringe projection profilometry," Appl. Opt. 43, 2906-2914 (2004).
    [CrossRef] [PubMed]
  11. H. Farid, "Blind inverse gamma correction," IEEE Trans. Image Process. 10, 1428-1433 (2001).
    [CrossRef]
  12. F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
    [CrossRef]
  13. H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
    [CrossRef]
  14. D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
    [CrossRef]
  15. D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
    [CrossRef]
  16. D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
    [CrossRef]
  17. G. Zhang and Z. Wei, "A novel calibration approach to structured light 3D vision inspection," Opt. Laser Technol. 34, 373-380 (2002).
    [CrossRef]
  18. F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
    [CrossRef]
  19. M. Chang and W. Tai, "360-deg profile noncontact measurement using a neural network," Opt. Eng. 34, 3572-3576 (1995).
    [CrossRef]
  20. S. Toyooka, Y. Iwaasa, "Automatic profilometry of 3-D diffuse objects by spatial phase detection," Appl. Opt. 25, 1630-1633 (1986).
    [CrossRef] [PubMed]
  21. M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).
  22. R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses," IEEE J. Rob. Autom. RA-3, 323-344 (1987).
    [CrossRef]
  23. R. M. Haralick and L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, 1992), Vol. 1.
  24. E. R. Davies, Machine Vision: Theory Algorithms Practicalities, 3rd ed. (Elsevier, 2005).
  25. G. Horvath, Neural Networks for Instrumentation, Measurement and Related Industrial Applications (IOS Press, 2003).

2005

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

2004

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

L. Kinell, "Multichannel method for absolute shape measurement using projected fringes," Opt. Lasers Eng. 41, 57-71 (2004).
[CrossRef]

H. Guo, H. He, and M. Chen, "Gamma correction for digital fringe projection profilometry," Appl. Opt. 43, 2906-2914 (2004).
[CrossRef] [PubMed]

2003

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
[CrossRef]

2002

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

G. Zhang and Z. Wei, "A novel calibration approach to structured light 3D vision inspection," Opt. Laser Technol. 34, 373-380 (2002).
[CrossRef]

2001

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

H. Farid, "Blind inverse gamma correction," IEEE Trans. Image Process. 10, 1428-1433 (2001).
[CrossRef]

2000

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

S. Ryoo and T. Choi, "3D profilometry by analysis of noisy white-light interferograms," in Three-dimensional and Multidimensional Microscopy: Image Acquisition Processing VII,Proc. SPIE 3919, 152-160 (2000).
[CrossRef]

1999

J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
[CrossRef]

C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Optical Engineering 38, 1573-1581 (1999).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

S. Kakunai, T. Sakamoto, and K. Iwata, "Profile measurement taken with liquid-crystal grating," Appl. Opt. 38, 2824-2828 (1999).
[CrossRef]

1995

M. Chang and W. Tai, "360-deg profile noncontact measurement using a neural network," Opt. Eng. 34, 3572-3576 (1995).
[CrossRef]

H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
[CrossRef]

1991

H. Zhi and R. B. Johansson, "Adaptive filter for enhancement of fringe patterns," Opt. Lasers Eng. 15, 241-251 (1991).
[CrossRef]

1987

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses," IEEE J. Rob. Autom. RA-3, 323-344 (1987).
[CrossRef]

1986

1984

Baker, M. J.

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

Burton, D. R.

H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
[CrossRef]

Castillo, L.

J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
[CrossRef]

Chang, M.

M. Chang and W. Tai, "360-deg profile noncontact measurement using a neural network," Opt. Eng. 34, 3572-3576 (1995).
[CrossRef]

Chen, M.

Chen, W.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Chicharo, J.

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

Choi, T.

S. Ryoo and T. Choi, "3D profilometry by analysis of noisy white-light interferograms," in Three-dimensional and Multidimensional Microscopy: Image Acquisition Processing VII,Proc. SPIE 3919, 152-160 (2000).
[CrossRef]

Coggrave, C. R.

C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Optical Engineering 38, 1573-1581 (1999).
[CrossRef]

Cuevas, F. J.

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

Davies, E. R.

E. R. Davies, Machine Vision: Theory Algorithms Practicalities, 3rd ed. (Elsevier, 2005).

Farid, H.

H. Farid, "Blind inverse gamma correction," IEEE Trans. Image Process. 10, 1428-1433 (2001).
[CrossRef]

Ganotra, D.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

Gao, C.

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

Guo, H.

Halioua, M.

Haralick, R. M.

R. M. Haralick and L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, 1992), Vol. 1.

He, H.

Horvath, G.

G. Horvath, Neural Networks for Instrumentation, Measurement and Related Industrial Applications (IOS Press, 2003).

Huntley, J. M.

