Abstract

Fourier ptychographic microscopy (FPM) is a recently developed imaging approach aiming at circumventing the limitation of the space-bandwidth product (SBP) and acquiring a complex image with both wide field and high resolution. So far, in many algorithms that have been proposed to solve the FPM reconstruction problem, the pupil function is set to be a fixed value such as the coherent transfer function (CTF) of the system. However, the pupil aberration of the optical components in an FPM imaging system can significantly degrade the quality of the reconstruction results. In this paper, we build a trainable network (FINN-P) which combines the pupil recovery with the forward imaging process of FPM based on TensorFlow. Both the spectrum of the sample and pupil function are treated as the two-dimensional (2D) learnable weights of layers. Therefore, the complex object information and pupil function can be obtained simultaneously by minimizing the loss function in the training process. Simulated datasets are used to verify the effectiveness of pupil recovery, and experiments on the open source measured dataset demonstrate that our method can achieve better reconstruction results even in the presence of a large aberration. In addition, the recovered pupil function can be used as a good estimate before further analysis of the system optical transmission capability.

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

Full Article  |  PDF Article
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2019 (2)

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

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[Crossref]

2018 (5)

2017 (3)

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

Y. Zhang, P. Song, and Q. Dai, “Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood,” Opt. Express 25(1), 168–179 (2017).
[Crossref]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

2016 (6)

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336–1350 (2016).
[Crossref]

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18), 20724–20744 (2016).
[Crossref]

K. Guo, S. Dong, and G. Zheng, “Fourier Ptychography for Brightfield, Phase, Darkfield, Reflective, Multi-Slice, and Fluorescence Imaging,” IEEE J. Sel. Top. Quantum Electron. 22(4), 77–88 (2016).
[Crossref]

T. Dozat, “Incorporating Nesterov Momentum into Adam,” ICLR Workshop 1, 2013–2016 (2016).

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24(14), 15765 (2016).
[Crossref]

2015 (8)

2014 (3)

2013 (3)

2009 (1)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

2008 (2)

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

2006 (1)

2004 (1)

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

1997 (1)

1983 (1)

Y. U. Nesterov, “A method for unconstrained convex minimization problem with convergence rate o(1/k2),” Doklady AN SSSR 269, 543–547 (1983).

Abbas, F.

F. Shamshad, F. Abbas, and A. Ahmed, “Deep Ptych: Subsampled Fourier Ptychography using Generative Priors,” arXiv preprint arXiv: 1812.11065 (2018).

Acosta, A.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Ahmed, A.

F. Shamshad, F. Abbas, and A. Ahmed, “Deep Ptych: Subsampled Fourier Ptychography using Generative Priors,” arXiv preprint arXiv: 1812.11065 (2018).

Aitken, A.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Ames, B.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

Baburaj, R.

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

Bengio, Y.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Bian, L.

Bian, Z.

Boominathan, L.

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Caballero, J.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Carone, D.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

Chen, F.

Chen, M.

Chen, N.

Chen, Q.

Chen, R. Y.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

Chen, S.

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

Cheng, Y. F.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

Cossairt, O.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

Courville, A.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Cunningham, A.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Dai, Q.

Dan, D.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Deb, M.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

Di, J.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Dong, C.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

Dong, J.

Dong, S.

K. Guo, S. Dong, and G. Zheng, “Fourier Ptychography for Brightfield, Phase, Darkfield, Reflective, Multi-Slice, and Fluorescence Imaging,” IEEE J. Sel. Top. Quantum Electron. 22(4), 77–88 (2016).
[Crossref]

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400–32410 (2013).
[Crossref]

Dozat, T.

T. Dozat, “Incorporating Nesterov Momentum into Adam,” ICLR Workshop 1, 2013–2016 (2016).

ejani, A. T.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Fan, Q.

Fan, Y.

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

Fienup, J. R.

Ganapati, V.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

García, J.

García-Martínez, P.

Ghosh, S.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

Goodfellow, I. J.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Greenbaum, A.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4(3), e261 (2015).
[Crossref]

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(2), 17141 (2018).
[Crossref]

Guo, K.

Gupta, H.

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

He, K.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

Holloway, J.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

Horstmeyer, R.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref]

Hou, L.

