Abstract

Phase unwrapping is one of the key steps of interferogram analysis, and its accuracy relies primarily on the correct identification of phase discontinuities. This can be especially challenging for inherently noisy phase fields, such as those produced through shearography and other speckle-based interferometry techniques. We showed in a recent work how a relatively small 10×10 pixel kernel was trained, through machine learning methods, for predicting the locations of phase discontinuities within noisy wrapped phase maps. We describe here how this kernel can be applied in a sliding-window fashion, such that each pixel undergoes 100 phase-discontinuity examinations—one test for each of its possible positions relative to its neighbors within the kernel’s extent. We explore how the resulting predictions can be accumulated, and aggregated through a voting system, and demonstrate that the reliability of this method outperforms processing the image by segmenting it into more conventional 10×10 nonoverlapping tiles. When used in this way, we demonstrate that our 10×10 pixel kernel is large enough for effective processing of full-field interferograms. Avoiding, thus, the need for substantially more formidable computational resources which otherwise would have been necessary for training a kernel of a significantly larger size.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  6. A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, “Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval,” Opt. Lett. 34, 1522–1524 (2009).
    [CrossRef]
  7. R. Leach, ed., Optical Measurement of Surface Topography (Springer, 2011).
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    [CrossRef]
  9. L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
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    [CrossRef]
  11. M. Qudeisat, M. Gdeisat, D. Burton, and F. Lilley, “A simple method for phase wraps elimination or reduction in spatial fringe patterns,” Opt. Commun. 284, 5105–5109 (2011).
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  13. H. Abdul-Rahman, M. Arevalillo-Herraez, M. Gdeisat, D. Burton, M. Lalor, F. Lilley, C. Moore, D. Sheltraw, and M. Qudeisat, “Robust three-dimensional best-path phase-unwrapping algorithm that avoids singularity loops,” Appl. Opt. 48, 4582–4596 (2009).
    [CrossRef]
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    [CrossRef]
  15. F. Sawaf and R. P. Tatam, “Finding minimum spanning trees more efficiently for tile-based phase unwrapping,” Meas. Sci. Technol. 17, 1428–1435 (2006).
    [CrossRef]
  16. T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
    [CrossRef]
  17. D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
    [CrossRef]
  18. K. Falaggis, D. P. Towers, and C. E. Towers, “Generalized theory of phase unwrapping: approaches and optimal wavelength selection strategies for multiwavelength interferometric techniques,” Proc. SPIE 8493, 84930O (2012).
    [CrossRef]
  19. K. Falaggis, D. P. Towers, and C. E. Towers, “Method of excess fractions with application to absolute distance metrology: analytical solution,” Appl. Opt. 52, 5758–5765 (2013).
    [CrossRef]
  20. K. Falaggis, D. P. Towers, and C. E. Towers, “Algebraic solution for phase unwrapping problems in multiwavelength interferometry,” Appl. Opt. 53, 3737–3747 (2014).
    [CrossRef]
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  24. D. Barber, Bayesian Reasoning and Machine Learning (Cambridge University, 2012).
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  26. P. Flach, Machine Learning: The Art and Science of Algorithms That Make Sense of Data (Cambridge University, 2012).
  27. C. O’Neal and R. Schutt, Doing Data Science (O’Reilly Books, 2013).
  28. D. W. Robinson and G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurements Techniques (Institute of Physics Publishing, 1993).
  29. M. Minami and A. Hirose, “Phase singular points reduction by a layered complex-valued neural network in combination with constructive Fourier synthesis,” Lect. Notes Comput. Sci. 2714, 943–950 (2003).
    [CrossRef]
  30. D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
    [CrossRef]
  31. C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and L. Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46, 7475–7484 (2007).
    [CrossRef]
  32. S. Karout, “Two-dimensional phase unwrapping, chapter 3: artificial intelligence,” Ph.D. thesis (Liverpool John Moores University, 2007).
  33. S. J. D. Prince, Computer Vision: Models, Learning, and Inference (Cambridge University, 2012).
  34. G. E. Hinton and J. A. Anderson, eds., Parallel Models of Associative Memory: Updated Edition—Communication Textbook (Psychology, 2014).
  35. F. Sawaf and R. M. Groves, “Statistically guided improvements in speckle phase discontinuity predictions by machine learning systems,” Opt. Eng. 52, 101907 (2013).
    [CrossRef]
  36. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995), p. 119.
  37. K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
    [CrossRef]
  38. G. Dougherty, Pattern Recognition and Classification: An Introduction (Springer, 2012).
  39. M. B. Gordon, “Discrimination,” in Neural Networks: Methodology and Applications, G. Dreyfus, ed. (Springer, 2005), pp. 329–377.
  40. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995), pp. 126–127.
  41. J. A. Anderson, “Logistic discrimination,” in Handbook of Statistics 2 (North Holland, 1982), pp. 169–191.
  42. A. Field, J. Miles, and Z. Field, Discovering Statistics Using R (SAGE, 2012).
  43. D. T. Goto, “3D shearogrophy for strain measurement,” Thesis (Universidade Federal de Santa Catarina, 2010).
  44. L. Fu, K. Frenner, and W. Osten, “Rigorous speckle simulation using surface integral equations and boundary element methods,” in Fringe 2013, W. Osten, ed. (Springer, 2014), pp. 361–364.
  45. R. E. Schapire and Y. Freund, Boosting: Foundations and Algorithms (MIT, 2014).

