Abstract

It is well known that in-line digital holography (DH) makes use of the full pixel count in forming the holographic imaging. But it usually requires phase-shifting or phase retrieval techniques to remove the zero-order and twin-image terms, resulting in the so-called two-step reconstruction process, i.e., phase recovery and focusing. Here, we propose a one-step end-to-end learning-based method for in-line holography reconstruction, namely, the eHoloNet, which can reconstruct the object wavefront directly from a single-shot in-line digital hologram. In addition, the proposed learning-based DH technique has strong robustness to the change of optical path difference between reference beam and object light and does not require the reference beam to be a plane or spherical wave.

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

Full Article  |  PDF Article
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References

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2018 (6)

2017 (6)

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 717865 (2017).
[Crossref] [PubMed]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
[Crossref]

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] [PubMed]

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] [PubMed]

K. H. Jin, M. T. McCann, E. Froustey, and M. Unser, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26, 4509–4522 (2017).
[Crossref]

M. T. McCann, K. H. Jin, and M. Unser, “Convolutional neural networks for inverse problems in imaging: A review,” IEEE Signal Process. Mag. 34, 85–95 (2017).
[Crossref]

2016 (1)

2015 (1)

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

2014 (1)

N. Srivastava, G. 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).

2013 (1)

L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
[Crossref]

2009 (2)

2008 (2)

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

2004 (2)

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[Crossref] [PubMed]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

1998 (1)

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

1997 (1)

1991 (1)

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67, 3106–3109 (1991).
[Crossref] [PubMed]

1987 (2)

1986 (1)

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

1982 (1)

T. S. Ferguson, “An inconsistent maximum likelihood estimate,” J. Am. Stat. Asso. 77, 831–834 (1982).
[Crossref]

Asundi, A.

Awatsuji, Y.

Ba, J.

K. Diederik and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv: 1412.6980 (2014).

Barbastathis, G.

Barton, J. J.

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67, 3106–3109 (1991).
[Crossref] [PubMed]

Bengio, Y.

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

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

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]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” arXiv preprint arXiv:1505.04597 (2015).

Bui, V.

Cai, J.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

Cai, L. Z.

Chang, L.-C.

Chen, N.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 717865 (2017).
[Crossref] [PubMed]

H. Wang, M. Lyu, N. Chen, and G. Situ, “In-line hologram reconstruction with deep learning,” in Image and Applied Optics, OSA Technical Digest (Optical Society of America, 2018), paper DW2F.2.

Chen, T.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

Diederik, K.

K. Diederik and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv: 1412.6980 (2014).

Dong, G. Y.

Dumoulin, V.

V. Dumoulin and F. Visin, “A guide to convolution arithmetic for deep learning,” arXive preprint arXiv:1603.07285 (2016).

Ferguson, T. S.

T. S. Ferguson, “An inconsistent maximum likelihood estimate,” J. Am. Stat. Asso. 77, 831–834 (1982).
[Crossref]

Fink, H.-W.

Fischer, P.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” arXiv preprint arXiv:1505.04597 (2015).

Froustey, E.

K. H. Jin, M. T. McCann, E. Froustey, and M. Unser, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26, 4509–4522 (2017).
[Crossref]

Gopinathan, U.

Gu, J.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydin, 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. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).
[Crossref]

Guo, K.

Guo, Z.

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]

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” arXiv preprint arXiv:1512.03385 (2015).

Hinton, G.

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

N. Srivastava, G. 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).

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

Horisaki, R.

Jiang, S.

Jin, K. H.

K. H. Jin, M. T. McCann, E. Froustey, and M. Unser, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26, 4509–4522 (2017).
[Crossref]

M. T. McCann, K. H. Jin, and M. Unser, “Convolutional neural networks for inverse problems in imaging: A review,” IEEE Signal Process. Mag. 34, 85–95 (2017).
[Crossref]

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Kaneko, A.

Koyama, T.

Krizhevsky, A.

N. Srivastava, G. 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).

Kubota, T.

Kuen, J.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

Lam, E. Y.

Lam, V.

Latychevskaia, T.

LeCun, Y.

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

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.

Li, D.

Li, G.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 717865 (2017).
[Crossref] [PubMed]

M. Lyu, H. Wang, G. Li, and G. Situ, “Exploit imaging through opaque wall via deep learning,” arXiv preprint arXiv:1708.07881 (2017).

Li, S.

Li, Y.

L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
[Crossref]

Liao, J.

Lin, X.

Liu, G.

Liu, J.-P.

Liu, S.

L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
[Crossref]

Liu, T.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

Lyu, M.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 717865 (2017).
[Crossref] [PubMed]

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] [PubMed]

M. Lyu, H. Wang, G. Li, and G. Situ, “Exploit imaging through opaque wall via deep learning,” arXiv preprint arXiv:1708.07881 (2017).

