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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 7 — Jul. 1, 2004
  • pp: 1172–1178

Phase imaging with a half-plane aperture

W. McBride and L. J. Allen  »View Author Affiliations

JOSA A, Vol. 21, Issue 7, pp. 1172-1178 (2004)

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A method that effects phase reconstruction from a single image of a phase object is presented. The method, which is founded on the iterative transform algorithm, more specifically the error reduction version of this algorithm, applies this algorithm in an unusual way, in that it attempts to solve the phase problem from the measurement of a single image of the object taken by using a half-plane aperture rather than its diffraction pattern. A description of the method, an analysis of its performance, and suggestions as to its potential application are given.

© 2004 Optical Society of America

OCIS Codes
(100.3020) Image processing : Image reconstruction-restoration
(100.5070) Image processing : Phase retrieval
(110.0180) Imaging systems : Microscopy

Original Manuscript: December 19, 2003
Revised Manuscript: March 2, 2004
Manuscript Accepted: March 2, 2004
Published: July 1, 2004

W. McBride and L. J. Allen, "Phase imaging with a half-plane aperture," J. Opt. Soc. Am. A 21, 1172-1178 (2004)

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  1. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  2. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  3. J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1987). [CrossRef]
  4. H. Takajo, T. Takahashi, R. Ueda, M. Taninaka, “Study on the convergence property of the hybrid input–output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 15, 2849–2861 (1998). [CrossRef]
  5. I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (four pages) (2001). [CrossRef] [PubMed]
  6. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003). [CrossRef] [PubMed]
  7. J. Miao, T. Ishikawa, E. H. Anderson, K. O. Hodgson, “Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method,” Phys. Rev. B 67, 174104 (six pages) (2003). [CrossRef]
  8. H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Cryst. Phys. Diffr. Theor. Gen. Crystallogr. 59, 143–152 (2003). [CrossRef]
  9. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]
  10. R. G. Lane, “Recovery of complex images from Fourier magnitude,” Opt. Commun. 63, 6–10 (1987). [CrossRef]
  11. R. P. Millane, “Phase problems for periodic images: effects of support and symmetry,” J. Opt. Soc. Am. A 10, 1037–1045 (1993). [CrossRef]
  12. U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2002). [CrossRef] [PubMed]
  13. J. C. H. Spence, M. Howells, L. D. Marks, J. Miao, “Lensless imaging: a workshop on new approaches to the phase problem for non-periodic objects,” Ultramicroscopy 90, 1–6 (2001). [CrossRef]
  14. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  15. D. Paganin, K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998). [CrossRef]
  16. W. M. J. Coene, A. Thust, M. Op de Beeck, D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996). [CrossRef]
  17. A. Thust, W. M. J. Coene, M. Op de Beeck, D. Van Dyck, “Focal-series reconstruction in HRTEM: simulation studies on non-periodic objects,” Ultramicroscopy 64, 211–230 (1996). [CrossRef]
  18. L. J. Allen, W. McBride, N. L. O’Leary, M. P. Oxley, “Exit wave reconstruction at atomic resolution,” Ultramicroscopy doi:. [CrossRef]
  19. D. J. Smith, “The realization of atomic resolution with the electron microscope,” Rep. Prog. Phys. 60, 1513–1580 (1997). [CrossRef]
  20. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).
  21. F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955). [CrossRef] [PubMed]
  22. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transport Media (Springer-Verlag, Berlin, 2001).
  23. D. L. Misell, A. H. Greenaway, “An application of the Hilbert transform in electron microscopy: I. Bright-field microscopy,” J. Phys. D 7, 832–855 (1974). [CrossRef]
  24. J. C. H. Spence, “Complex image determination in electron microscopy,” Opt. Acta 21, 835–837 (1974). [CrossRef]
  25. J. G. Walker, “The phase retrieval problem: a solution based on zero location by exponential apodization,” Opt. Acta 28, 735–738 (1981). [CrossRef]
  26. J. C. Bortz, B. J. Thompson, “Phase retrieval by optical differentiation,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds, Proc. SPIE351, 71–79 (1983). [CrossRef]
  27. A. Levi, H. Stark, “Restorations from phase and magnitude by generalised projections,” in Image Recovery Theory and Application, H. Stark, ed. (Academic, London, 1987), pp. 277–320.
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

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