Abstract

In this paper, a lensless microscope based on ptychography is presented. It disposes of the mechanic movement necessary for conventional ptychography, instead using an LED matrix to obtain a diverse set of diffraction data. This data is subject to multiple experimental factors that deviate from the standard version of ptychography: namely, imprecise knowledge of the LED positions, partial temporal and spatial coherence, and varying brightness and illumination distribution between individual LEDs. Despite these difficulties, we show here that the diversity in the ptychographic data allows an iterative phase retrieval algorithm to recover excellent, high-resolution images of a resolution test target and a biological sample.

© 2018 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2017 (1)

2016 (4)

2015 (1)

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

2014 (1)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

2013 (3)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref]

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

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

2012 (2)

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

2011 (2)

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

2009 (2)

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

A. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

2008 (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

2005 (1)

1996 (1)

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

1987 (1)

S. Wold, K. Esbensen, and P. Geladi, “Principal component analysis,” Chemom. Intell. Lab. Syst. 2, 37–52 (1987).
[Crossref]

1983 (1)

1982 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1955 (1)

G. Nomarski, “Microinterferometre differentiel a ondes polarisees,” J. Phys. Radium 16, S9–S13 (1955).

1942 (1)

F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects,” Physica 9, 686–698 (1942).
[Crossref]

Abbey, B.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Almoro, P. F.

Baksh, P.

Balaur, E.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Batey, D.

Batey, D. J.

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

Boden, S. A.

Brocklesby, W. S.

Bunk, O.

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Cadenazzi, G. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Card, R.

Chad, J. E.

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

Coene, W. M. J.

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Colomb, T.

Coskun, A. F.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Cuche, E.

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

de Beeck, M. O.

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Depeursinge, C.

Dierolf, M.

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Edo, T.

Edo, T. B.

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

Emery, Y.

Esbensen, K.

S. Wold, K. Esbensen, and P. Geladi, “Principal component analysis,” Chemom. Intell. Lab. Syst. 2, 37–52 (1987).
[Crossref]

Fienup, J. R.

Frey, J. G.

Geladi, P.

S. Wold, K. Esbensen, and P. Geladi, “Principal component analysis,” Chemom. Intell. Lab. Syst. 2, 37–52 (1987).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, J. W. Goodman, ed. (Roberts & Company, 2005).

Gorocs, Z.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Greenbaum, A.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Halko, N.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

Hasegawa, S.

Hayasaki, Y.

Henderson, C. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Horstmeyer, R.

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

Humphry, M. J.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

Isikman, S. O.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Johnson, D.

Li, P.

Luo, W.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Magistretti, P. J.

Maiden, A.

Maiden, A. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

Marquet, P.

Marriott, P.

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

Marrison, J.

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

Martinsson, P. G.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

McNulty, I.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Mudanyali, O.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Nomarski, G.

G. Nomarski, “Microinterferometre differentiel a ondes polarisees,” J. Phys. Radium 16, S9–S13 (1955).

Nugent, K. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

O’Toole, P.

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

Odstrcil, M.

Ozcan, A.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Parsons, A. D.

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

Peele, A. G.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Pfeiffer, F.

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Pham, Q. D.

Putkunz, C. T.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Quiney, H. M.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Rappaz, B.

Raty, L.

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

Rau, C.

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

Rodenburg, J.

Rodenburg, J. M.

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

A. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

Sarahan, M. C.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schramm, S. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

Serrano-Garcia, D. I.

Shkolnisky, Y.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

Stagg, M. D.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

Su, T. W.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Takeda, M.

Teague, M. R.

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Thust, A.

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Tygert, M.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

Van Dyck, D.

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

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[Crossref]

Whitehead, L. W.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Williams, G. J.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
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S. Wold, K. Esbensen, and P. Geladi, “Principal component analysis,” Chemom. Intell. Lab. Syst. 2, 37–52 (1987).
[Crossref]

Xue, L.

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Yang, C.

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

Yatagai, T.

Zernike, F.

F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects,” Physica 9, 686–698 (1942).
[Crossref]

Zheng, G.

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

Appl. Opt. (1)

Chemom. Intell. Lab. Syst. (1)

S. Wold, K. Esbensen, and P. Geladi, “Principal component analysis,” Chemom. Intell. Lab. Syst. 2, 37–52 (1987).
[Crossref]

J. Opt. (1)

P. Li, D. J. Batey, T. B. Edo, A. D. Parsons, C. Rau, and J. M. Rodenburg, “Multiple mode x-ray ptychography using a lens and a fixed diffuser optic,” J. Opt. 18, 054008 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. Radium (1)

G. Nomarski, “Microinterferometre differentiel a ondes polarisees,” J. Phys. Radium 16, S9–S13 (1955).

Nat. Methods (1)

A. Greenbaum, W. Luo, T. W. Su, Z. Gorocs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9, 889–895 (2012).
[Crossref]

Nat. Photonics (2)

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

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

Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optica (1)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Physica (1)

F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects,” Physica 9, 686–698 (1942).
[Crossref]

Sci. Rep. (2)

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

SIAM J. Sci. Comput. (1)

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci. Comput. 33, 2580–2594 (2011).
[Crossref]

Ultramicroscopy (4)

A. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

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

W. M. J. Coene, A. Thust, M. O. de Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Other (1)

J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, J. W. Goodman, ed. (Roberts & Company, 2005).

