Abstract

In digital holography, it is crucial to extract the object distance from a hologram in order to reconstruct its amplitude and phase. This is known as autofocusing, which is conventionally solved by first reconstructing a stack of images, and then the sharpness of each reconstructed image is computed using a focus metric such as entropy or variance. The distance corresponding to the sharpest image is considered the focal position. This approach, while effective, is computationally demanding and time-consuming. To cope with this problem, we turn to machine learning, where we cast the autofocusing as a regression problem, with the focal distance being a continuous response corresponding to each hologram. Therefore, distance estimation is converted to hologram prediction, which we solve by designing a powerful convolutional neural network trained by a set of holograms acquired a priori. Experimental results show that this allows fast autofocusing without reconstructing an image stack, even when the physical parameters of the optical setup are unknown.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W.H. Freeman, 2017).
  2. U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).
  3. A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
    [Crossref]
  4. P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 020901 (2014).
    [Crossref]
  5. Y. Pourvais, P. Asgari, P. Abdollahi, R. Khamedi, and A.-R. Moradi, “Microstructural surface characterization of stainless and plain carbon steel using digital holographic microscopy,” J. Opt. Soc. Am. B 34, B36–B41 (2017).
    [Crossref]
  6. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [Crossref]
  7. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
    [Crossref]
  8. M. Lyu, C. Yuan, D. Li, and G. Situ, “Fast autofocusing in digital holography using the magnitude differential,” Appl. Opt. 56, F152–F157 (2017).
    [Crossref]
  9. P. Langehanenberg, G. von Bally, and B. Kemper, “Autofocusing in digital holographic microscopy,” 3D Res. 2, 1–11 (2011).
    [Crossref]
  10. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
    [Crossref]
  11. Z. Ren, N. Chen, and E. Y. Lam, “Extended focused imaging and depth map reconstruction in optical scanning holography,” Appl. Opt. 55, 1040–1047 (2016).
    [Crossref]
  12. A. C. Chan, K. K. Tsia, and E. Y. Lam, “Subsampled scanning holographic imaging (SuSHI) for fast, non-adaptive recording of three-dimensional objects,” Optica 3, 911–917 (2016).
    [Crossref]
  13. P. Gao, B. Yao, J. Min, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, and T. Ye, “Autofocusing of digital holographic microscopy based on off-axis illuminations,” Opt. Lett. 37, 3630–3632 (2012).
    [Crossref]
  14. J. Zheng, P. Gao, and X. Shao, “Opposite-view digital holographic microscopy with autofocusing capability,” Sci. Rep. 7, 4255 (2017).
    [Crossref]
  15. M. Subbarao and J. K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
    [Crossref]
  16. H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
    [Crossref]
  17. Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2015), paper DT4A-4.
  18. Z. Ren, N. Chen, and E. Y. Lam, “Automatic focusing for multisectional objects in digital holography using the structure tensor,” Opt. Lett. 42, 1720–1723 (2017).
    [Crossref]
  19. Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42, 3824–3827 (2017).
    [Crossref]
  20. S. Oh, C.-Y. Hwang, I. K. Jeong, S.-K. Lee, and J.-H. Park, “Fast focus estimation using frequency analysis in digital holography,” Opt. Express 22, 28926–28933 (2014).
    [Crossref]
  21. P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47, D176–D182 (2008).
    [Crossref]
  22. A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems (2012), pp. 1097–1105.
  23. Y. LeCun, Y. Bengio, and G. E. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
    [Crossref]
  24. D. Shen, G. Wu, and H.-I. Suk, “Deep learning in medical image analysis,” Ann. Rev. Biomed. Eng. 19, 221–248 (2017).
    [Crossref]
  25. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2, 517–522 (2015).
    [Crossref]
  26. A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
    [Crossref]
  27. Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
    [Crossref]
  28. T. Nguyen, V. Bui, V. Lam, C. B. Raub, L.-C. Chang, and G. Nehmetallah, “Automatic phase aberration compensation for digital holographic microscopy based on deep learning background detection,” Opt. Express 25, 15043–15057 (2017).
    [Crossref]
  29. T. Pitkäaho, A. Manninen, and T. J. Naughton, “Performance of autofocus capability of deep convolutional neural networks in digital holographic microscopy,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2017), paper W2A-5.
  30. Z. Ren, Z. Xu, and E. Y. Lam, “Autofocusing in digital holography using deep learning,” Proc. SPIE 10499, 104991V (2018).
    [Crossref]
  31. M. W. Gardner and S. Dorling, “Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences,” Atmos. Environ. 32, 2627–2636 (1998).
    [Crossref]
  32. J. Huang, J. Lu, and C. X. Ling, “Comparing naive Bayes, decision trees, and SVM with AUC and accuracy,” in Proceedings of International Conference on Data Mining (IEEE, 2003), pp. 553–556.
  33. K. Q. Weinberger, J. Blitzer, and L. K. Saul, “Distance metric learning for large margin nearest neighbor classification,” in Advances in Neural Information Processing Systems (2006), pp. 1473–1480.
  34. M. Jaderberg, A. Vedaldi, and A. Zisserman, “Deep features for text spotting,” in European Conference on Computer Vision (Springer, 2014), pp. 512–528.
  35. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).
  36. Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
    [Crossref]
  37. N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).
  38. S. Menard, “Coefficients of determination for multiple logistic regression analysis,” Am. Stat. 54, 17–24 (2000).
  39. M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).
  40. T. Colomb, J. Kühn, F. Charriere, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006).
    [Crossref]

