Abstract

Information multiplexing is important for biomedical imaging and chemical sensing. In this paper, we report a microscopy imaging technique, termed state-multiplexed Fourier ptychography (FP), for information multiplexing and coherent-state decomposition. Similar to a typical Fourier ptychographic setting, we use an array of light sources to illuminate the sample from different incident angles and acquire corresponding low-resolution images using a monochromatic camera. In the reported technique, however, multiple light sources are lit up simultaneously for information multiplexing, and the acquired images thus represent incoherent summations of the sample transmission profiles corresponding to different coherent states. We show that, by using the state-multiplexed FP recovery routine, we can decompose the incoherent mixture of the FP acquisitions to recover a high-resolution sample image. We also show that, color-multiplexed imaging can be performed by simultaneously turning on R/G/B LEDs for data acquisition. The reported technique may provide a solution for handling the partially coherent effect of light sources used in Fourier ptychographic imaging platforms. It can also be used to replace spectral filter, gratings or other optical components for spectral multiplexing and demultiplexing. With the availability of cost-effective broadband LEDs, the reported technique may open up exciting opportunities for computational multispectral imaging.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics7(9), 739–745 (2013).
    [CrossRef]
  2. M. Ryle and A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc.120, 220 (1960).
  3. A. B. Meinel, “Aperture synthesis using independent telescopes,” Appl. Opt.9(11), 2501 (1970).
    [CrossRef] [PubMed]
  4. R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237 (1972).
  5. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett.3(1), 27–29 (1978).
    [CrossRef] [PubMed]
  6. L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag.29(2), 386–391 (1981).
    [CrossRef]
  7. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982).
    [CrossRef] [PubMed]
  8. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 215829 (1982).
  9. R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A.4(1), 166–170 (1987).
    [CrossRef]
  10. L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
    [CrossRef]
  11. B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A20(8), 1490–1504 (2003).
    [CrossRef] [PubMed]
  12. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A20(1), 40–55 (2003).
    [CrossRef] [PubMed]
  13. L. Waller, S. S. Kou, C. J. R. Sheppard, and G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express18(22), 22817–22825 (2010).
    [CrossRef] [PubMed]
  14. C.-H. Lu, C. Barsi, M. O. Williams, J. N. Kutz, and J. W. Fleischer, “Phase retrieval using nonlinear diversity,” Appl. Opt.52(10), D92–D96 (2013).
    [CrossRef] [PubMed]
  15. H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett.93(2), 023903 (2004).
    [CrossRef] [PubMed]
  16. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(10), 7264–7278 (2008).
    [CrossRef] [PubMed]
  17. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
    [CrossRef] [PubMed]
  18. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
    [CrossRef] [PubMed]
  19. M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
    [CrossRef]
  20. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett.35(15), 2585–2587 (2010).
    [CrossRef] [PubMed]
  21. F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
    [CrossRef] [PubMed]
  22. A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
    [CrossRef]
  23. M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
    [CrossRef] [PubMed]
  24. T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
    [CrossRef]
  25. S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
    [CrossRef]
  26. W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
    [CrossRef]
  27. J. M. Rodenburg and R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci.339(1655), 521–553 (1992).
    [CrossRef]
  28. X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett.38(22), 4845–4848 (2013).
    [CrossRef] [PubMed]
  29. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am.72(3), 343–351 (1982).
    [CrossRef]
  30. L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
    [CrossRef] [PubMed]
  31. 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. Photonics5(7), 420–424 (2011).
    [CrossRef]
  32. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
    [CrossRef] [PubMed]
  33. D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy138, 13–21 (2014).
    [CrossRef] [PubMed]
  34. G. Zheng, “Breakthroughs in Photonics 2013: Fourier Ptychographic Imaging,” IEEE Photon. J.6(2), 1–7 (2014).
    [CrossRef]
  35. S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express22(5), 5455–5464 (2014).
    [CrossRef] [PubMed]
  36. Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express21(26), 32400–32410 (2013).
    [CrossRef] [PubMed]
  37. M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
    [CrossRef] [PubMed]
  38. H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
    [CrossRef] [PubMed]
  39. F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).
  40. D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
    [CrossRef] [PubMed]
  41. K. Hoshino, P. P. Joshi, G. Bhave, K. V. Sokolov, and X. Zhang, “Use of colloidal quantum dots as a digitally switched swept light source for gold nanoparticle based hyperspectral microscopy,” Biomed. Opt. Express5(5), 1610–1615 (2014).
    [CrossRef]
  42. R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
    [CrossRef]
  43. D. Brady and M. Gehm, “Compressive imaging spectrometers using coded apertures,” in Defense and Security Symposium, (International Society for Optics and Photonics, 2006), 62460A–62460A.
  44. M. Parmar, S. Lansel, and B. A. Wandell, “Spatio-spectral reconstruction of the multispectral datacube using sparse recovery,” in Image Processing,2008. ICIP 2008. 15th IEEE International Conference on, (IEEE, 2008), 473–476.
    [CrossRef]
  45. R. Willett, M. E. Gehm, and D. J. Brady, “Multiscale reconstruction for computational spectral imaging,” in Electronic Imaging 2007, (International Society for Optics and Photonics, 2007), 64980L–64980L–64915. 1.