C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Optical Engineering 38, 1573-1581 (1999).
[CrossRef]

Iwaasa, Y.

Iwata, K.

Johansson, R. B.

H. Zhi and R. B. Johansson, "Adaptive filter for enhancement of fringe patterns," Opt. Lasers Eng. 15, 241-251 (1991).
[CrossRef]

Joseph, J.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

Kakunai, S.

Kinell, L.

L. Kinell, "Multichannel method for absolute shape measurement using projected fringes," Opt. Lasers Eng. 41, 57-71 (2004).
[CrossRef]

Lalor, M. J.

H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
[CrossRef]

Li, E.

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

Lui, H. C.

Mills, H.

H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
[CrossRef]

Rodriguez-Vera, R.

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

Ryoo, S.

S. Ryoo and T. Choi, "3D profilometry by analysis of noisy white-light interferograms," in Three-dimensional and Multidimensional Microscopy: Image Acquisition Processing VII,Proc. SPIE 3919, 152-160 (2000).
[CrossRef]

Sakamoto, T.

Servin, M.

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

Shapiro, L. G.

R. M. Haralick and L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, 1992), Vol. 1.

Si, S.

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

Singh, K.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

Srinivasan, V.

Stavroudis, O. N.

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

Su, X.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Tai, W.

M. Chang and W. Tai, "360-deg profile noncontact measurement using a neural network," Opt. Eng. 34, 3572-3576 (1995).
[CrossRef]

Toyooka, S.

Tsai, R. Y.

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses," IEEE J. Rob. Autom. RA-3, 323-344 (1987).
[CrossRef]

Villa, J.

J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
[CrossRef]

Wang, Y.

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

Wei, Z.

G. Zhang and Z. Wei, "A novel calibration approach to structured light 3D vision inspection," Opt. Laser Technol. 34, 373-380 (2002).
[CrossRef]

Xi, J.

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

Xu, J.

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

Yun, D.

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

Zhang, G.

G. Zhang and Z. Wei, "A novel calibration approach to structured light 3D vision inspection," Opt. Laser Technol. 34, 373-380 (2002).
[CrossRef]

Zhi, H.

H. Zhi and R. B. Johansson, "Adaptive filter for enhancement of fringe patterns," Opt. Lasers Eng. 15, 241-251 (1991).
[CrossRef]

Appl. Opt.

IEEE J. Rob. Autom.

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses," IEEE J. Rob. Autom. RA-3, 323-344 (1987).
[CrossRef]

IEEE Trans. Image Process.

H. Farid, "Blind inverse gamma correction," IEEE Trans. Image Process. 10, 1428-1433 (2001).
[CrossRef]

Opt. Commun.

F. J. Cuevas, M. Servin, O. N. Stavroudis, and R. Rodriguez-Vera, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

J. Villa, M. Servin, and L. Castillo, "Profilometry for the measurement of 3D object shapes based on regularized filters," Opt. Commun. 161, 13-18 (1999).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of three-dimensional object shape using radial basis function, and multilayer perceptron neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Second- and first-order phase locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion," Opt. Commun. 217, 85-96 (2003).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

Opt. Eng.

M. Chang and W. Tai, "360-deg profile noncontact measurement using a neural network," Opt. Eng. 34, 3572-3576 (1995).
[CrossRef]

Opt. Laser Technol.

G. Zhang and Z. Wei, "A novel calibration approach to structured light 3D vision inspection," Opt. Laser Technol. 34, 373-380 (2002).
[CrossRef]

Opt. Lasers Eng.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

H. Zhi and R. B. Johansson, "Adaptive filter for enhancement of fringe patterns," Opt. Lasers Eng. 15, 241-251 (1991).
[CrossRef]

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

H. Mills, D. R. Burton, and M. J. Lalor, "Applying backpropagation neural networks to fringe analysis," Opt. Lasers Eng. 23, 331-341 (1995).
[CrossRef]

L. Kinell, "Multichannel method for absolute shape measurement using projected fringes," Opt. Lasers Eng. 41, 57-71 (2004).
[CrossRef]

Optical Engineering

C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Optical Engineering 38, 1573-1581 (1999).
[CrossRef]

Proc. SPIE

J. Xu, Y. Wang, S. Si, C. Gao, and D. Yun, "Research on application of special filter in projecting grating profilometry," in Optical Technology and Image Processing for Fluids and Solids Diagnostics, Proc. SPIE 5058, 532-536 (2003).
[CrossRef]

S. Ryoo and T. Choi, "3D profilometry by analysis of noisy white-light interferograms," in Three-dimensional and Multidimensional Microscopy: Image Acquisition Processing VII,Proc. SPIE 3919, 152-160 (2000).
[CrossRef]

M. J. Baker, J. Xi, J. Chicharo, and E. Li, "A contrast between dlp and lcd digital projection technology for triangulation-based phase measuring optical profilometers," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. Harding, ed., Proc. SPIE 600C, 151-162 (2005).