2018 (2)

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Z. Ren, Z. Xu, and E. Y. Lam, “Autofocusing in digital holography using deep learning,” Proc. SPIE 10499, 104991V (2018).
[Crossref]

2017 (8)

2016 (2)

2015 (2)

2014 (5)

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 020901 (2014).
[Crossref]

S. Oh, C.-Y. Hwang, I. K. Jeong, S.-K. Lee, and J.-H. Park, “Fast focus estimation using frequency analysis in digital holography,” Opt. Express 22, 28926–28933 (2014).
[Crossref]

2012 (1)

2011 (1)

P. Langehanenberg, G. von Bally, and B. Kemper, “Autofocusing in digital holographic microscopy,” 3D Res. 2, 1–11 (2011).
[Crossref]

2009 (1)

2008 (2)

2006 (1)

2000 (1)

S. Menard, “Coefficients of determination for multiple logistic regression analysis,” Am. Stat. 54, 17–24 (2000).

1999 (1)

1998 (3)

M. Subbarao and J. K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[Crossref]

M. W. Gardner and S. Dorling, “Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences,” Atmos. Environ. 32, 2627–2636 (1998).
[Crossref]

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Abadi, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Abdollahi, P.

Agarwal, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Asgari, P.

Aspert, N.

Barbastathis, G.

Barham, P.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Bengio, Y.

Y. LeCun, Y. Bengio, and G. E. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

Blitzer, J.

K. Q. Weinberger, J. Blitzer, and L. K. Saul, “Distance metric learning for large margin nearest neighbor classification,” in Advances in Neural Information Processing Systems (2006), pp. 1473–1480.

Bottou, L.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Brady, D. J.

Brevdo, E.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Bui, V.

Chan, A.

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2015), paper DT4A-4.

Chan, A. C.

Chang, L.-C.

Charriere, F.

Chen, N.

Chen, Z.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Choi, K.

Citro, C.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Colomb, T.

Corrado, G. S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Courville, A.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

Cuche, E.

Dan, D.

Davis, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Dean, J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Depeursinge, C.

Devin, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Dirksen, D.

Doblas, A.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

Dogar, M.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Dorling, S.

M. W. Gardner and S. Dorling, “Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences,” Atmos. Environ. 32, 2627–2636 (1998).
[Crossref]

Falldorf, C.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).

Gao, P.

Garcia-Sucerquia, J.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

Gardner, M. W.

M. W. Gardner and S. Dorling, “Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences,” Atmos. Environ. 32, 2627–2636 (1998).
[Crossref]

Ghemawat, S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Goodfellow, I.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

Goodfellow, I. J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W.H. Freeman, 2017).

Goy, A.

Gunaydin, H.

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Guo, R.

Haffner, P.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Harp, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Hinton, G. E.

Y. LeCun, Y. Bengio, and G. E. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems (2012), pp. 1097–1105.

Horisaki, R.

