Abstract

Deep neural networks have emerged as effective tools for computational imaging, including quantitative phase microscopy of transparent samples. To reconstruct phase from intensity, current approaches rely on supervised learning with training examples; consequently, their performance is sensitive to a match of training and imaging settings. Here we propose a new approach to phase microscopy by using an untrained deep neural network for measurement formation, encapsulating the image prior and the system physics. Our approach does not require any training data and simultaneously reconstructs the phase and pupil-plane aberrations by fitting the weights of the network to the captured images. To demonstrate experimentally, we reconstruct quantitative phase from through-focus intensity images without knowledge of the aberrations.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Y. Xue, S. Cheng, Y. Li, and L. Tian, Optica 6, 618 (2019).
[Crossref]

2018 (7)

Y. Li, Y. Xue, and L. Tian, Optica 5, 1181 (2018).
[Crossref]

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

M. Chen, Z. F. Phillips, and L. Waller, Opt. Express 26, 32888 (2018).
[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, Opt. Express 26, 26470 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, Optica 5, 803 (2018).
[Crossref]

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, Optica 5, 960 (2018).
[Crossref]

2017 (1)

2016 (2)

A. Pein, S. Loock, G. Plonka, and T. Salditt, Opt. Express 24, 8332 (2016).
[Crossref]

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

2015 (4)

2014 (5)

2013 (1)

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

2011 (1)

2010 (1)

2005 (1)

1998 (1)

1982 (1)

Aino, M.

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Barbastathis, G.

Barty, A.

Borhani, N.

Bostan, E.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for Fourier ptychographic microscopy,” in Proceesings of the IEEE International Conference for Computational Photography (2019). In press

M. Kellman, E. Bostan, N. Repina, and L. Waller, IEEE Trans Comput. Imaging (IEEE, 2019).

Bouwens, A.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Candès, E. J.

E. J. Candès, X. Li, and M. Soltanolkotabi, IEEE Trans. Inf. Theory 61, 1985 (2015).
[Crossref]

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Chen, M.

M. Chen, Z. F. Phillips, and L. Waller, Opt. Express 26, 32888 (2018).
[Crossref]

L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, Opt. Express 23, 33214 (2015).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for Fourier ptychographic microscopy,” in Proceesings of the IEEE International Conference for Computational Photography (2019). In press

Cheng, S.

Cho, H.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Choi, G.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Claus, R. A.

Colomb, T.

Cuche, É.

Dauwels, J.

Deng, M.

Depeursinge, C.

Descloux, A.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Ding, H.

Dong, J.

Emery, Y.

Fienup, J. R.

Froustey, E.

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

Geissbuehler, S.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Gillette, M. U.

Goddard, L. L.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Grußmayer, K.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Hand, P.

R. Heckel and P. Hand, “Deep decoder: concise image representations from untrained non-convolutional networks,” in International Conference on Learning Representations (ICLR) (2019).

Heckel, R.

R. Heckel and P. Hand, “Deep decoder: concise image representations from untrained non-convolutional networks,” in International Conference on Learning Representations (ICLR) (2019).

R. Heckel and M. Soltanolkotabi, “Denoising and regularization via exploiting the structural bias of convolutional generators,” in International Conference on Learning Representations (ICLR) (2020).

Horisaki, R.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Jingshan, Z.

Jo, Y.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Kakkava, E.

Kellman, M.

M. Kellman, E. Bostan, N. Repina, and L. Waller, IEEE Trans Comput. Imaging (IEEE, 2019).

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for Fourier ptychographic microscopy,” in Proceesings of the IEEE International Conference for Computational Photography (2019). In press

Kim, G.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Kim, T.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Lashuel, H.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Lasser, T.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Lee, J.

Lee, S. Y.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Lempitsky, V.

D. Ulyanov, A. Vedaldi, and V. Lempitsky, “Deep image prior,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2018), pp. 9446–9454.

Leutenegger, M.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Li, S.

Li, X.

E. J. Candès, X. Li, and M. Soltanolkotabi, IEEE Trans. Inf. Theory 61, 1985 (2015).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, Biomed. Opt. Express 5, 2376 (2014).
[Crossref]

Li, Y.

Loock, S.

Lukes, T.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Magistretti, P. J.

Mahul-Mellier, A.-L.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Marquet, P.

Millet, L.

Min, H.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Mir, M.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, Opt. Express 19, 1016 (2011).
[Crossref]

Moser, C.

Nehmetallah, G.

Nguyen, T.

Nilchian, M.

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

Nugent, K. A.

Ogura, Y.

Ou, X.

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Paganin, D.

Park, Y.

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

Pein, A.

Phillips, Z. F.

Plonka, G.

Popescu, G.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, Opt. Express 19, 1016 (2011).
[Crossref]

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

Psaltis, D.

Ramchandran, K.

Rappaz, B.