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Huszar, F.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Jiang, H.

Jiang, S.

Jiang, W.

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Kaikai, G.

Kappeler, A.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

Katsaggelos, A.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

Kim, J.

J. Kim, J. K. Lee, and K. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” arXiv preprint arXiv: 1511.04491v2 (2015).

J. Kim, J. K. Lee, and K. M. Lee, “Accurate Image Super-Resolution Using Very Deep Convolutional Networks,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 1646–1654.

Lam, E. Y.

Ledig, C.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Lee, B.

Lee, J. K.

J. Kim, J. K. Lee, and K. M. Lee, “Accurate Image Super-Resolution Using Very Deep Convolutional Networks,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 1646–1654.

J. Kim, J. K. Lee, and K. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” arXiv preprint arXiv: 1511.04491v2 (2015).

Lee, K. M.

J. Kim, J. K. Lee, and K. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” arXiv preprint arXiv: 1511.04491v2 (2015).

J. Kim, J. K. Lee, and K. M. Lee, “Accurate Image Super-Resolution Using Very Deep Convolutional Networks,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 1646–1654.

Lei, M.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

Li, X.

Li, Y.

Liang, Y.

Liao, J.

Liu, H.

Loy, C. C.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

Luo, W.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4(3), e261 (2015).
[Crossref]

Mainiparambil, M.

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

Menzel, A.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Mico, V.

Mirza, M.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Mitra, K.

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

Nehmetallah, G.

Nesterov, Y. U.

Y. U. Nesterov, “A method for unconstrained convex minimization problem with convergence rate o(1/k2),” Doklady AN SSSR 269, 543–547 (1983).

Nguyen, T.

Ou, X.

Ozair, S.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

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(2), 17141 (2018).
[Crossref]

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4(3), e261 (2015).
[Crossref]

Pan, A.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

Pariksheet, N.

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Pouget-Abadie, J.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Ramchandran, K.

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(2), 17141 (2018).
[Crossref]

Rodenburg, J. M.

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

Ruber, S.

S. Ruber, “An overview of gradient descent optimization algorithms,” arXiv preprint arXiv: 1609.04747v2 (2016).

Shamshad, F.

F. Shamshad, F. Abbas, and A. Ahmed, “Deep Ptych: Subsampled Fourier Ptychography using Generative Priors,” arXiv preprint arXiv: 1812.11065 (2018).

Shi, W.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Situ, G.

Siyuan, D.

Soltanolkotabi, M.

Song, P.

Sticker, M.

Stoppe, L.

Strachan, M.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

Sun, J.

Sun, W.

Suo, J.

Tang, G.

Tang, X.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

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(2), 17141 (2018).
[Crossref]

Theis, L.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Tian, L.

Totz, J.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Tropp, J. A.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

Waller, L.

Wang, H.

Wang, J.

Wang, M.

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

Wang, W.

Wang, X.

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

Wang, Z.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

Warde-Farley, D.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Weiss, Z.

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

Xu, B.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

Xu, M.

Xu, T.

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

Xue, Y.

Yang, C.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref]

Yang, D.

Yao, B.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

Yeh, L. H.

Zalevsky, Z.

Zhang, J.

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

Zhang, L.

Zhang, M.

Zhang, P.

Zhang, Y.

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

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(2), 17141 (2018).
[Crossref]

Y. Zhang, P. Song, and Q. Dai, “Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood,” Opt. Express 25(1), 168–179 (2017).
[Crossref]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336–1350 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24(14), 15765 (2016).
[Crossref]

Y. Zhang, W. Jiang, L. Tian, L. Waller, and Q. Dai, “Self-learning based Fourier ptychographic microscopy,” Opt. Express 23(14), 18471–18486 (2015).
[Crossref]

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4(3), e261 (2015).
[Crossref]

Y. Zhang, W. Jiang, and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23(26), 33822 (2015).
[Crossref]

Zhao, J.

Zhao, T.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

Zheng, G.

Zhong, J.

Zhou, A.

Zuo, C.