Huang, J.

J. Huang, J. Lu, and C. X. Ling, “Comparing naive Bayes, decision trees, and SVM with AUC and accuracy,” in Proceedings of International Conference on Data Mining (IEEE, 2003), pp. 553–556.

Hwang, C.-Y.

Ilhan, H. A.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Irving, G.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Isard, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Jaderberg, M.

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Deep features for text spotting,” in European Conference on Computer Vision (Springer, 2014), pp. 512–528.

Jeong, I. K.

Jia, Y.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Józefowicz, R.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Jüptner, W.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).

Kaiser, L.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Kamilov, U. S.

Kemper, B.

Khamedi, R.

Krizhevsky, A.

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems (2012), pp. 1097–1105.

Kudlur, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Kühn, J.

Lam, E. Y.

Lam, V.

Langehanenberg, P.

LeCun, Y.

Y. LeCun, Y. Bengio, and G. E. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Lee, J.

Lee, S.-K.

Lei, M.

Levenberg, J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Li, D.

Li, S.

Lim, S.

Ling, C. X.

J. Huang, J. Lu, and C. X. Ling, “Comparing naive Bayes, decision trees, and SVM with AUC and accuracy,” in Proceedings of International Conference on Data Mining (IEEE, 2003), pp. 553–556.

Lu, J.

J. Huang, J. Lu, and C. X. Ling, “Comparing naive Bayes, decision trees, and SVM with AUC and accuracy,” in Proceedings of International Conference on Data Mining (IEEE, 2003), pp. 553–556.

Lyu, M.

Ma, B.

Magistretti, P. J.

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 020901 (2014).
[Crossref]

Mané, D.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Manninen, A.

T. Pitkäaho, A. Manninen, and T. J. Naughton, “Performance of autofocus capability of deep convolutional neural networks in digital holographic microscopy,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2017), paper W2A-5.

Marks, D. L.

Marquet, P.

Martínez-Corral, M.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

Menard, S.

S. Menard, “Coefficients of determination for multiple logistic regression analysis,” Am. Stat. 54, 17–24 (2000).

Min, J.

Monga, R.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Moore, S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Moradi, A.-R.

Murray, D. G.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Naughton, T. J.

T. Pitkäaho, A. Manninen, and T. J. Naughton, “Performance of autofocus capability of deep convolutional neural networks in digital holographic microscopy,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2017), paper W2A-5.

Nehmetallah, G.

Nguyen, T.

Oh, S.

Olah, C.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42, 3824–3827 (2017).
[Crossref]

Özcan, M.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Papadopoulos, I. N.

Park, J.-H.

Pitkäaho, T.

T. Pitkäaho, A. Manninen, and T. J. Naughton, “Performance of autofocus capability of deep convolutional neural networks in digital holographic microscopy,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2017), paper W2A-5.

Poon, T.-C.

Pourvais, Y.

Psaltis, D.

Raub, C. B.

Ren, Z.

Z. Ren, Z. Xu, and E. Y. Lam, “Autofocusing in digital holography using deep learning,” Proc. SPIE 10499, 104991V (2018).
[Crossref]

Z. Ren, N. Chen, and E. Y. Lam, “Automatic focusing for multisectional objects in digital holography using the structure tensor,” Opt. Lett. 42, 1720–1723 (2017).
[Crossref]

Z. Ren, N. Chen, and E. Y. Lam, “Extended focused imaging and depth map reconstruction in optical scanning holography,” Appl. Opt. 55, 1040–1047 (2016).
[Crossref]

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2015), paper DT4A-4.

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Saavedra, G.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

Salakhutdinov, R.

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

Sánchez-Ortiga, E.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

Saul, L. K.

K. Q. Weinberger, J. Blitzer, and L. K. Saul, “Distance metric learning for large margin nearest neighbor classification,” in Advances in Neural Information Processing Systems (2006), pp. 1473–1480.

Schnars, U.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).

Schuster, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Shao, X.

J. Zheng, P. Gao, and X. Shao, “Opposite-view digital holographic microscopy with autofocusing capability,” Sci. Rep. 7, 4255 (2017).
[Crossref]

Shen, D.

