Abstract

Two-dimensional phase unwrapping algorithms are widely used in optical metrology and measurements. The high noise from interference measurements, however, often leads to the failure of conventional phase unwrapping algorithms. In this paper, we propose a deep convolutional neural network (DCNN) based method to perform rapid and robust two-dimensional phase unwrapping. In our approach, we employ a DCNN architecture, DeepLabV3+, with noise suppression and strong feature representation capabilities. The employed DCNN is first used to perform semantic segmentation to obtain the segmentation result of the wrapped phase map. We then combine the wrapped phase map with the segmentation result to generate the unwrapped phase. We benchmarked our results by comparing them with well-established methods. The reported approach out-performed the conventional path-dependent and path-independent algorithms. We also tested the robustness of the reported approach using interference measurements from optical metrology setups. Our results, again, clearly out-performed the conventional phase unwrap algorithms. The reported approach may find applications in optical metrology and microscopy imaging.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [Crossref] [PubMed]
  2. S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
    [Crossref]
  3. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7444 (2002).
    [Crossref] [PubMed]
  4. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [Crossref]
  5. H. Xia, S. Montresor, R. Guo, J. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
    [Crossref] [PubMed]
  6. M. F. Kasim, “Fast 2D phase unwrapping implementation in MATLAB,” https://github.com/mfkasim91/unwrap_phase/ .
  7. C. Prati, M. Giani, and N. Leuratti, “SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium, (IEEE, 1990), pp. 2043–2046.
    [Crossref]
  8. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
    [Crossref]
  9. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988).
    [Crossref]
  10. J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation,” Appl. Opt. 56, 7079–7088 (2017).
    [Crossref] [PubMed]
  11. Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
    [Crossref]
  12. C. Zuo, “Connections between transport of intensity equation and two-dimensional phase unwrapping,” arXiv preprint arXiv:1704.03950 (2017).
  13. J. Arines, “Least-squares modal estimation of wrapped phases: application to phase unwrapping,” Appl. Opt. 42, 3373–3378 (2003).
    [Crossref] [PubMed]
  14. W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.
  15. G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Computational Optical Sensing and Imaging, (Optical Society of America, 2018), pp. CW3B–5.
    [Crossref]
  16. G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
    [Crossref]
  17. V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
    [Crossref]
  18. S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.
  19. W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.
  20. K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” arXiv preprint arXiv:1409.1556 (2014).
  21. F. Chollet, “Xception: Deep learning with depthwise separable convolutions,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2017), pp. 1251–1258.
  22. J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2015), pp. 3431–3440.
  23. O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, (Springer, 2015), pp. 234–241.
  24. L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.
  25. K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.
  26. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.
  27. S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).
  28. J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
    [Crossref]

2019 (2)

G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
[Crossref]

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

2018 (1)

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

2017 (2)

V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
[Crossref]

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation,” Appl. Opt. 56, 7079–7088 (2017).
[Crossref] [PubMed]

2016 (1)

2013 (1)

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

2003 (1)

2002 (1)

1997 (1)

1991 (1)

1988 (2)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988).
[Crossref]

Adam, H.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

Anguelov, D.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Arines, J.

Badrinarayanan, V.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
[Crossref]

Berg, A. C.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Bone, D. J.

Bovik, A. C.

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, (Springer, 2015), pp. 234–241.

Burton, D. R.

Carazo, J.

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

Chao, Z.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Chen, L.-C.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

Cheng, H.

Chollet, F.

F. Chollet, “Xception: Deep learning with depthwise separable convolutions,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2017), pp. 1251–1258.

Cipolla, R.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
[Crossref]

Dai, J.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Dardikman, G.

G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Computational Optical Sensing and Imaging, (Optical Society of America, 2018), pp. CW3B–5.
[Crossref]

Darrell, T.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2015), pp. 3431–3440.

Dollár, P.

K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.

Du, H.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Erhan, D.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Estrada, J.

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

Evans, B. L.

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

Falaggis, K.

Fan, C.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Feng, S.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Fischer, P.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, (Springer, 2015), pp. 234–241.

Flynn, T. J.

Fu, C.-Y.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Gdeisat, M. A.

Ghosh, J.

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

Giani, M.

C. Prati, M. Giani, and N. Leuratti, “SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium, (IEEE, 1990), pp. 2043–2046.
[Crossref]

Girshick, R.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.