2014 (4)

2013 (7)

C.-H. Lu, C. Barsi, M. O. Williams, J. N. Kutz, and J. W. Fleischer, “Phase retrieval using nonlinear diversity,” Appl. Opt.52(10), D92–D96 (2013).
[CrossRef] [PubMed]

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

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express21(26), 32400–32410 (2013).
[CrossRef] [PubMed]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics7(9), 739–745 (2013).
[CrossRef]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

2012 (2)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

2011 (3)

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. Photonics5(7), 420–424 (2011).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

2010 (3)

2009 (3)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

2008 (2)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(10), 7264–7278 (2008).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

2007 (1)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

2006 (1)

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

2004 (1)

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

2003 (2)

2001 (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

1999 (1)

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

1992 (1)

J. M. Rodenburg and R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci.339(1655), 521–553 (1992).
[CrossRef]

1987 (1)

R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A.4(1), 166–170 (1987).
[CrossRef]

1982 (3)

1981 (1)

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag.29(2), 386–391 (1981).
[CrossRef]

1978 (1)

1972 (1)

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

1970 (1)

1969 (1)

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

1960 (1)

M. Ryle and A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc.120, 220 (1960).

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. Photonics5(7), 420–424 (2011).
[CrossRef]

Akbari, H.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

Allen, L.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

Barbastathis, G.

Barsi, C.

Barth, S. F.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Bates, R. H. T.

J. M. Rodenburg and R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci.339(1655), 521–553 (1992).
[CrossRef]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy138, 13–21 (2014).
[CrossRef] [PubMed]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Bhave, G.

Bian, Z.

Boucheron, L. E.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Bowers, C. W.

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

Can, A.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Chen, G. Z.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy138, 13–21 (2014).
[CrossRef] [PubMed]

Coifman, R.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Davis, G.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

Dean, B. H.

Dicker, D. T.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Dierolf, M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dilanian, R. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Dong, S.

Edo, T. B.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

El-Deiry, W. S.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Elder, D. E.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Elser, V.

Faulkner, H. M. L.

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

Fei, B.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

Fienup, J. R.

Fleischer, J. W.

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Gerchberg, R.

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

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A.4(1), 166–170 (1987).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 215829 (1982).

Guerry, D.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

Gurcan, M. N.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Halig, L. V.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

Herlyn, M.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Hewish, A.

M. Ryle and A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc.120, 220 (1960).

Hoppe, W.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics7(9), 739–745 (2013).
[CrossRef]

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

Hoshino, K.

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

Humphry, M. J.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett.35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Joshi, P. P.

Kewish, C. M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Kou, S. S.

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

Kutz, J. N.

Lerner, J.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Lu, C.-H.