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Figures (9)

Fig. 1.
Fig. 1. Experimental geometry of the proposed imaging method.
Fig. 2.
Fig. 2. Experimental reconstructions. (a) Moduli and (b) phases of the specimen and the aperture (inset). The scale bars indicate a length of 40 μm.
Fig. 3.
Fig. 3. Experimental reconstructions with angle correction. (a) Moduli and (b) phases of the specimen and the aperture (inset). (c) The offsets of the diffraction patterns before (blue points) and after (red points) the angle correction. The scale bars indicate a length of 40 μm.
Fig. 4.
Fig. 4. Coherence property of the experiment. The measured diffraction pattern from (a) one of the LEDs and (b) a diode laser. (c) The measured spectra of 10 randomly chosen LEDs.
Fig. 5.
Fig. 5. Experimental reconstructions after taking into account both angle correction and temporal coherence. (a) Moduli and (b) phases of the specimen and the aperture (inset). The scale bars indicate a length of 40 μm.
Fig. 6.
Fig. 6. Diffraction patterns measured at different LED aperture distances.
Fig. 7.
Fig. 7. Experimental reconstructions after taking into account angle correction, temporal coherence, and spatial coherence. (a) Moduli and (b) phases of the specimen and the main aperture mode (inset). (c) The four aperture modes in HSV colorscale together with their relative power. The scale bars indicate a length of 40 μm.
Fig. 8.
Fig. 8. Experimental reconstructions after taking into account angle correction, temporal coherence, spatial coherence, and LED variance. (a) Moduli and (b) phases of the specimen and the average of the main illumination mode in the aperture plane (inset). (c) The zoom in view of the area marked by the red rectangle in (a). (d) The zoom in view of the same area of the reconstruction shown in Fig. 7(a). (e) The reconstruction error plot. (f) The four principle components and (g) their according linear coefficients for the main incoherent mode of the 64 illumination functions in HSV colorscale. The scale bars indicate a length of 40 μm.
Fig. 9.
Fig. 9. Imaging demonstration of human blood cells. (a) The reconstruction result of the proposed method. (b) The optical microscope image using a 10× objective. (c) The optical microscope image using a 20× objective.

Equations (20)

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Δuj=maxΔu{uIref(u)Ij(u+Δu)}.
Γj(r)=exp[i2π(ΔujMr)].
Pjn(r)=Δz{Γj(r)An(r)}.
ψjn(r)=Pjn(r)On(r).
Ψjn(u)=F{ψjn(r)exp(iπλzr2)}.
ψ^jn(r)=F1{Ij(u)Ψjn(u)|Ψjn(u)|}exp(iπλzr2).
P^jn(r)=Pjn(r)+On*(r)[ψ^jn(r)ψjn(r)](1αP)|On(r)|2+αP|On(r)|max2.
On+1(r)=On(r)+Pjn*(r)[ψ^jn(r)ψjn(r)](1αO)|Pjn(r)|2+αO|Pjn(r)|max2.
An+1(r)=Δz1{P^jn(r)}Γj*(r).
Δvjn=maxΔv{uIj(u)|Ψjn(u+Δv)|2}.
Δujn+1=Δujn+Δvjn.
Iλ(u)=Iλ¯(λλ¯u).
Iest(u)=ξλIλ(u)dλ.
ψ^j,λ¯n(r)=F1{Ijmea(u)Ψj,λ¯n(u)Ijest(u)}exp(iπλ¯zr2).
Ej=k,jr|Pj(k)(r)O(l)(r)ψ^j(k,l)(r)|2+k,ju(r)|P(k)(r)P(k)(r)|2.
u(r)=α{[l|O(l)(r)|2]maxl|O(l)(r)|2},
Pj(k)(r)=Pj(k)(r)+lO(l)*(r)[ψ^j(k,l)(r)ψj(k,l)(r)](1αP)l|O(l)(r)|2+αP[l|O(l)(r)|2]max.
O(l)(r)=O(l)(r)+kPj(k)*(r)[ψ^j(k,l)(r)ψj(k,l)(r)](1αO)k|Pj(k)(r)|2+αO[k|Pj(k)(r)|2]max.
[U,S,V]=tSVD(P,n).
P^=USV*.

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