2014 (1)

2013 (3)

K. Falaggis, D. P. Towers, and C. E. Towers, “Method of excess fractions with application to absolute distance metrology: analytical solution,” Appl. Opt. 52, 5758–5765 (2013).
[CrossRef]

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

F. Sawaf and R. M. Groves, “Statistically guided improvements in speckle phase discontinuity predictions by machine learning systems,” Opt. Eng. 52, 101907 (2013).
[CrossRef]

2012 (3)

K. Falaggis, D. P. Towers, and C. E. Towers, “Generalized theory of phase unwrapping: approaches and optimal wavelength selection strategies for multiwavelength interferometric techniques,” Proc. SPIE 8493, 84930O (2012).
[CrossRef]

N. Lazar, “Big data hits the big time,” Chance 25, 47–49 (2012).

C. Y. Chang and C. C. Ma, “Measurement of resonant mode of piezoelectric thin plate using speckle interferometry and frequency-sweeping function,” Rev. Sci. Instrum. 83, 95004–95009 (2012).
[CrossRef]

2011 (2)

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
[CrossRef]

M. Qudeisat, M. Gdeisat, D. Burton, and F. Lilley, “A simple method for phase wraps elimination or reduction in spatial fringe patterns,” Opt. Commun. 284, 5105–5109 (2011).
[CrossRef]

2010 (1)

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

2009 (3)

2008 (1)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).

2007 (2)

2006 (1)

F. Sawaf and R. P. Tatam, “Finding minimum spanning trees more efficiently for tile-based phase unwrapping,” Meas. Sci. Technol. 17, 1428–1435 (2006).
[CrossRef]

2003 (1)

M. Minami and A. Hirose, “Phase singular points reduction by a layered complex-valued neural network in combination with constructive Fourier synthesis,” Lect. Notes Comput. Sci. 2714, 943–950 (2003).
[CrossRef]

1996 (2)

D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
[CrossRef]

Y. Y. Hung, “Shearography for non-destructive evaluation of composite structures,” Opt. Lasers Eng. 24, 161–182 (1996).
[CrossRef]

1992 (1)

T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
[CrossRef]

1991 (1)

D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

1989 (1)

K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

1982 (1)

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

Abdul-Rahman, H.

Abdul-Rahman, H. S.

Almoro, P.

Anand, A.

Anderson, J. A.

J. A. Anderson, “Logistic discrimination,” in Handbook of Statistics 2 (North Holland, 1982), pp. 169–191.

Arevalillo-Herraez, M.

Arevalillo-Herráez, M.

Asundi, A.

Barber, D.

D. Barber, Bayesian Reasoning and Machine Learning (Cambridge University, 2012).

Bishop, C. M.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2006).

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995), pp. 126–127.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995), p. 119.

Bryanston-Cross, P. J.

T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
[CrossRef]

D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Burton, D.

Burton, D. R.

H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46, 6623–6635 (2007).
[CrossRef]

D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
[CrossRef]

Chang, C. Y.

C. Y. Chang and C. C. Ma, “Measurement of resonant mode of piezoelectric thin plate using speckle interferometry and frequency-sweeping function,” Rev. Sci. Instrum. 83, 95004–95009 (2012).
[CrossRef]

Chen, S.

Chhaniwal, V. K.

Dong, M.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

Dougherty, G.