Adv. Imaging Electron Phys. (1)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

Appl. Opt. (3)

Biomed. Opt. Express (3)

Doklady AN SSSR (1)

Y. U. Nesterov, “A method for unconstrained convex minimization problem with convergence rate o(1/k2),” Doklady AN SSSR 269, 543–547 (1983).

ICLR Workshop (1)

T. Dozat, “Incorporating Nesterov Momentum into Adam,” ICLR Workshop 1, 2013–2016 (2016).

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

K. Guo, S. Dong, and G. Zheng, “Fourier Ptychography for Brightfield, Phase, Darkfield, Reflective, Multi-Slice, and Fluorescence Imaging,” IEEE J. Sel. Top. Quantum Electron. 22(4), 77–88 (2016).
[Crossref]

IEEE Photonics J. (1)

S. Chen, T. Xu, J. Zhang, X. Wang, and Y. Zhang, “Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow,” IEEE Photonics J. 11(1), 1–14 (2019).
[Crossref]

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

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a Deep Convolutional Network for Image Super-Resolution,” IEEE Trans. Pattern Anal. Machine Intell. 38(2), 295–307 (2016).
[Crossref]

J. Biomed. Opt. (1)

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(09), 1–11 (2017).
[Crossref]

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

Light: Sci. Appl. (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(2), 17141 (2018).
[Crossref]

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4(3), e261 (2015).
[Crossref]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

New J. Phys. (1)

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New J. Phys. 17(5), 053044 (2015).
[Crossref]

Opt. Commun. (1)

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

Opt. Express (13)

Y. Zhang, P. Song, and Q. Dai, “Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood,” Opt. Express 25(1), 168–179 (2017).
[Crossref]

L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
[Crossref]

Y. Zhang, W. Jiang, and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23(26), 33822 (2015).
[Crossref]

L. H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214–33240 (2015).
[Crossref]

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18), 20724–20744 (2016).
[Crossref]

Y. Zhang, W. Jiang, L. Tian, L. Waller, and Q. Dai, “Self-learning based Fourier ptychographic microscopy,” Opt. Express 23(14), 18471–18486 (2015).
[Crossref]

A. Zhou, W. Wang, N. Chen, E. Y. Lam, B. Lee, and G. Situ, “Fast and robust misalignment correction of Fourier ptychographic microscopy for full field of view reconstruction,” Opt. Express 26(18), 23661–23674 (2018).
[Crossref]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref]

M. Zhang, L. Zhang, D. Yang, H. Liu, and Y. Liang, “Symmetrical illumination based extending depth of field in Fourier ptychographic microscopy,” Opt. Express 27(3), 3583–3597 (2019).
[Crossref]

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400–32410 (2013).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26(20), 26470 (2018).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24(14), 15765 (2016).
[Crossref]

G. Kaikai, D. Siyuan, and N. Pariksheet, “Optimization of sampling pattern and the design of Fourier ptychographic illuminator,” Opt. Express 23(5), 6171 (2015).
[Crossref]

Opt. Lett. (2)

Optica (1)

Phys. Rev. Lett. (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Ultramicroscopy (1)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Other (9)

S. Ruber, “An overview of gradient descent optimization algorithms,” arXiv preprint arXiv: 1609.04747v2 (2016).

F. Shamshad, F. Abbas, and A. Ahmed, “Deep Ptych: Subsampled Fourier Ptychography using Generative Priors,” arXiv preprint arXiv: 1812.11065 (2018).

L. Boominathan, M. Mainiparambil, H. Gupta, R. Baburaj, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv preprint arXiv: 1805.03593 (2018).

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot fourier ptychographic microscopy,” arXiv preprint arXiv: 1810.03481 (2018).

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” IEEE International Conference on Image Processing (ICIP) (IEEE, 2017), pp. 1712–1716.

J. Kim, J. K. Lee, and K. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” arXiv preprint arXiv: 1511.04491v2 (2015).

J. Kim, J. K. Lee, and K. M. Lee, “Accurate Image Super-Resolution Using Very Deep Convolutional Networks,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 1646–1654.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Networks,” arXiv preprint arXiv: 1406.2661v1 (2014).

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. T. ejani, J. Totz, Z. Wang, and W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 105–114.

