Abstract

On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a tradeoff between the per-frame pixel count and frame rate of the captured video. In this report, we propose a subsampled phase retrieval (SPR) algorithm to overcome the spatial-temporal trade-off in holographic video. Compared to traditional phase retrieval approaches, our SPR algorithm uses over an order of magnitude less pixel measurements while maintaining suitable reconstruction quality. We use an on-chip holographic video setup with pixel sub-sampling to experimentally demonstrate a factor of 5.5 increase in sensor frame rate while monitoring the in vivo movement of Peranema microorganisms.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (2)

2015 (3)

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
[Crossref] [PubMed]

K. He, M. K. Sharma, and O. Cossairt, “High dynamic range coherent imaging using compressed sensing,” Opt. Express 23(24), 30904–30916 (2015).
[Crossref] [PubMed]

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] [PubMed]

2014 (5)

Siyuan Dong, Zichao Bian, Radhika Shiradkar, and Guoan Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express,  22(5) 5455–5464, (2014).
[Crossref] [PubMed]

I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
[PubMed]

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mistunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36(2), 248–260 (2014).
[Crossref]

A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 16, 74–77 (2014).
[Crossref]

2013 (3)

2012 (3)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

T-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Nat. Acad. Sci. 109, 16018–16022 (2012).
[Crossref] [PubMed]

J. Weidling, S.O. Isikman, A. Greenbaum, A. Ozcan, and E. Botvinick, “Lensfree Computational Imaging of Capillary Morphogenesis within 3D Substrates,” J. Biomed. Opt. 17, 126018 (2012).
[Crossref]

2011 (2)

W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
[Crossref] [PubMed]

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19(8), 7289–7298 (2011).
[Crossref] [PubMed]

2010 (4)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Display Technol. 6(10), 506–509 (2010).
[Crossref]

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseinia, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 101417–1428 (2010).
[Crossref] [PubMed]

D. Tseng, O. Mudanyali, C. Oztoprak, S.O. Isikman, I. Sencan, O. Yaglidere, and A. Ozcan, “Lensfree Microscopy on a Cell-phone,” Lab Chip 10, 1787–1792 (2010).
[Crossref] [PubMed]

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7(3), 209–211 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (2)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[Crossref]

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique 346,  9, 589–592 (2008).
[Crossref]

2007 (1)

S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. /bf 78, 011301 (2007).
[Crossref]

2003 (2)

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A Vol.  20(1), 40–55 (2003).
[Crossref]

1982 (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Optics 21, 2758–2769 (1982).
[Crossref]

1978 (1)

Agrawal, A.

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal Coded Sampling for Temporal Super-Resolution,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2011).

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] [PubMed]

Baumbach, T.

Bian, Zichao

Bishara, W.

W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
[Crossref] [PubMed]

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseinia, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 101417–1428 (2010).
[Crossref] [PubMed]

Bishop, A. I.

S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” arXiv preprint ar Xiv:0911.0520 (2009).

Botvinick, E.

J. Weidling, S.O. Isikman, A. Greenbaum, A. Ozcan, and E. Botvinick, “Lensfree Computational Imaging of Capillary Morphogenesis within 3D Substrates,” J. Biomed. Opt. 17, 126018 (2012).
[Crossref]

Brady, D. J.

Bub, G.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7(3), 209–211 (2010).
[Crossref] [PubMed]

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[Crossref]

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique 346,  9, 589–592 (2008).
[Crossref]

Carin, L.

Cecilia, A.

Chapman, H. N.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Chellappa, R.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable Pixel Compressive Camera for High Speed Imaging,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2011).

Chen, H.

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] [PubMed]

Choi, K.

Chung, P.

A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
[Crossref]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

Cossairt, O.

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

Denis, L.

Di Carlo, D.

I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
[PubMed]

Dincer, T.U.

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
[Crossref] [PubMed]

Dong, Siyuan

Eldar, Y. C.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

K. Jaganathan, Y. C. Eldar, and B. Hassibi, “Phase retrieval: An overview of recent developments,” arXiv preprint arXiv:1510.07713 (2016).