G. Dougherty, Pattern Recognition and Classification: An Introduction (Springer, 2012).

Falaggis, K.

Field, A.

A. Field, J. Miles, and Z. Field, Discovering Statistics Using R (SAGE, 2012).

Field, Z.

A. Field, J. Miles, and Z. Field, Discovering Statistics Using R (SAGE, 2012).

Flach, P.

P. Flach, Machine Learning: The Art and Science of Algorithms That Make Sense of Data (Cambridge University, 2012).

Francis, D.

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

Frenner, K.

L. Fu, K. Frenner, and W. Osten, “Rigorous speckle simulation using surface integral equations and boundary element methods,” in Fringe 2013, W. Osten, ed. (Springer, 2014), pp. 361–364.

Freund, Y.

R. E. Schapire and Y. Freund, Boosting: Foundations and Algorithms (MIT, 2014).

Fu, L.

L. Fu, K. Frenner, and W. Osten, “Rigorous speckle simulation using surface integral equations and boundary element methods,” in Fringe 2013, W. Osten, ed. (Springer, 2014), pp. 361–364.

Gdeisat, M.

Gdeisat, M. A.

Gordon, M. B.

M. B. Gordon, “Discrimination,” in Neural Networks: Methodology and Applications, G. Dreyfus, ed. (Springer, 2005), pp. 329–377.

Goto, D. T.

D. T. Goto, “3D shearogrophy for strain measurement,” Thesis (Universidade Federal de Santa Catarina, 2010).

Groves, R. M.

F. Sawaf and R. M. Groves, “Statistically guided improvements in speckle phase discontinuity predictions by machine learning systems,” Opt. Eng. 52, 101907 (2013).
[CrossRef]

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

Han, L.

Hirose, A.

M. Minami and A. Hirose, “Phase singular points reduction by a layered complex-valued neural network in combination with constructive Fourier synthesis,” Lect. Notes Comput. Sci. 2714, 943–950 (2003).
[CrossRef]

Hornik, K.

K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

Huang, L.

Hung, Y. Y.

Y. Y. Hung, “Shearography for non-destructive evaluation of composite structures,” Opt. Lasers Eng. 24, 161–182 (1996).
[CrossRef]

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

Jacquot, P.

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).

Judge, T. R.

T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
[CrossRef]

D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Karout, S.

S. Karout, “Two-dimensional phase unwrapping, chapter 3: artificial intelligence,” Ph.D. thesis (Liverpool John Moores University, 2007).

Kemao, Q.

Lalor, M.

Lalor, M. J.

H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46, 6623–6635 (2007).
[CrossRef]

D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
[CrossRef]

Lazar, N.

N. Lazar, “Big data hits the big time,” Chance 25, 47–49 (2012).

Li, B.

Lilley, F.

Lu, W.

Ma, C. C.

C. Y. Chang and C. C. Ma, “Measurement of resonant mode of piezoelectric thin plate using speckle interferometry and frequency-sweeping function,” Rev. Sci. Instrum. 83, 95004–95009 (2012).
[CrossRef]

Miles, J.

A. Field, J. Miles, and Z. Field, Discovering Statistics Using R (SAGE, 2012).

Minami, M.

M. Minami and A. Hirose, “Phase singular points reduction by a layered complex-valued neural network in combination with constructive Fourier synthesis,” Lect. Notes Comput. Sci. 2714, 943–950 (2003).
[CrossRef]

Moore, C.

Moore, C. J.

O’Neal, C.

C. O’Neal and R. Schutt, Doing Data Science (O’Reilly Books, 2013).

Osten, W.

A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, “Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval,” Opt. Lett. 34, 1522–1524 (2009).
[CrossRef]

L. Fu, K. Frenner, and W. Osten, “Rigorous speckle simulation using surface integral equations and boundary element methods,” in Fringe 2013, W. Osten, ed. (Springer, 2014), pp. 361–364.

Pedrini, G.

Prince, S. J. D.

S. J. D. Prince, Computer Vision: Models, Learning, and Inference (Cambridge University, 2012).

Quan, T. R.

T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
[CrossRef]

Qudeisat, M.

Sawaf, F.

F. Sawaf and R. M. Groves, “Statistically guided improvements in speckle phase discontinuity predictions by machine learning systems,” Opt. Eng. 52, 101907 (2013).
[CrossRef]

F. Sawaf and R. P. Tatam, “Finding minimum spanning trees more efficiently for tile-based phase unwrapping,” Meas. Sci. Technol. 17, 1428–1435 (2006).
[CrossRef]

Schapire, R. E.