H. Wang, M. Lyu, N. Chen, and G. Situ, “In-line hologram reconstruction with deep learning,” in Image and Applied Optics, OSA Technical Digest (Optical Society of America, 2018), paper DW2F.2.

Ma, L.

J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,” Pattern Recognit. 77, 354–377 (2018).
[Crossref]

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, OSA Technical Digest (online) (Optical Society of America), paper W2A.5,” (2017).

Matoba, O.

McCann, M. T.

M. T. McCann, K. H. Jin, and M. Unser, “Convolutional neural networks for inverse problems in imaging: A review,” IEEE Signal Process. Mag. 34, 85–95 (2017).
[Crossref]

K. H. Jin, M. T. McCann, E. Froustey, and M. Unser, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26, 4509–4522 (2017).
[Crossref]

Meng, X. F.

Miao, J.

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, OSA Technical Digest (online) (Optical Society of America), paper W2A.5,” (2017).

Nehmetallah, G.

Nguyen, T.

Nishio, K.

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[Crossref]

Osten, W.

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Günaydin, 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. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).
[Crossref]

Pan, F.

L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
[Crossref]

Pedrini, G.

Peng, X.

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, OSA Technical Digest (online) (Optical Society of America), paper W2A.5,” (2017).

Poon, T.-C.

Pu, Y.

Raub, C. B.

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” arXiv preprint arXiv:1512.03385 (2015).

Ren, Z.

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Günaydin, 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. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).
[Crossref]

Rong, L.

L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
[Crossref]

Ronneberger, O.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” arXiv preprint arXiv:1505.04597 (2015).

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

Ryle, J. P.

Salakhutdinov, R.

N. Srivastava, G. 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).

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Scott, P. D.

Shahroudy, A.

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Figures (6)

Fig. 1
Fig. 1 In-line hologram structure. L: collimating lens; P: linear polarizer; BS: beam splitter; SLM: spatial light modulator; M: mirror.
Fig. 2
Fig. 2 The proposed eHoloNet. (a) the overall network architecture and (b) detailed structure of the convolutional block, the residual block and the upsampling block. In (a), the digits in the format mn below each layer denote the number of input channels, n, and the number output channels, n, in this hidden layer, and (5, 5) and (3, 3) denote the size of the convolutional kernel.
Fig. 3
Fig. 3 The images of the USAF resolution chart and the MNIST digits that are displayed on the SLM in the experiments.
Fig. 4
Fig. 4 Reconstruction results using the eHoloNet. (a) In-line holograms of some typical images in the MNIST dataset shown in (c), and (b) the reconstructed images from (a). (d) In-line holograms of some typical images in the USAF chart shown in (f), and (e) the reconstructed images from (d).
Fig. 5
Fig. 5 Robustness of the eHoloNet. (a) Samples of in-line holographic images for training, (b) samples of holograms in the test set, (c) the reconstructed images from (b) by using the eHoloNet, and (d) the ground-truth images of (c).
Fig. 6
Fig. 6 Robustness of the eHoloNet. (a) The ground truth images, (b) the in-line hologram of (a), (c) the reconstructed image from the in-line hologram (b) using the eHoloNet, (d) the in-line hologram of (a) with a π phase retardation in the reference beam with respect to (b), (e) the reconstructed image from (d) using the eHoloNet, (f) the reconstructed image from (d) by using phase-shifting holography, and (g) the central 768 × 768 part of (f).

Equations (8)

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I ( x , y ) = | P { O 0 ( x 0 , y 0 ) ; z } ( x , y ) | 2 + | C | 2 + C * P { O 0 ( x 0 , y 0 ) ; z } ( x , y ) + C P { O 0 ( x 0 , y 0 ) ; z } ( x , y ) *
I ( x , y ) = { O ( x 0 , y 0 ) } ,
O 0 ( x 0 , y 0 ) = { I ( x , y ) } ,
learn = arg min θ , θ Θ n = 1 N f ( O n , θ { I n } ) + Ψ ( θ ) .
v i , j x , y = r = 1 R p = 0 P 1 q = 0 Q 1 w i , j , r p , q v i 1 , r x + p , y + q + b i , j
MSE = min 1 W H N 1 n = 1 N 1 u = 1 W v = 1 H ( O ˜ n ( u , v ) O n ( u , v ) ) 2 ,
RMSE = [ 1 W H u = 1 W v = 1 H ( O ˜ n ( u , v ) O n ( u , v ) ) 2 ] 1 2
SSIM = ( 2 μ o ˜ μ o + c 1 ) ( 2 σ o ˜ o + c 2 ) ( μ o ˜ 2 + μ o 2 + c 1 ) ( σ o ˜ 2 + σ o 2 + c 2 )

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