Abstract

Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample’s Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released our source code for non-commercial use, and it may find wide applications in related FP platforms such as endoscopy and transmission electron microscopy.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Fourier ptychographic reconstruction using Wirtinger flow optimization

Liheng Bian, Jinli Suo, Guoan Zheng, Kaikai Guo, Feng Chen, and Qionghai Dai
Opt. Express 23(4) 4856-4866 (2015)

Embedded pupil function recovery for Fourier ptychographic microscopy

Xiaoze Ou, Guoan Zheng, and Changhuei Yang
Opt. Express 22(5) 4960-4972 (2014)

Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood

Yongbing Zhang, Pengming Song, and Qionghai Dai
Opt. Express 25(1) 168-179 (2017)

References

  • View by:
  • |
  • |
  • |

  1. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
    [Crossref]
  2. X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
    [Crossref] [PubMed]
  3. S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
    [Crossref] [PubMed]
  4. L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2, 104–111 (2015).
    [Crossref]
  5. S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22, 20856–20870 (2014).
    [Crossref] [PubMed]
  6. J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
    [Crossref] [PubMed]
  7. S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, “FPscope: a field-portable high-resolution microscope using a cellphone lens,” Biomed. Opt. Express 5, 3305–3310 (2014).
    [Crossref] [PubMed]
  8. Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
    [Crossref] [PubMed]
  9. L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).
    [Crossref]
  10. J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).
  11. Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
    [Crossref]
  12. X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
    [Crossref] [PubMed]
  13. 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, 053044 (2015).
    [Crossref] [PubMed]
  14. L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23, 4856–4866 (2015).
    [Crossref] [PubMed]
  15. 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, 33214–33240 (2015).
    [Crossref]
  16. L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
    [Crossref] [PubMed]
  17. E. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” arXiv preprint arXiv:1407.1065 (2014).
  18. E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
    [Crossref]
  19. I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. pp. 1–35 (2012).
  20. D. Swift and L. Birdsill, “Method and system for automatic correction of motion artifacts,” (2005). US Patent 6,842,196.
  21. T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
    [Crossref] [PubMed]
  22. X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
    [Crossref] [PubMed]
  23. M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
    [Crossref] [PubMed]
  24. S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
    [Crossref]
  25. 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, 1–12 (2016).
    [Crossref]
  26. L. Bian, J. Suo, G. Situ, G. Zheng, F. Chen, and Q. Dai, “Content adaptive illumination for Fourier ptychography,” Opt. Lett. 39, 6648–6651 (2014).
    [Crossref] [PubMed]
  27. S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22, 5455–5464 (2014).
    [Crossref] [PubMed]
  28. X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (2015).
    [Crossref] [PubMed]
  29. A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
    [Crossref] [PubMed]
  30. Y. Chen and E. J. Candès, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” arXiv preprint arXiv: 1505.05114 (2015).
  31. A. G. Weber, “The USC-SIPI image database version 5,” USC-SIPI Rep. 315, 1–24 (1997).
  32. D. G. Luenberger, Introduction to Linear and Nonlinear Programming, vol. 28 (Addison-WesleyReading, MA, 1973).
  33. D. Fish, J. Walker, A. Brinicombe, and E. Pike, “Blind deconvolution by means of the Richardson–Lucy algorithm,” J. Opt. Soc. Am. A 12, 58–65 (1995).
    [Crossref]
  34. Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
    [Crossref]
  35. S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphic. 28, 145 (2009).
    [Crossref]
  36. P. C. Hansen, J. G. Nagy, and D. P. O’leary, Deblurring Images: Matrices, Spectra, and Filtering, vol. 3 (Siam, 2006).
    [Crossref]

2016 (4)

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (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, 1–12 (2016).
[Crossref]

2015 (8)

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (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, 053044 (2015).
[Crossref] [PubMed]

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

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, 33214–33240 (2015).
[Crossref]

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2, 104–111 (2015).
[Crossref]

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).
[Crossref]

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

2014 (6)

2013 (5)

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

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

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

2012 (1)

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

2009 (1)

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphic. 28, 145 (2009).
[Crossref]

2008 (1)

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
[Crossref]

2006 (1)

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

1997 (1)

A. G. Weber, “The USC-SIPI image database version 5,” USC-SIPI Rep. 315, 1–24 (1997).

1995 (1)

Agard, D. A.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Agarwala, A.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
[Crossref]

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, 053044 (2015).
[Crossref] [PubMed]

Ayache, N.

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Bian, L.

Bian, Z.

Birdsill, L.

D. Swift and L. Birdsill, “Method and system for automatic correction of motion artifacts,” (2005). US Patent 6,842,196.

Booth, C. R.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Braunfeld, M. B.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Brinicombe, A.

Candes, E.

E. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” arXiv preprint arXiv:1407.1065 (2014).