R. E. Schapire and Y. Freund, Boosting: Foundations and Algorithms (MIT, 2014).

Schutt, R.

C. O’Neal and R. Schutt, Doing Data Science (O’Reilly Books, 2013).

Sciammarella, A.

A. Sciammarella and F. M. Sciammarella, Experimental Mechanics of Solids (Wiley, 2012), p. 276.

Sciammarella, F. M.

A. Sciammarella and F. M. Sciammarella, Experimental Mechanics of Solids (Wiley, 2012), p. 276.

Sheltraw, D.

Stinchecombe, M.

K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

Su, X.

Tang, C.

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]

F. Sawaf and R. P. Tatam, “Finding minimum spanning trees more efficiently for tile-based phase unwrapping,” Meas. Sci. Technol. 17, 1428–1435 (2006).
[CrossRef]

Tipper, D. J.

D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
[CrossRef]

Towers, C. E.

Towers, D. P.

K. Falaggis, D. P. Towers, and C. E. Towers, “Algebraic solution for phase unwrapping problems in multiwavelength interferometry,” Appl. Opt. 53, 3737–3747 (2014).
[CrossRef]

K. Falaggis, D. P. Towers, and C. E. Towers, “Method of excess fractions with application to absolute distance metrology: analytical solution,” Appl. Opt. 52, 5758–5765 (2013).
[CrossRef]

K. Falaggis, D. P. Towers, and C. E. Towers, “Generalized theory of phase unwrapping: approaches and optimal wavelength selection strategies for multiwavelength interferometric techniques,” Proc. SPIE 8493, 84930O (2012).
[CrossRef]

D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Wang, W.

Wang, Y.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

White, H.

K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

Wu, S.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

Xu, N.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

Yang, L.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

Zhang, Q.

Zhang, Z.

Zhao, M.

Zhu, L.

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

Appl. Opt. (6)

Chance (1)

N. Lazar, “Big data hits the big time,” Chance 25, 47–49 (2012).

Lect. Notes Comput. Sci. (1)

M. Minami and A. Hirose, “Phase singular points reduction by a layered complex-valued neural network in combination with constructive Fourier synthesis,” Lect. Notes Comput. Sci. 2714, 943–950 (2003).
[CrossRef]

Meas. Sci. Technol. (2)

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

F. Sawaf and R. P. Tatam, “Finding minimum spanning trees more efficiently for tile-based phase unwrapping,” Meas. Sci. Technol. 17, 1428–1435 (2006).
[CrossRef]

Neural Netw. (1)

K. Hornik, M. Stinchecombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

Nondestr. Test. Eval. (1)

D. J. Tipper, D. R. Burton, and M. J. Lalor, “A neural network approach to the phase unwrapping problem in fringe analysis,” Nondestr. Test. Eval. 12, 391–400 (1996).
[CrossRef]

Opt. Commun. (1)

M. Qudeisat, M. Gdeisat, D. Burton, and F. Lilley, “A simple method for phase wraps elimination or reduction in spatial fringe patterns,” Opt. Commun. 284, 5105–5109 (2011).
[CrossRef]

Opt. Eng. (4)

F. Sawaf and R. M. Groves, “Statistically guided improvements in speckle phase discontinuity predictions by machine learning systems,” Opt. Eng. 52, 101907 (2013).
[CrossRef]

T. R. Judge, T. R. Quan, and P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. 31, 533–543 (1992).
[CrossRef]

L. Zhu, Y. Wang, N. Xu, S. Wu, M. Dong, and L. Yang, “Real-time monitoring of phase maps of digital shearography,” Opt. Eng. 52, 101902 (2013).
[CrossRef]

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

Opt. Lasers Eng. (2)

Y. Y. Hung, “Shearography for non-destructive evaluation of composite structures,” Opt. Lasers Eng. 24, 161–182 (1996).
[CrossRef]

D. P. Towers, T. R. Judge, and P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

K. Falaggis, D. P. Towers, and C. E. Towers, “Generalized theory of phase unwrapping: approaches and optimal wavelength selection strategies for multiwavelength interferometric techniques,” Proc. SPIE 8493, 84930O (2012).
[CrossRef]

Rev. Sci. Instrum. (1)

C. Y. Chang and C. C. Ma, “Measurement of resonant mode of piezoelectric thin plate using speckle interferometry and frequency-sweeping function,” Rev. Sci. Instrum. 83, 95004–95009 (2012).
[CrossRef]

Strain (1)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).