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Figures (7)

Fig. 1.
Fig. 1. Schematic of a typical Fourier ptychographic microscopy.
Fig. 2.
Fig. 2. Overall workflow of FINN-P method
Fig. 3.
Fig. 3. Reconstruction results of Jiang’s method, AS, FINN and FINN-P using the simulated dataset. (a1-a2) The ground-truth amplitude (Baboon) and phase (Aerial) for comparison. (a3) The truncated spectrum based on the synthetic NA. (a4-a5) The actual pupil function added into the imaging system. (b1-b3) The reconstruction amplitude, phase and spectrum using Jiang’s method. (c1-c3) The reconstruction amplitude, phase and spectrum using the AS method. (d1-d3) The reconstruction amplitude, phase and spectrum using FINN. (b4-b5) the amplitude and phase of the circular low-pass filter defined in Eq. (4), which is also the initial guess of the pupil function in all the four methods. (e1-e3) The reconstruction results using FINN-P. (e4-e5) The reconstructed amplitude and phase of the pupil function through FINN-P, showing a similar distribution as Figs. 3(a4) and 3(a5).
Fig. 4.
Fig. 4. The NMSE between the reconstruction results of different methods and the ground truth at different epochs. (a1) To ensure the convergence of different algorithms, FINN and FINN-P are trained for 40 epochs, the AS algorithm stops automatically after 21 steps, Jiang’s method is trained for 200 epochs. (a2) the locally enlarged image of Fig. 4(a1).
Fig. 5.
Fig. 5. The comparison of reconstruction results using the USAF dataset. (a-d) The reconstruction results by GS, AS, Jiang’s and FINN-P respectively. (e1). The amplitude of the pupil function recovered through FINN-P. (e2) The phase of the pupil function recovered through FINN-P.
Fig. 6.
Fig. 6. The comparison of reconstruction results using the open source dataset (U2OS). The reconstruction region located at the center of the FOV. (a1-a3) The reconstruction results by the AS method. (b) The low-resolution image captured under the illumination of the center LED. (c1-c3) The reconstruction results by FINN-P. (c4) The recovered pupil phase by FINN-P.
Fig. 7.
Fig. 7. The comparison of reconstruction results using the open source dataset (U2OS). The reconstruction region located in the upper-right corner with a non-negligible pupil aberration. (a1-a3) The reconstruction amplitude and phase by the AS method. (b) The low-resolution image captured under the illumination of the center LED. (c1-c3) The reconstruction results using FINN-P method. (c4) The reconstruction phase of pupil function which could represent the wavefront aberration of the system. (d) The Zernike decomposition of the reconstruction pupil phase.

Tables (2)

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Table 1. The comparison between the recovered pupil function and ground truth

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Table 2. The comparison of reconstruction results

Equations (11)

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I m ( r ) = | F 1 { F { o ( r ) e x p ( i 2 π u m r ) } P ( u ) } | 2 ,
u m = ( s i n θ x ( m ) λ , s i n θ y ( m ) λ ) ,
I m ( r ) = | F 1 { O ( u u m ) P ( u ) } | 2 ,
P ( f x , f y ) = CTF = { 1 , if ( f x 2 + f y 2 ) ( N A λ ) 2 0 , otherwise ,
E e , m ( r ) = F 1 { O e ( u u m ) P ( u ) } .
O e ( u ) = O r ( u ) + i O j ( u ) P ( u ) = P r ( u ) + i P j ( u )
E e , m ( r ) = F 1 { [ O r ( u u m ) P r ( u ) O j ( u u m ) P j ( u ) ] + i [ O r ( u u m ) P j ( u ) + O j ( u u m ) P r ( u ) ] }
E ~ e , m ( r ) = p i x I ^ m ( r ) p i x E e , m ( r ) E e , m ( r ) ,
l o s s = m = 1 M p i x | | E ~ e , m ( r ) | I ^ m ( r ) | 2 ,
O T F ( u ) = C T F ( u ) C T F ( u ) p i x | C T F ( u ) | 2 ,
NMSE = p i x | O ^ ( u ) p i x O ^ ( u ) O e ( u ) p i x ( | O e ( u ) | 2 ) O e ( u ) | 2 p i x | O ^ ( u ) | 2 ,

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