Candes, E. J.

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

Candès, E. J.

Y. Chen and E. J. Candès, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” arXiv preprint arXiv: 1505.05114 (2015).

Cao, E.

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

Chapman, H.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

Chen, F.

Chen, M.

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, 053044 (2015).
[Crossref] [PubMed]

Chen, Y.

Y. Chen and E. J. Candès, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” arXiv preprint arXiv: 1505.05114 (2015).

Cheng, Y.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

Cho, S.

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphic. 28, 145 (2009).
[Crossref]

Chung, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[Crossref] [PubMed]

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

Cohen, O.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

D’Ambrosio, M. V.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

d’Aspremont, A.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. pp. 1–35 (2012).

Dai, Q.

Dong, J.

Dong, S.

Eldar, Y.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

Fish, D.

Fletcher, D. A.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Gande, A. V.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Gubbens, S.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Guo, K.

Hansen, P. C.

P. C. Hansen, J. G. Nagy, and D. P. O’leary, Deblurring Images: Matrices, Spectra, and Filtering, vol. 3 (Siam, 2006).
[Crossref]

Horstmeyer, R.

Humphry, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Jia, J.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
[Crossref]

Julius, D.

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

Kim, J.

Kraus, B.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Lee, S.

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphic. 28, 145 (2009).
[Crossref]

Li, X.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

E. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” arXiv preprint arXiv:1407.1065 (2014).

Liang, R.

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

Liao, M.

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

Liu, Z.

Lu, H.

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

Luenberger, D. G.

D. G. Luenberger, Introduction to Linear and Nonlinear Programming, vol. 28 (Addison-WesleyReading, MA, 1973).

Maiden, A.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Malandain, G.

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Mallat, S.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. pp. 1–35 (2012).

Miao, J.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

Mooney, P.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Nagy, J. G.

P. C. Hansen, J. G. Nagy, and D. P. O’leary, Deblurring Images: Matrices, Spectra, and Filtering, vol. 3 (Siam, 2006).
[Crossref]

Nanda, P.

O’leary, D. P.

P. C. Hansen, J. G. Nagy, and D. P. O’leary, Deblurring Images: Matrices, Spectra, and Filtering, vol. 3 (Siam, 2006).
[Crossref]

Ou, X.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[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, 053044 (2015).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (2015).
[Crossref] [PubMed]

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

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
[Crossref] [PubMed]

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

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

Pacheco, S.

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

Patel, H. S.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Pennec, X.

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Perchant, A.

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Phillips, Z. F.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Pike, E.

Rodenburg, J.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Rulison, J. J.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Sadras, N.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Sarahan, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Segev, M.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

Shan, Q.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

Shiradkar, R.

Situ, G.

Soltanolkotabi, M.

Strohmer, T.

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

Suo, J.

Swift, D.

D. Swift and L. Birdsill, “Method and system for automatic correction of motion artifacts,” (2005). US Patent 6,842,196.

Switz, N. A.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Tang, G.

Tian, L.

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, 053044 (2015).
[Crossref] [PubMed]

Vercauteren, T.

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Voroninski, V.

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

Waldspurger, I.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. pp. 1–35 (2012).

Walker, J.

Waller, L.

Weber, A. G.

A. G. Weber, “The USC-SIPI image database version 5,” USC-SIPI Rep. 315, 1–24 (1997).

Xin, H.

Yang, C.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[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, 053044 (2015).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (2015).
[Crossref] [PubMed]

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

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

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

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

Yeh, L.-H.

Zheng, G.

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (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, 1–12 (2016).
[Crossref]

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

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (2015).
[Crossref] [PubMed]

L. Bian, J. Suo, G. Situ, G. Zheng, F. Chen, and Q. Dai, “Content adaptive illumination for Fourier ptychography,” Opt. Lett. 39, 6648–6651 (2014).
[Crossref] [PubMed]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22, 20856–20870 (2014).
[Crossref] [PubMed]

S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, “FPscope: a field-portable high-resolution microscope using a cellphone lens,” Biomed. Opt. Express 5, 3305–3310 (2014).
[Crossref] [PubMed]

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

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
[Crossref] [PubMed]

S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22, 5455–5464 (2014).
[Crossref] [PubMed]

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

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

Zheng, S.

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Zhong, J.

Zhou, H.