Elser, V.

Ertas, Y.N.

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
[Crossref] [PubMed]

Feizi, A.

Y. Rivenson, Y. Wu, H. Wang, Y. Zhang, A. Feizi, and A. Ozcan, “Sparsity-based multi-height phase recovery in holographic microscopy,” Sci. Rep. 6, 37862–3477(2016).
[Crossref] [PubMed]

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
[Crossref] [PubMed]

A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
[Crossref]

Feng, S.

S. Feng, M. Wang, and J. Wu, “Digital in-line holographic microscope based on the grating illumination with improved resolution by interpolation,” In SPIE/COS Photonics Asia (pp. 1002205), International Society for Optics and Photonics (2016).

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Optics 21, 2758–2769 (1982).
[Crossref]

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 21, 27–29 (1978).
[Crossref] [PubMed]

Fournier, C.

Gao, L.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 16, 74–77 (2014).
[Crossref]

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
[Crossref] [PubMed]

Gimenez-Navarro, E.

Greenbaum, A.

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
[Crossref] [PubMed]

A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
[Crossref]

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I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
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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).
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Y. Rivenson, Y. Wu, H. Wang, Y. Zhang, A. Feizi, and A. Ozcan, “Sparsity-based multi-height phase recovery in holographic microscopy,” Sci. Rep. 6, 37862–3477(2016).
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D. Tseng, O. Mudanyali, C. Oztoprak, S.O. Isikman, I. Sencan, O. Yaglidere, and A. Ozcan, “Lensfree Microscopy on a Cell-phone,” Lab Chip 10, 1787–1792 (2010).
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W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
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S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
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Su, T.

W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
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I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
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T-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Nat. Acad. Sci. 109, 16018–16022 (2012).
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J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter Shutter Video Camera for Compressive Sensing of Videos,” in IEEE Conference on Computational Photography (ICCP) (2012).

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G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7(3), 209–211 (2010).
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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseinia, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 101417–1428 (2010).
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L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 16, 74–77 (2014).
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S. Feng, M. Wang, and J. Wu, “Digital in-line holographic microscope based on the grating illumination with improved resolution by interpolation,” In SPIE/COS Photonics Asia (pp. 1002205), International Society for Optics and Photonics (2016).

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Weaver, W.

I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
[PubMed]

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J. Weidling, S.O. Isikman, A. Greenbaum, A. Ozcan, and E. Botvinick, “Lensfree Computational Imaging of Capillary Morphogenesis within 3D Substrates,” J. Biomed. Opt. 17, 126018 (2012).
[Crossref]

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Y. Rivenson, Y. Wu, H. Wang, Y. Zhang, A. Feizi, and A. Ozcan, “Sparsity-based multi-height phase recovery in holographic microscopy,” Sci. Rep. 6, 37862–3477(2016).
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W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
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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).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic imaging,” Nat. Photonics 7, 739–745 (2013).
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A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
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Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic imaging,” Nat. Photonics 7, 739–745 (2013).
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X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
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Zheng, Guoan

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
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ACS Nano (1)

E. McLeod, T.U. Dincer, M. Veli, Y.N. Ertas, C. Nguyen, W. Luo, A. Greenbaum, A. Feizi, and A. Ozcan, “High-Throughput and Label-Free Single Nanoparticle Sizing Based on Time-Resolved On-Chip Microscopy,” ACS Nano 9, 3265–3273 (2015).
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IEEE Sig. Proc. Mag. (1)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
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IEEE Trans. Pattern Anal. Mach. Intell. (1)

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mistunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36(2), 248–260 (2014).
[Crossref]

J. Biomed. Opt. (1)

J. Weidling, S.O. Isikman, A. Greenbaum, A. Ozcan, and E. Botvinick, “Lensfree Computational Imaging of Capillary Morphogenesis within 3D Substrates,” J. Biomed. Opt. 17, 126018 (2012).
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J. Display Technol. (1)