Madabhushi, A.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Maggioni, M.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

Maia, F.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

Maiden, A. M.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett.35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

Marchesini, S.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

Master, V.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Meinel, A. B.

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

Nieh, P. T.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Osunkoya, A.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

Ou, X.

Oxley, M.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Pešic, Z. D.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Pfeiffer, F.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

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. Photonics5(7), 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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Rajpoot, N. M.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Rau, C.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Rodenburg, J. M.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy138, 13–21 (2014).
[CrossRef] [PubMed]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett.35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

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

J. M. Rodenburg and R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci.339(1655), 521–553 (1992).
[CrossRef]

Ryle, M.

M. Ryle and A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc.120, 220 (1960).

Schirotzek, A.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Schuster, D. M.

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

Shenfield, A.

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

Sheppard, C. J. R.

Shiradkar, R.

Sokolov, K. V.

Strube, G.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Taylor, L.

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag.29(2), 386–391 (1981).
[CrossRef]

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Van Belle, P.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

Vine, D. 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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

von König, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Wagner, U.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Waigh, T. A.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Waller, L.

Warner, F.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

Williams, M. O.

Wolf, E.

Woolfe, F.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

Wu, H.-

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

Yang, C.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics7(9), 739–745 (2013).
[CrossRef]

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

Yener, B.

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

Zhang, X.

Zheng, G.

Zucker, S.

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

Acta Crystallogr. A (1)

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Appl. Opt. (3)

Biomed. Opt. Express (1)

Cancer Biol. Ther. (1)

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of Normal Skin and Melanoma using High Resolution Hyperspectral Imaging,” Cancer Biol. Ther.5(8), 1033–1038 (2006).
[CrossRef] [PubMed]

IEEE Photon. J. (1)

G. Zheng, “Breakthroughs in Photonics 2013: Fourier Ptychographic Imaging,” IEEE Photon. J.6(2), 1–7 (2014).
[CrossRef]

IEEE Rev. Biomed. Eng. (1)

M. N. Gurcan, L. E. Boucheron, A. Can, A. Madabhushi, N. M. Rajpoot, and B. Yener, “Histopathological image analysis: A review,” IEEE Rev. Biomed. Eng.2, 147–171 (2009).
[CrossRef] [PubMed]

IEEE Signal Process. Mag. (1)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag.29(2), 386–391 (1981).
[CrossRef]

IEEE Trans. Med. Imaging (1)

F. Woolfe, M. Maggioni, G. Davis, F. Warner, R. Coifman, and S. Zucker, “Hyper-spectral microscopic discrimination between normal and cancerous colon biopsies,” IEEE Trans. Med. Imaging99, 9999 (1999).

Inverse Probl. (1)

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl.29(11), 115009 (2013).
[CrossRef]

J. Appl. Phys. (1)

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

J. Biomed. Opt. (1)

H. Akbari, L. V. Halig, D. M. Schuster, A. Osunkoya, V. Master, P. T. Nieh, G. Z. Chen, and B. Fei, “Hyperspectral imaging and quantitative analysis for prostate cancer detection,” J. Biomed. Opt.17(7), 0760051 (2012).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

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

R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A.4(1), 166–170 (1987).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

M. Ryle and A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc.120, 220 (1960).

Nat. Commun. (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun.3, 730 (2012).
[CrossRef] [PubMed]

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. Photonics5(7), 420–424 (2011).
[CrossRef]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics7(9), 739–745 (2013).
[CrossRef]

Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Opt. Commun. (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 215829 (1982).

Opt. Express (4)

Opt. Lett. (3)

Optik (Stuttg.) (1)

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

Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci. (1)

J. M. Rodenburg and R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philosoph. Trans. R. Soc. London. Ser. A: Phys. Eng. Sci.339(1655), 521–553 (1992).
[CrossRef]

Phys. Rev. A (1)

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A87(5), 053850 (2013).
[CrossRef]

Phys. Rev. Lett. (2)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett.103(24), 243902 (2009).
[CrossRef] [PubMed]

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

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Ultramicroscopy (3)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy138, 13–21 (2014).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

Other (3)

D. Brady and M. Gehm, “Compressive imaging spectrometers using coded apertures,” in Defense and Security Symposium, (International Society for Optics and Photonics, 2006), 62460A–62460A.