D. Shen, G. Wu, and H.-I. Suk, “Deep learning in medical image analysis,” Ann. Rev. Biomed. Eng. 19, 221–248 (2017).
[Crossref]

Shlens, J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Shoreh, M. H.

Sinha, A.

Situ, G.

Srivastava, N.

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

Steiner, B.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Subbarao, M.

M. Subbarao and J. K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[Crossref]

Suk, H.-I.

D. Shen, G. Wu, and H.-I. Suk, “Deep learning in medical image analysis,” Ann. Rev. Biomed. Eng. 19, 221–248 (2017).
[Crossref]

Sutskever, I.

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems (2012), pp. 1097–1105.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Talwar, K.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Tamamitsu, M.

Teng, D.

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Tsia, K. K.

Tucker, P. A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Tyan, J. K.

M. Subbarao and J. K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[Crossref]

Unser, M.

Vanhoucke, V.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Vasudevan, V.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Vedaldi, A.

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Deep features for text spotting,” in European Conference on Computer Vision (Springer, 2014), pp. 512–528.

Viégas, F. B.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Vinyals, O.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

von Bally, G.

Vonesch, C.

Wang, H.

Warden, P.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Watson, J.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).

Wattenberg, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Weinberger, K. Q.

K. Q. Weinberger, J. Blitzer, and L. K. Saul, “Distance metric learning for large margin nearest neighbor classification,” in Advances in Neural Information Processing Systems (2006), pp. 1473–1480.

Wicke, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Wu, G.

D. Shen, G. Wu, and H.-I. Suk, “Deep learning in medical image analysis,” Ann. Rev. Biomed. Eng. 19, 221–248 (2017).
[Crossref]

Wu, Y.

Xu, Z.

Z. Ren, Z. Xu, and E. Y. Lam, “Autofocusing in digital holography using deep learning,” Proc. SPIE 10499, 104991V (2018).
[Crossref]

Yan, S.

Yao, B.

Ye, T.

Yu, Y.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Yuan, C.

Zhang, X.

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42, 3824–3827 (2017).
[Crossref]

Zheng, J.

Zheng, X.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

Zisserman, A.

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Deep features for text spotting,” in European Conference on Computer Vision (Springer, 2014), pp. 512–528.

3D Res. (1)

P. Langehanenberg, G. von Bally, and B. Kemper, “Autofocusing in digital holographic microscopy,” 3D Res. 2, 1–11 (2011).
[Crossref]

Am. Stat. (1)

S. Menard, “Coefficients of determination for multiple logistic regression analysis,” Am. Stat. 54, 17–24 (2000).

Ann. Rev. Biomed. Eng. (1)

D. Shen, G. Wu, and H.-I. Suk, “Deep learning in medical image analysis,” Ann. Rev. Biomed. Eng. 19, 221–248 (2017).
[Crossref]

Appl. Opt. (4)

Atmos. Environ. (1)

M. W. Gardner and S. Dorling, “Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences,” Atmos. Environ. 32, 2627–2636 (1998).
[Crossref]

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

M. Subbarao and J. K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[Crossref]

J. Biomed. Opt. (1)

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19, 046022 (2014).
[Crossref]

J. Mach. Learn. Res. (1)

N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

J. Microsc. (1)

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

Y. Rivenson, Y. Zhang, H. Gunaydin, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Nature (1)

Y. LeCun, Y. Bengio, and G. E. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

Neurophotonics (1)

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 020901 (2014).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Optica (3)

Proc. IEEE (1)

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Proc. SPIE (1)

Z. Ren, Z. Xu, and E. Y. Lam, “Autofocusing in digital holography using deep learning,” Proc. SPIE 10499, 104991V (2018).
[Crossref]

Sci. Rep. (1)

J. Zheng, P. Gao, and X. Shao, “Opposite-view digital holographic microscopy with autofocusing capability,” Sci. Rep. 7, 4255 (2017).
[Crossref]

Other (10)

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2015), paper DT4A-4.

J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W.H. Freeman, 2017).

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (Springer, 2015).

T. Pitkäaho, A. Manninen, and T. J. Naughton, “Performance of autofocus capability of deep convolutional neural networks in digital holographic microscopy,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2017), paper W2A-5.