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

Lab Chip (3)

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseinia, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 101417–1428 (2010).
[Crossref] [PubMed]

D. Tseng, O. Mudanyali, C. Oztoprak, S.O. Isikman, I. Sencan, O. Yaglidere, and A. Ozcan, “Lensfree Microscopy on a Cell-phone,” Lab Chip 10, 1787–1792 (2010).
[Crossref] [PubMed]

W. Bishara, U. Sikora, O. Mudanyali, T. Su, O. Yaglidere, S. Luckhart, and A. Ozcan, “Holographic pixel super-resolution in portable lensless on-chip microscopy using a fiber-optic array,” Lab Chip 11, 1276–1779 (2011).
[Crossref] [PubMed]

Nat. Mater. (1)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012)
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Nat. Methods (1)

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7(3), 209–211 (2010).
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Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic imaging,” Nat. Photonics 7, 739–745 (2013).
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Nature (1)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 16, 74–77 (2014).
[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] [PubMed]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. B (1)

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Proc. Nat. Acad. Sci. (1)

T-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Nat. Acad. Sci. 109, 16018–16022 (2012).
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I. Pushkarsky, Y. Lyb, W. Weaver, T-W. Su, O. Mudanyali, A. Ozcan, and D. Di Carlo, “Automated single-cell motility analysis on a chip using lensfree microscopy,” Sci. Rep. 4, 4717 (2014).
[PubMed]

Y. Rivenson, Y. Wu, H. Wang, Y. Zhang, A. Feizi, and A. Ozcan, “Sparsity-based multi-height phase recovery in holographic microscopy,” Sci. Rep. 6, 37862–3477(2016).
[Crossref] [PubMed]

Sci. Trans. Med. (1)

A. Greenbaum, Y. Zhang, A. Feizi, P. Chung, W. Luo, S.R. Kandukuri, and A. Ozcan, “Wide-field Computational Imaging of Pathology Slides using Lensfree On-Chip Microscopy,” Sci. Trans. Med. 6, 267ra175 (2014).
[Crossref]

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A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal Coded Sampling for Temporal Super-Resolution,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2011).

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable Pixel Compressive Camera for High Speed Imaging,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2011).

J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter Shutter Video Camera for Compressive Sensing of Videos,” in IEEE Conference on Computational Photography (ICCP) (2012).

K. Jaganathan, Y. C. Eldar, and B. Hassibi, “Phase retrieval: An overview of recent developments,” arXiv preprint arXiv:1510.07713 (2016).

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M. Wang and J. Wu, “Iterative digital in-line holographic reconstruction with improved resolution by data interpolation,” In SPIE/COS Photonics Asia, pp. 927110. International Society for Optics and Photonics, 2014.

S. Feng, M. Wang, and J. Wu, “Digital in-line holographic microscope based on the grating illumination with improved resolution by interpolation,” In SPIE/COS Photonics Asia (pp. 1002205), International Society for Optics and Photonics (2016).

Supplementary Material (3)

NameDescription
» Visualization 1: MP4 (520 KB)      Full resolution phase retrieval, 4.4FPS
» Visualization 2: MP4 (312 KB)      2x2 subsampled phase retrieval, 13.6FPS
» Visualization 3: MP4 (222 KB)      3x3 subsampled phase retrieval, 24.8 FPS

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Figures (10)

Fig. 1
Fig. 1

Subsampled phase retrieval (SPR) setup. (a) A detector array images the in-line hologram of a nearby complex sample, f (x, y). The computational goal of “standard” lensless holography is to determine the complex sample f given the measured hologram amplitudes, |h|, from every pixel int the detector array. SPR measures only a subset of values from the detector array (denoted in yellow), selected from (b) a spaced rectilinear grid or (c) randomly.

Fig. 2
Fig. 2

Phase retrieval algorithm for on-chip holography. Each step is detailed in the text. Subsampling (SPR) only modifies the constraint in step 3. This modification results in over an order of magnitude potential speedup for lensless holographic video.