Repina, N.

M. Kellman, E. Bostan, N. Repina, and L. Waller, IEEE Trans Comput. Imaging (IEEE, 2019).

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Roberts, A.

Rogers, J.

Sage, D.

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

Salditt, T.

Sharipov, A.

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

Sinha, A.

Soltanolkotabi, M.

L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, Opt. Express 23, 33214 (2015).
[Crossref]

E. J. Candès, X. Li, and M. Soltanolkotabi, IEEE Trans. Inf. Theory 61, 1985 (2015).
[Crossref]

R. Heckel and M. Soltanolkotabi, “Denoising and regularization via exploiting the structural bias of convolutional generators,” in International Conference on Learning Representations (ICLR) (2020).

Tang, G.

Tanida, J.

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Tian, L.

Ulyanov, D.

D. Ulyanov, A. Vedaldi, and V. Lempitsky, “Deep image prior,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2018), pp. 9446–9454.

Unarunotai, S.

Unser, M.

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

Vedaldi, A.

D. Ulyanov, A. Vedaldi, and V. Lempitsky, “Deep image prior,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2018), pp. 9446–9454.

Waller, L.

Wang, Z.

Xue, Y.

Yang, C.

X. Ou, G. Zheng, and C. Yang, Opt. Express 22, 4960 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Yeh, L.-H.

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Zheng, G.

X. Ou, G. Zheng, and C. Yang, Opt. Express 22, 4960 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Zhong, J.

Zhou, R.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (2)

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. Min, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 25, 1 (2019).
[Crossref]

IEEE Trans. Image Process. (1)

E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, IEEE Trans. Image Process. 25, 807 (2016).
[Crossref]

IEEE Trans. Inf. Theory (1)

E. J. Candès, X. Li, and M. Soltanolkotabi, IEEE Trans. Inf. Theory 61, 1985 (2015).
[Crossref]

Light Sci. Appl. (1)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, Light Sci. Appl. 7, 17141 (2018).
[Crossref]

Nat. Photonics (3)

A. Descloux, K. Grußmayer, E. Bostan, T. Lukes, A. Bouwens, A. Sharipov, S. Geissbuehler, A.-L. Mahul-Mellier, H. Lashuel, M. Leutenegger, and T. Lasser, Nat. Photonics 12, 165 (2018).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, Nat. Photonics 8, 256 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Opt. Express (8)

Opt. Lett. (3)

Optica (6)

Other (6)

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

M. Kellman, E. Bostan, N. Repina, and L. Waller, IEEE Trans Comput. Imaging (IEEE, 2019).

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for Fourier ptychographic microscopy,” in Proceesings of the IEEE International Conference for Computational Photography (2019). In press

D. Ulyanov, A. Vedaldi, and V. Lempitsky, “Deep image prior,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2018), pp. 9446–9454.

R. Heckel and M. Soltanolkotabi, “Denoising and regularization via exploiting the structural bias of convolutional generators,” in International Conference on Learning Representations (ICLR) (2020).

R. Heckel and P. Hand, “Deep decoder: concise image representations from untrained non-convolutional networks,” in International Conference on Learning Representations (ICLR) (2019).

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Figures (3)

Fig. 1.
Fig. 1. Our deep phase decoder (DPD) algorithm aims to minimize the Euclidean distance between the measured intensity images and the hypothetical ones generated by our untrained deep network. The optimization problem, which is nonlinear and nonconvex, is stated in terms of the network’s weights and is solved iteratively using a gradient-based procedure. Once the weights are optimized, the sought phase image is retrieved as the output of the deep decoder part of the network.
Fig. 2.
Fig. 2. We experimentally validate our method in a microscope by capturing intensity images with varying defocus distances. The images are fed into the DPD algorithm to computationally reconstruct the sample’s phase and wavefront aberrations without knowing the pupil functions (defocus distances) that were used during acquisition.
Fig. 3.
Fig. 3. Experimental validation of our DPD phase retrieval method from a stack of through-focus intensity images of a phase target with expected height of 150 nm (0.95 radians phase shift). (Left) Reconstructions by the accelerated Wirtinger flow algorithm [32] are shown for comparison, with different numbers of measurements in the focus stack and known defocus distances. (Right) Our proposed DPD reconstruction achieves a similar phase result without any explicit knowledge of the aberrations.

Equations (8)

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

o ( r ) = exp ( j ϕ ( r ) ) ,
y ( r ) = | c psf o | 2 ( r ) ,
y = | F 1 P circ Fo | 2 ,
P = P circ exp ( j Zc ) ,
o = arg min o n = 1 N y n | F 1 P n Fo | 2 2 .
W = arg min W Y G ( W ) 2 2 ,
B i + 1 = cn ( ReLU ( U i B i W i p ) ) , i = 0 , , d 1.
ϕ = 2 π sigmoid ( B d W d p ) .