K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.

Gkioxari, G.

K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Gorthi, R. K. S. S.

G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
[Crossref]

Gorthi, S.

G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
[Crossref]

Gu, G.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Guo, R.

He, K.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.

K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.

Herráez, M. A.

Hu, H.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Ioffe, S.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

Kendall, A.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
[Crossref]

Kozacki, T.

Lalor, M. J.

Leuratti, N.

C. Prati, M. Giani, and N. Leuratti, “SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium, (IEEE, 1990), pp. 2043–2046.
[Crossref]

Li, J.

Li, Y.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Liang, Z.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Liu, W.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Long, J.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2015), pp. 3431–3440.

Martinez-Carranza, J.

Milner, T. E.

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

Montresor, S.

Papandreou, G.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

Picart, P.

Prati, C.

C. Prati, M. Giani, and N. Leuratti, “SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium, (IEEE, 1990), pp. 2043–2046.
[Crossref]

Qi, H.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Qian, C.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Reed, S.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

Ren, S.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.

Ronneberger, O.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, (Springer, 2015), pp. 234–241.

Schroff, F.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

Schwartzkopf, W.

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

Shaked, N. T.

G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Computational Optical Sensing and Imaging, (Optical Society of America, 2018), pp. CW3B–5.
[Crossref]

Shelhamer, E.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2015), pp. 3431–3440.

Simonyan, K.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” arXiv preprint arXiv:1409.1556 (2014).

Sorzano, C.

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

Spoorthi, G. E.

G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
[Crossref]

Sun, J.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.

Szegedy, C.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

Takahashi, T.

Takajo, H.

Tao, T.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Vargas, J.

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

Wei, Y.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Xia, H.

Xiao, Z.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Xiong, Y.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Yan, F.

Yan, H.

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Zhang, G.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

Zhang, H.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Zhao, H.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Zhao, Z.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Zhu, Y.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

Zhuang, Y.

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Zisserman, A.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” arXiv preprint arXiv:1409.1556 (2014).

Zuo, C.

C. Zuo, “Connections between transport of intensity equation and two-dimensional phase unwrapping,” arXiv preprint arXiv:1704.03950 (2017).

Adv. Photonics (1)

S. Feng, C. Qian, G. Gu, T. Tao, Z. Liang, H. Yan, Y. Wei, and Z. Chao, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Appl. Opt. (4)

IEEE Signal Process. Lett. (1)

G. E. Spoorthi, S. Gorthi, and R. K. S. S. Gorthi, “Phasenet: A deep convolutional neural network for two-dimensional phase unwrapping,” IEEE Signal Process. Lett. 26, 54–58 (2019).
[Crossref]

IEEE Transactions on Pattern Analysis Mach. Intell. (1)

V. Badrinarayanan, A. Kendall, and R. Cipolla, “Segnet: A deep convolutional encoder-decoder architecture for image segmentation,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 2481–2495 (2017).
[Crossref]

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

Meas. Sci. Technol. (1)

Z. Zhao, H. Zhang, Z. Xiao, H. Du, Y. Zhuang, C. Fan, and H. Zhao, “Robust 2D phase unwrapping algorithm based on the transport of intensity equation,” Meas. Sci. Technol. 30, 015201 (2018).
[Crossref]

Opt. Commun. (1)

J. Vargas, C. Sorzano, J. Estrada, and J. Carazo, “Generalization of the principal component analysis algorithm for interferometry,” Opt. Commun. 286, 130–134 (2013).
[Crossref]

Opt. Express (1)

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Other (15)

M. F. Kasim, “Fast 2D phase unwrapping implementation in MATLAB,” https://github.com/mfkasim91/unwrap_phase/ .

C. Prati, M. Giani, and N. Leuratti, “SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium, (IEEE, 1990), pp. 2043–2046.
[Crossref]

W. Schwartzkopf, T. E. Milner, J. Ghosh, B. L. Evans, and A. C. Bovik, “Two-dimensional phase unwrapping using neural networks,” in Proceedings of IEEE Conference on Image Analysis and Interpretation, (IEEE, 2000), pp. 274–277.

G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Computational Optical Sensing and Imaging, (Optical Society of America, 2018), pp. CW3B–5.
[Crossref]

C. Zuo, “Connections between transport of intensity equation and two-dimensional phase unwrapping,” arXiv preprint arXiv:1704.03950 (2017).