Fig. 3
Fig. 3

Simulation of standard in-line holography for a set of 5 microspheres. (a)–(b) Simulated sample’s original amplitude and phase, leading to (c) detected hologram intensities at sensor plane (d = 1 mm). (d)–(e) Recovered amplitude and phase using the ER phase retrieval algorithm (updating all pixel amplitudes). (f) The final sample support.

Fig. 4
Fig. 4

SPR algorithm simulation using the same sample as Fig. 3 under two different sampling scenarios: (a) Rectilinear subsampling and (b) random subsampling. For comparison, we also attempt reconstruction after interpolating between our subsampled pixels to form a full-resolution hologram estimate. The results of this interpolation strategy are in (c), where we use the standard ER phase retrieval algorithm for reconstruction.

Fig. 5
Fig. 5

NMSE versus subsampling factor at the detector plane for two simulations: (left) the microscope sample in Fig. 4, and (right) the circular sample in Fig. 6.

Fig. 6
Fig. 6

Simulation of standard in-line holography using a circular sample in (a)–(b), with a sharp support boundary. The ER algorithm uses all of the hologram intensities in (c) to recover the sample amplitude (d), phase (e) and support (f).

Fig. 7
Fig. 7

SPR algorithm simulation using the circular sample from Fig. 6 under two different scenarios: (a) rectilinear subsampling and (b) random subsampling. For comparison, we also test pixel interpolation after rectilinear subsampling to recover a full-resolution hologram estimate for standard ER phase retrieval. The results of this interpolation strategy are in (c).

Fig. 8
Fig. 8

Experimental results, on-chip imaging of polystyrene microspheres. (a) Raw detected hologram with one region of interest highlighted. (b) The recovered sample phase from the region of interest using the SPR algorithm (top and middle) and standard ER phase retrieval with interpolation (bottom). (c) Line traces through the center of the recovered microsphere phase (dashed lines) reveal quantitative agreement with the expected phase shift, even after reducing the number of pixels in factor of 9, 16 and 25.

Fig. 9
Fig. 9

Experimental results for on-chip imaging of live peranema microorganisms. (a) Full field-of-view hologram. (a1) Inset of interest. (b) Reconstructed amplitude with standard ER phase retrieval. (b1) Recovered amplitude of single peranema. (c) Reconstructed phase with standard ER phase retrieval. (c1) Recovered phase of single peranema. (d) 10X microscope image of live peranema. (d1) Inset of single peranema offers a useful “ground truth” comparison.

Fig. 10
Fig. 10

Example: subsampled holographic reconstruction of in vivo Peranema in motion (subsampling factor vs. time). Horizontal axis depicts time and vertical axis represents subsampling factor. Reconstructions of both amplitude and phase using all pixels on the detector are shown at top, while reconstructions from subsampled pixel array data, using a factor of 4 and 9, are in middle and bottom, respectively. Consecutive frames show Peranema motion from left to right. Frame rate: first row – 4.4FPS, second row – 13.6FPS, third row – 24.8FPS. Scale bar is 22 µm. See Visualization 1, Visualization 2 and Visualization 3 for the full videos.

Equations (6)

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| h ( x , y ) | 2 = | P d [ f ( x , y ) ] | 2 ,
G k ( x , y ) = | h ( x , y ) | G k ( x , y ) | G k ( x , y ) | , ( x , y ) D ,
g k + 1 ( x , y ) = { g k ( x , y ) ( x , y ) S k b ( x , y ) S k
G k ( x , y ) = { | h ( x , y ) | G k ( x , y ) | G k ( x , y ) | , ( x , y ) R G k ( x , y ) , ( x , y ) R
E ( k ) = ( x , y ) S n | t ( x , y ) γ g n ( x , y ) | 2 ( x , y ) S n | t ( x , y ) | 2
γ = ( x , y ) S n t ( x , y ) g n * ( x , y ) ( x , y ) S n | g n ( x , y ) | 2 ,

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