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

ACM Trans. Graphic. (2)

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphic. 27, 73 (2008).
[Crossref]

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphic. 28, 145 (2009).
[Crossref]

Biomed. Opt. Express (2)

Commun. Pure Appl. Math. (1)

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Commun. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

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, 1–12 (2016).
[Crossref]

IEEE Signal Proc. Mag. (1)

Y. Shechtman, Y. Eldar, O. Cohen, H. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Proc. Mag. 32, 87–109 (2015).
[Crossref]

J. Biomed. Opt. (1)

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

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

Med. Image Anal. (1)

T. Vercauteren, A. Perchant, G. Malandain, X. Pennec, and N. Ayache, “Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy,” Med. Image Anal. 10, 673–692 (2006).
[Crossref] [PubMed]

Nat. Methods (1)

X. Li, P. Mooney, S. Zheng, C. R. Booth, M. B. Braunfeld, S. Gubbens, D. A. Agard, and Y. Cheng, “Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM,” Nat. Methods 10, 584–590 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Nature (1)

M. Liao, E. Cao, D. Julius, and Y. Cheng, “Structure of the TRPV1 ion channel determined by electron cryo-microscopy,” Nature 504, 107–112 (2013).
[Crossref] [PubMed]

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, 053044 (2015).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (2)

Optica (2)

PLoS ONE (1)

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS ONE 10, e0124938 (2015).
[Crossref] [PubMed]

Sci. Rep. (1)

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Ultramicroscopy (1)

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

USC-SIPI Rep. (1)

A. G. Weber, “The USC-SIPI image database version 5,” USC-SIPI Rep. 315, 1–24 (1997).

Other (7)

D. G. Luenberger, Introduction to Linear and Nonlinear Programming, vol. 28 (Addison-WesleyReading, MA, 1973).

P. C. Hansen, J. G. Nagy, and D. P. O’leary, Deblurring Images: Matrices, Spectra, and Filtering, vol. 3 (Siam, 2006).
[Crossref]

Y. Chen and E. J. Candès, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” arXiv preprint arXiv: 1505.05114 (2015).

E. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” arXiv preprint arXiv:1407.1065 (2014).

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. pp. 1–35 (2012).

D. Swift and L. Birdsill, “Method and system for automatic correction of motion artifacts,” (2005). US Patent 6,842,196.

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” arXiv preprint arXiv:1602.02901 (2016).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

The FPM system and its image formation in the case with sample motion.

Fig. 2
Fig. 2

The algorithmic scheme of the proposed mcFP method.

Fig. 3
Fig. 3

Reconstruction comparison between the proposed mcFP method and conventional AP algorithm, in the case with ideal circular sample motion. The quantitative evaluation is plotted on the left side, and the reconstructed amplitude and phase images by the two methods are shown on the right side.

Fig. 4
Fig. 4

Reconstruction comparison between the proposed mcFP method and conventional AP algorithm, in the case with non-ideal circular sample motion (the sample region moving outside of the FOV is not the same as that moving inside).

Fig. 5
Fig. 5

Reconstruction results by conventional AP and the proposed mcFP on real captured datasets (USAF target and red blood cell) by an FPM setup. We also show the ground-truth motion shift and corresponding reconstruction of each measurement on the right, where each sub-square stands for the motion space of the sample when capturing corresponding LR image, and the boundary represents the maximum motion shift being 4% of the system’s FOV scale.

Equations (6)

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

I = | 1 [ P ( k x , k u ) ( ϕ ( x , y ) e ( j x 2 π λ sin θ x , j y 2 π λ sin θ y ) ) ] | 2 = | 1 [ P ( k x , k y ) Φ ( k x 2 π λ sin θ x , k y 2 π λ sin θ y ) ] | 2 ,
I motion = | 1 [ P ( k x , k y ) ( ϕ ( x Δ x , y Δ y ) e ( j x 2 π λ sin θ x , j y 2 π λ sin θ y ) ) ] | 2 = | 1 [ P ( k x , k y ) Φ ( k x 2 π λ sin θ x , k y 2 π λ sin θ y ) e ( j k x Δ x , j k y Δ y ) ] | 2 .
( Δ x opt , Δ y opt ) = arg min ( Δ x , Δ y ) I motion | 1 [ P ( k x , k y ) Φ ( k x 2 π λ sin θ x , k y 2 π λ sin θ y ) e ( j k x Δ x , j k y Δ y ) ] | 2 .
ϕ = I motion 1 [ P ( k x , k y ) Φ ( k x 2 π λ sin θ x , k y 2 π λ sin θ y ) e ( j k x Δ x opt , j k y Δ y opt ) ] | 1 [ P ( k x , k y ) Φ ( k x 2 π λ sin θ x , k y 2 π λ sin θ y ) e ( j k x Δ x opt , j k y Δ y opt ) ] | .
Φ updated = Φ + P * ( k x + 2 π λ sin θ x , k y + 2 π λ sin θ y ) | P ( k x + 2 π λ sin θ x , k y + 2 π λ sin θ y ) | max 2 [ Φ ( k x + 2 π λ sin θ x , k y + 2 π λ sin θ y ) e ( j k x Δ x opt , j k y Δ y opt ) Φ ] .
RE ( z , z ^ ) = min ϕ [ 0 , 2 π ) e j ϕ z z ^ 2 z ^ 2 .

Metrics