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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 22 — Oct. 22, 2012
  • pp: 24778–24790

A generalization for optimized phase retrieval algorithms

Daniel E. Adams, Leigh S. Martin, Matthew D. Seaberg, Dennis F. Gardner, Henry C. Kapteyn, and Margaret M. Murnane  »View Author Affiliations

Optics Express, Vol. 20, Issue 22, pp. 24778-24790 (2012)

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In this work, we demonstrate an improved method for iterative phase retrieval with application to coherent diffractive imaging. By introducing additional operations inside the support term of existing iterated projection algorithms, we demonstrate improved convergence speed, higher success rate and, in some cases, improved reconstruction quality. New algorithms take a particularly simple form with the introduction of a generalized projection-based reflector. Numerical simulations verify that these new algorithms surpass the current standards without adding complexity to the reconstruction process. Thus the introduction of this new class of algorithms offers a new array of methods for efficiently deconvolving intricate data.

© 2012 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
(170.0180) Medical optics and biotechnology : Microscopy
(110.1758) Imaging systems : Computational imaging

ToC Category:
Image Processing

Original Manuscript: September 6, 2012
Revised Manuscript: October 4, 2012
Manuscript Accepted: October 4, 2012
Published: October 15, 2012

Daniel E. Adams, Leigh S. Martin, Matthew D. Seaberg, Dennis F. Gardner, Henry C. Kapteyn, and Margaret M. Murnane, "A generalization for optimized phase retrieval algorithms," Opt. Express 20, 24778-24790 (2012)

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  1. J. Miao and R. Sandberg, “Coherent x-ray diffraction imaging,” J. Sel. Top. Quantum Electron.18, 399– 410 (2012). [CrossRef]
  2. C. La-O-Vorakiat, E. Turgut, C. Teale, H. Kapteyn, M. Murnane, S. Mathias, M. Aeschlimann, C. Schneider, J. Shaw, H. Nembach, and T. Silva, “Ultrafast demagnetization measurements using extreme ultraviolet light: comparison of electronic and magnetic contributions,” Phys. Rev. X2, 1–7 (2012). [CrossRef]
  3. S. Mathias, C. La-O-Vorakiat, P. Grychtol, P. Granitzka, E. Turgut, J. M. Shaw, R. Adam, H. T. Nembach, M. E. Siemens, S. Eich, C. M. Schneider, T. J. Silva, M. Aeschlimann, M. M. Murnane, and H. C. Kapteyn, “Probing the timescale of the exchange interaction in a ferromagnetic alloy.” Proc. Nat. Acad. Sci. USA pp. 1–6 (2012).
  4. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400, 342–344 (1999). [CrossRef]
  5. C. a. Larabell and K. a. Nugent, “Imaging cellular architecture with x-rays.” Curr. Opin. Struct. Biol.20, 623–631 (2010). [CrossRef] [PubMed]
  6. H. Jiang, C. Song, C. Chen, R. Xu, K. Raines, B. Fahimian, C.-h. Lu, T. Lee, A. Nakashima, and J. Urano, and Others, “Quantitative 3D imaging of whole, unstained cells by using x-ray diffraction microscopy,” Proc. Nat. Acad. Sci. USA107, 11234 (2010). [CrossRef] [PubMed]
  7. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Nat. Acad. Sci. USA107, 529 (2010). [CrossRef] [PubMed]
  8. I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nature Mater.8, 291–298 (2009). [CrossRef]
  9. M. D. Seaberg, D. E. Adams, E. L. Townsend, D. A. Raymondson, W. F. Schlotter, Y. Liu, C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane, “Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source.” Opt. Express19, 22470–22479 (2011). [CrossRef] [PubMed]
  10. D. J. Brady, M. E. Gehm, R. a. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography.” Nature486, 386–389 (2012). [CrossRef] [PubMed]
  11. S. Marchesini, “Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval.” Rev. Sci. Instrum.78, 011301 (2007). [CrossRef] [PubMed]
  12. S. Marchesini, “Phase retrieval and saddle-point optimization.” J. Opt. Soc. Am. A24, 3289–3296 (2007). [CrossRef]
  13. D. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl.21,37 (2005). [CrossRef]
  14. J. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. lett.3, 27–29 (1978). [CrossRef] [PubMed]
  15. J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
  16. R. Gerchberg and W. O. Saxton, “Phase determination from Image and diffraction plane pictures in the electron microscope,” Optik34, 275–283 (1971).
  17. R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35 (1972).
  18. H. H. Bauschke, P. L. Combettes, and D. R. Luke, “Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization,” J. Opt. Soc. Am. A vol. 19, 1334–1345 (2002). [CrossRef]
  19. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A20, 40–55 (2003). [CrossRef]
  20. H. H. Bauschke, P. L. Combettes, and D. Luke, “Finding best approximation pairs relative to two closed convex sets in Hilbert spaces,” J. Approx. Theory127, 178–192 (2004). [CrossRef]
  21. A. Levi and H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A1, 932 (1984). [CrossRef]
  22. K. Goebel, Topics in metric fixed point theory (Cambridge University Press, 1990). [CrossRef]
  23. Y. Censor and S. A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications. (Oxford University Press: 1997).
  24. D. F. Gardner, B. Zhang, M. D. Seaberg, L. S. Martin, D. E. Adams, F. Salmassi, E. Gullikson, H. Kapteyn, and M. Murnane, “High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination,” Opt. Express20, 19050 (2012). [CrossRef] [PubMed]
  25. A. DAlfonso, A. Morgan, A. Martin, H. Quiney, and L. Allen, “Fast deterministic approach to exit-wave reconstruction,” Phys. Rev. A85, 1–9 (2012).
  26. D. Luke, “Local linear convergence of approximate projections onto regularized sets,” Nonlinear Analysis: Theory, Methods & Applications (2011). [PubMed]

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