M. Parmar, S. Lansel, and B. A. Wandell, “Spatio-spectral reconstruction of the multispectral datacube using sparse recovery,” in Image Processing,2008. ICIP 2008. 15th IEEE International Conference on, (IEEE, 2008), 473–476.
[CrossRef]

R. Willett, M. E. Gehm, and D. J. Brady, “Multiscale reconstruction for computational spectral imaging,” in Electronic Imaging 2007, (International Society for Optics and Photonics, 2007), 64980L–64980L–64915. 1.

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 (7)

Fig. 1
Fig. 1

The recovery procedures of the state-multiplexed Fourier ptychography scheme.

Fig. 2
Fig. 2

Simulations of the single-state and state-multiplexed FP schemes. (a1) and (a2) The input intensity and phase images of the simulated object. (b1) Raw data of the single-state FP scheme. Each low-resolution image (0.1 NA) corresponds to one LED element in the array. (b2) and (b3) The recovered sample intensity and phase images using the single-state FP scheme. (c1) Raw data of the state-multiplexed FP scheme. Two adjacent LED elements are lit up simultaneously for sample illumination, and each low-resolution intensity image (0.1 NA) represents an incoherent summation of two coherent states. (c2) and (c3) The recovered sample intensity and phase images (0.5 NA) using the state-multiplexed FP scheme. (d1) and (d2) The reconstructions of state-mixed raw data using the single-state FP scheme (for comparison).

Fig. 3
Fig. 3

Experiments of the single-state and state-multiplexed FP schemes. (a1) and (a2) The experimental setups for the two schemes. (b1) Raw data of the single-state FP scheme (0.1 NA). (b2) and (b3) The recovered sample intensity and phase images using the single-state FP scheme (0.5 NA). (c1) Raw data of the state-multiplexed FP scheme (0.1 NA). Two adjacent LED elements are lit up simultaneously for sample illumination, and each low-resolution intensity image represents an incoherent summation of two coherent states. (c2) and (c3) The recovered sample intensity and phase images using the state-multiplexed FP scheme (0.5 NA). (d1) and (d2) The reconstructions of state-mixed raw data using the single-state FP scheme (for comparison).

Fig. 4
Fig. 4

Color-multiplexed FP scheme. R/G/B LEDs are turned on simultaneously for illumination. Low-resolution images are acquired using a 0.1 NA objective lens and a monochrome camera. A color-multiplexed FP recovery algorithm is then used to decouple the R/G/B channels from the low-resolution images. A high-resolution color image of the sample can be recovered using computation instead of spectral filters.

Fig. 5
Fig. 5

Color-multiplexed FP recovery routine.

Fig. 6
Fig. 6

Simulations of the color-multiplexed FP scheme. (a) Input R/G/B channels and the color image. (b) The low-resolution intensity measurement of the object, representing an incoherent summation of 3 object profiles at different wavelengths. (c) The color-multiplexed FP recovery (0.5 NA). The mean-square errors for (c1)-(c3) are 0.5%, 0.4%, and 0.1%, respectively.

Fig. 7
Fig. 7

Experimental demonstration of the color-multiplexed FP scheme. (a) Raw data of the color-multiplexed FP acquisition, representing incoherent summation of the sample profiles at three wavelengths. (b1)-(b3) The recovered color-multiplexed high-resolution images (0.5 NA) at red, green, and blue channels. (c) The recovered color image by combining (b1)-(b3) (with white balance). (d) The recovered color image (0.5 NA) using three separated FP acquisitions with individual red, green, and blue illumination (no state-mixing). (e) Color image using a conventional microscope with a 40X high-NA objective lens (0.6 NA).

Metrics