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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 3 — Mar. 6, 2014

A phase space model of Fourier ptychographic microscopy

Roarke Horstmeyer and Changhuei Yang  »View Author Affiliations

Optics Express, Vol. 22, Issue 1, pp. 338-358 (2014)

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A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychography’s and FPM’s captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment.

© 2014 Optical Society of America

OCIS Codes
(110.4980) Imaging systems : Partial coherence in imaging
(110.1758) Imaging systems : Computational imaging
(080.5084) Geometric optics : Phase space methods of analysis
(070.7425) Fourier optics and signal processing : Quasi-probability distribution functions

ToC Category:
Imaging Systems

Original Manuscript: October 22, 2013
Revised Manuscript: December 16, 2013
Manuscript Accepted: December 17, 2013
Published: January 2, 2014

Virtual Issues
Vol. 9, Iss. 3 Virtual Journal for Biomedical Optics

Roarke Horstmeyer and Changhuei Yang, "A phase space model of Fourier ptychographic microscopy," Opt. Express 22, 338-358 (2014)

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  1. P. D. Nellist, B. C. McCallum, J. M. Rodenburg, “Resolution beyond the ‘infromation limit’ in transmission electron microscopy,” Nature 374, 630–632 (1995). [CrossRef]
  2. F. Hue, J. M. Rodenburg, A. M. Maiden, F. Sweeney, P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010). [CrossRef]
  3. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, I. Johnson, “Hard-X-ray lensless imaging of extended objects,” PRL 98, 034801 (2007). [CrossRef]
  4. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pheiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008). [CrossRef] [PubMed]
  5. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pheiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 437–439 (2010). [CrossRef]
  6. A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010). [CrossRef] [PubMed]
  7. A. M. Maiden, M. J. Humphry, F. Zhang, J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A. 28(4), 604–612 (2011). [CrossRef]
  8. G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photon. 7, 739–745 (2013). [CrossRef]
  9. J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521–553 (1992). [CrossRef]
  10. H. N. Chapman, “Phase retrieval x-ray microscopy by Wigner distribution deconvolution,” Ultramicroscopy 66, 153 (1996). [CrossRef]
  11. J. N. Clark, X. Huang, R. Harder, I. K. Robinsion, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012). [CrossRef] [PubMed]
  12. P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013). [CrossRef] [PubMed]
  13. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  14. K. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010). [CrossRef]
  15. M. Testorf, B. M. Hennelly, J. Ojeda-Castaneda, Phase-Space Optics: Fundamentals and Applications (McGraw-Hill, 2010).
  16. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” JOSA A 3(8), 1227–1238 (1986). [CrossRef]
  17. R. Horstmeyer, S. B. Oh, R. Raskar, “Iterative aperture mask design in phase space using a rank constraint,” Opt. Express 18(21), 22545–22555 (2010). [CrossRef] [PubMed]
  18. H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004). [CrossRef] [PubMed]
  19. A. M. Maiden, J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1562 (2009). [CrossRef] [PubMed]
  20. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012). [CrossRef] [PubMed]
  21. M. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008). [CrossRef]
  22. C. Teale, D. Adams, M. Murnane, H. Kapteyn, D. J. Kane, “Imaging by integrating stitched spectrograms,” Opt. Express 21(6), 6783–6793 (2012). [CrossRef]
  23. G. Zheng, X. Ou, R. Horstmeyer, C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013). [CrossRef] [PubMed]
  24. D. Brady, Optical Imaging and Spectroscopy (John Wiley & Sons, 2009). [CrossRef]
  25. R. G. Brown, P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering (John Wiley & Sons, 1996).
  26. X. Ou, R. Horstmeyer, G. Zheng, C. Yang, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(2), 4845–4848 (2013). [CrossRef] [PubMed]

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