J. Huang, J. Lu, and C. X. Ling, “Comparing naive Bayes, decision trees, and SVM with AUC and accuracy,” in Proceedings of International Conference on Data Mining (IEEE, 2003), pp. 553–556.

K. Q. Weinberger, J. Blitzer, and L. K. Saul, “Distance metric learning for large margin nearest neighbor classification,” in Advances in Neural Information Processing Systems (2006), pp. 1473–1480.

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Deep features for text spotting,” in European Conference on Computer Vision (Springer, 2014), pp. 512–528.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems (2012), pp. 1097–1105.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. J. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Józefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. G. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. A. Tucker, V. Vanhoucke, V. Vasudevan, F. B. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: large-scale machine learning on heterogeneous distributed systems,” arXiv:1603.04467 (2016).

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Figures (13)

Fig. 1.
Fig. 1. Schematic diagram of a DH system. SF stands for the spatial filter. L is the collimation lens. BE is the beam expander. HWP1 and HWP2 are the half-wave plates. PBS and BS are the polarization and non-polarization beam splitters, respectively. M1 and M2 are the mirrors. OBJ is the object. PD is the camera. x axis and z axis denote the two motion controllers along the two directions. z is the distance between the object and the camera. The object shown here is a small region of a negative USAF 1951 resolution chart.
Fig. 2.
Fig. 2. Framework of the proposed CNN for autofocusing. In each “Layer,” a convolutional layer, a ReLU layer, a batch normalization layer, and a max-pooling layer are included. “FC1” and “FC2” represent fully connected layers, and “Dropout” means dropout layer. In “Input,” the input hologram size, which is cropped from the raw 1280 × 1024 image, is shown beneath. In “Feature Extraction,” the kernel size and depth are given at the bottom of each layer. In “Regression,” the input hologram is predicted with a response, denoting the estimated focal distance.
Fig. 3.
Fig. 3. USAF test target and its local area, as well as several biological specimens used in the experiment.
Fig. 4.
Fig. 4. Sixteen of the experimentally collected testing holograms recording various amplitude objects.
Fig. 5.
Fig. 5. Validation loss decreases along the training process. Only 1000 iterations are shown here.
Fig. 6.
Fig. 6. Back-propagated images of the testing holograms in Fig. 4 using the predicted distances with CNN.
Fig. 7.
Fig. 7. Customized groove used as the phase object.
Fig. 8.
Fig. 8. Sixteen experimentally collected testing holograms of a phase object shown in Fig. 7.
Fig. 9.
Fig. 9. Validation loss decreases and accuracy increases as the network is trained. Only 1000 iterations are shown here.
Fig. 10.
Fig. 10. Reconstructed and unwrapped phase images of the testing holograms in Fig. 8 using the predicted focal distances and double exposure method. The unit of the color bar is radian.
Fig. 11.
Fig. 11. Hologram and reconstructed image, respectively, with an exposure time of (a), (b) 5 ms and (c), (d) 18 ms.
Fig. 12.
Fig. 12. Reconstructed images with the holograms recorded at different distances.
Fig. 13.
Fig. 13. (a), (b) Holograms, (c), (d) frequency spectra, and (e), (f) reconstructed images under different angles.

Tables (3)

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Table 1. Comparison of the Regression Performance on the Validation and Test Datasets among kNN, SVM, MLP, and CNN for the Amplitude Object

Tables Icon

Table 2. Comparison of the Regression Performance on the Validation and Test Datasets among kNN, SVM, MLP, and CNN for the Phase Object

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Table 3. Comparison of Absolute Error and Computation Time among CNN and Conventional Methods on the Amplitude Samples

Equations (5)

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

h j ( ) = ψ ( i = 1 N ( 1 ) h i ( 1 ) * w i j ( ) + b j ( ) ) ,
L = 1 N i = 1 N y i y ^ i 2 2 ,
MAE ( y , y ^ ) = 1 N i = 1 N | y i y ^ i | ,
EV ( y , y ^ ) = 1 Var { y y ^ } Var { y } ,
R 2 ( y , y ^ ) = 1 i = 1 N ( y i y ^ i ) 2 i = 1 N ( y i y ¯ ) 2 ,

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