Other

R. M. Haralick and L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, 1992), Vol. 1.

E. R. Davies, Machine Vision: Theory Algorithms Practicalities, 3rd ed. (Elsevier, 2005).

G. Horvath, Neural Networks for Instrumentation, Measurement and Related Industrial Applications (IOS Press, 2003).

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Figures (9)

Fig. 1
Fig. 1

Typical crossed optical axes profilometry arrangement.

Fig. 2
Fig. 2

Proposed multilayer signal mapping calibration neural network for arbitrary aN .

Fig. 3
Fig. 3

(Color online) (a) Simulated phase distribution, (b) reference and (c) deformed fringe, and (d) fringe cross section.

Fig. 4
Fig. 4

(Color online) Simulated reconstructed surface for three-step PMP and FTP with and without neural network calibration.

Fig. 5
Fig. 5

Cross section of reconstructed phase maps for simulated images of a diffuse surface.

Fig. 6
Fig. 6

Cross section of reconstructed surface for neural and filtering calibration versus noncalibrated.

Fig. 7
Fig. 7

Experimental object and fringe patterns.

Fig. 8
Fig. 8

(Color online) Experimental reconstructed phase maps for three-step PMP and FTP with and without neural network calibration.

Fig. 9
Fig. 9

Cross section of reconstructed phase maps for experimental images of a diffuse surface.

Tables (3)

Tables Icon

Table 1 Calibrated and Noncalibrated Absolute Mean Profile Reconstruction Errors and Standard Deviations

Tables Icon

Table 2 Individual Fringe Distortions Neglecting Additive Gaussian Noise, Absolute Mean Errors ( ϵe ), and Standard Deviations ( σe ) for Calibrated and Noncalibrated Fringes

Tables Icon

Table 3 Absolute Mean Errors ( ϵe ) and Standard Deviations ( σe ) for Neural and Filter Calibration

Equations (31)

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

ACh(x,y)=d0l0h(x,y),
h(x,y)=l0ACACd0.
r(x,y)=a+bcos(2πf0x),
w=uγ,
w(x,y)=[a+bcos(2πf0x)]γ,
w(x,y)=[a+bcos(2πf0x)+m=2cmcos[m(2πf0x)]]γ
      w(x,y)=[a+bcos(2πf0x+ϕ0(x,y))+m=2cmcos[m(2πf0x+ϕ0(x,y))]]γ.
ϕ0(x,y)=2πf0x2sinθcosθl0+xsinθcosθ.
w(x,y)=[a+bcos(2πf0x+ϕ0(x,y))+m=0cmcos[m(2πf0x+ϕ0(x,y))]]γ+n0(x,y),
x=xd+xd(k1r2+k2r4+),
y=yd+yd(k1r2+k2r4+),
r=xd2+yd2,
w(xdp,ydp),
w(xdc,ydc),
I=w(xdc,ydc)for  MXdc  and  NYdc,
T=m=1Mn=1NtM,N,
tM,N=[I(m,n),R(m)],
R(m)=a+bcos[2πf0m+ϕ0(m,n)].
I^(m,a)=f2(W2f1(I(m,a)W1))for  m=0,1,2,3  …  M,
W1=[w11w12w13w14w15]T,
W2=[w11w21w31w41w51],
I^(m,n)=f2{Wn2f1[I(m,n)Wn1]}for  m=0,1,2,3  …  M,n=0,1,2,3  …  N,
D^(m,n)=f2{Wn2f1[D(m,n)Wn1]}for  m=0,1,2,3  …  M,n=0,1,2,3  …  N.
G(x)=kex2/2σ2,
k=1xWex2/2σ2,
gn(x,y)=[a+bcos(2πf0x+ϕ0(x,y)+2πn/N)+ccos(2π(2f0)x+2ϕ0(x,y)+4πn/N)]γ+n0(x,y)  for  n=0,1,2 …  N1,
xXdc,yYdc,
a=128256,b=100256,c=101256.
γ=2.2,
dn(x,y)=[a+bcos(2πf0x+ϕ0(x,y)+ϕ(x,y)+2πn/N)+ccos(2π(2f0)x+2ϕ0(x,y)+2ϕ(x,y)+4πn/N)]γ+n0(x,y)for  n=0,1,2  …  N1,
R(x)=a+bcos[2πf0x+ϕ0(x,y)].

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