S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” in Advances in Neural Information Processing Systems, (IEEE, 2015), pp. 91–99.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in Proceedings of the European Conference on Computer Vision, (Springer, 2016), pp. 21–37.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” arXiv preprint arXiv:1409.1556 (2014).

F. Chollet, “Xception: Deep learning with depthwise separable convolutions,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2017), pp. 1251–1258.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2015), pp. 3431–3440.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, (Springer, 2015), pp. 234–241.

L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-decoder with atrous separable convolution for semantic image segmentation,” in Proceedings of the European Conference on Computer Vision, (Springer, 2018), pp. 801–818.

K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask r-cnn,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 2961–2969.

J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei, “Deformable convolutional networks,” in Proceedings of the IEEE International Conference on Computer Vision, (IEEE, 2017), pp. 764–773.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

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Figures (12)

Fig. 1
Fig. 1 The flowchart of the proposed phase unwrapping method.
Fig. 2
Fig. 2 The structure of DeepLabV3+.
Fig. 3
Fig. 3 The structure of modified aligned Xception.
Fig. 4
Fig. 4 (a) Illustration of the refinement operation. (b) Some wrapped phase maps in the training set.
Fig. 5
Fig. 5 Phase unwrapping on simulation data without noise. (a) Simulated wrapped phase map. (b) Ground truth. Unwrapped phase maps are generated by using SRFNP (c) with RMSE 3.5e^−13, TIE (d) with RMSE 0.9067, ITIE (e) with RMSE 0.2096, RTIE (f) with RMSE 0.1627, Ours without refinement (g) with RMSE 0.5618, Ours with refinement (h) with RMSE 0.1410.
Fig. 6
Fig. 6 Phase unwrapping on simulation data with Gaussian white noise (standard deviation is set to 2.0). (a) Simulated wrapped phase map. (b) Ground truth. Unwrapped phase maps are generated by using SRFNP (c) with RMSE 19.7591, TIE (d) with RMSE 10.9604, ITIE (e) with RMSE 10.4928, RTIE (f) with RMSE 6.9038, Ours without refinement (g) with RMSE 1.2325, Ours with refinement (h) with RMSE 1.5608.
Fig. 7
Fig. 7 The effects of noise with different standard deviations.
Fig. 8
Fig. 8 Experimental setup. (a) Twyman-Green interferometer for testing an optical sphere. (b) Speckle interferometer for measuring deformation of a rough planar surface. (c) Phase shifted interferograms obtained by (a). (d) Phase shifted speckle fringe patterns obtained by (b).
Fig. 9
Fig. 9 Phase unwrapping on real data with low-level noise. (a) Wrapped phase map. Unwrapped phase maps are generated by using SRFNP (b), TIE (c), ITIE (d), RTIE (e), Ours (f).
Fig. 10
Fig. 10 Phase unwrapping on real data in circular shape with severe noise. (a) Wrapped phase map. Unwrapped phase maps are generated by using SRFNP (b), TIE (c), ITIE (d), RTIE (e), Ours (f).
Fig. 11
Fig. 11 Phase unwrapping on real data in rectangular shape with severe noise. (a) Wrapped phase map. Unwrapped phase maps are generated by using SRFNP (b), TIE (c), ITIE (d), RTIE (e), Ours (f).
Fig. 12
Fig. 12 Phase unwrapping via image stitching. (a) Original wrapped phase map with a resolution of 500 × 500. (b1) – (b4) Four sub-images with an overlap of 12 pixels. (c1) – (c4) Segmentation results of (b1) – (b4). (d) Final stitched unwrapping result.

Equations (9)

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φ ( x , y ) = ϕ ( x , y ) + 2 π k ( x , y ) ,
k ( x , y ) = F seg [ ϕ ( x , y ) ] ,
φ t ( x , y ) = ϕ ( x , y ) + 2 π k ( x , y ) ,
φ f ( x , y ) = F R [ φ t ( x , y ) ]
Δ = a + b + c + d + f + g + h + i 8 e ,
e = e + 2 π × Round ( Δ 2 π ) ,
φ ( x , y ) = i = 1 10 c i Z i ( x , y ) ,
ϕ ( x , y ) = angle ( exp ( 1 i × φ ( x , y ) ) ) .
k ( x , y ) = φ ( x , y ) ϕ ( x , y ) 2 π .

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