Other (21)

W. Osten and N. Reingand, eds., Optical Imaging and Metrology: Advanced Technologies (Wiley-VCH, 2012).

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Figures (13)

Fig. 1.
Fig. 1.

Two-layer neural network. We employed the hyperbolic tangent (tanh) as the activation function.

Fig. 2.
Fig. 2.

(a) Computer-simulated wrapped phase map used as a test subject throughout this work. (b) Noisy wrapped phase map; noise was added to the underlying object’s surface. (c) Actual phase discontinuity locations were recorded for performance comparison purposes.

Fig. 3.
Fig. 3.

Illustration of how the kernel can be applied to a full-field image, (a) by tiling and (b) through a sliding window, which is moved, horizontally and vertically, by one pixel at a time. Actual kernel size used is 10×10 pixels. 5×5 kernel size is shown in this figure for illustration.

Fig. 4.
Fig. 4.

(a) Predictions made by nonoverlapped tiling method. Actual phase discontinuity locations are shown in (b) for comparison. (c) artifacts of tiling can be seen even when applied to the noise-free phase map.

Fig. 5.
Fig. 5.

Phase discontinuity location, which is intersected by a tile in a tangential manner, can escape detection due to the lack of sufficient contextual information within the tile’s kernel.

Fig. 6.
Fig. 6.

(a) The pixel at the center of the overlapping kennels receives prediction verdicts from a combined effective neighborhood of 19×19 pixels. For illustration, a 5×5 kernel is shown, resulting in an effective neighborhood of 9×9 pixels. (b) Pixels sufficiently farther from boundary of full-field receive the full number of verdicts, i.e., 100 verdicts for a 10×10 kernel.

Fig. 7.
Fig. 7.

Phase discontinuity locations designated by applying a range of boundary lines. The boundary is applied to the accumulated number of times each pixel was predicted to be a phase discontinuity location.

Fig. 8.
Fig. 8.

Gray-scale representation of the accumulated number of times each pixel was predicted to be a phase discontinuity location, when visited by the sliding window, is shown in (a). Actual phase discontinuity locations are shown in (b) for comparison. Applying sliding window to noise-free phase map can be seen in (c), showing that tiling artifacts are largely overcome overall, and completely so in areas further than the kernel’s width (10 pixels) away from full-field boundary.

Fig. 9.
Fig. 9.

Gray-scale representation of accumulated predictions, with increasing effective combined neighborhoods’ size. Subcaptions read as follows: effective combined neighborhoods’ size in pixels, processing duration formatted as seconds: milliseconds, maximum number of predictions received by any pixel within the full-field image, mean number of predictions per pixel rounded to three significant figures. Bottom subplot shows the mean number of prediction received by pixels in full-field phase map, for a given effective combined neighborhoods’ size.

Fig. 10.
Fig. 10.

Measuring improvements in prediction performance obtained by increasing the effective combined neighborhoods’ size through the sliding-window mechanism. Mathews correlation coefficient (MCC) score across all possible voting boundary lines. Subplots axes: MCC on vertical axis, and voting boundary line of absolute number (as opposed to percentage) of votes received on horizontal axis. Subplot captions format: effective combined neighborhoods’ size in pixels, maximum MCC score in subplot.

Fig. 11.
Fig. 11.

(a) Mechanical sample is a cylinder that is 400 mm long, 190 mm in diameter, and 5 mm in wall thickness [43]. (b) Cylinder was pumped with oil and mounted in a shearography optical setup. (c) Applying the 10×10 kernel to the optically obtained noisy wrapped phase measuring 604×1024 pixels. The aggregated kernel’s predictions are shown (d) in gray-scale representation. Applying a voting ballot boundary line is shown in (e).

Fig. 12.
Fig. 12.

MCC% measure is defined as: MCC% = classification threshold% * MCC. The excitation level of the neural network’s output layer is compared against the threshold, where output levels equal to or exceeding the threshold are classified as phase discontinuity locations. A nominal 50% threshold (corresponding to zero on the vertical axis) is typical, though higher (or lower) values can be used to demand more confidence in (or relax) classification predictions.

Fig. 13.
Fig. 13.

Row performance of the machine-learning trained 10×10 kernel

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