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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 9 — Sep. 1, 2012
  • pp: 1847–1859

Phase retrieval with random phase illumination

Albert Fannjiang and Wenjing Liao  »View Author Affiliations


JOSA A, Vol. 29, Issue 9, pp. 1847-1859 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001847


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Abstract

This paper presents a detailed numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio σ=4 determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution RPI in the presence of additive as well multiplicative noises. It is shown that RPI with σ=2 is sufficient for phasing complex-valued images under a sector condition and σ=1 for phasing nonnegative images. The error-reduction algorithm with RPI is proved to converge to the true solution under proper conditions.

© 2012 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(170.1630) Medical optics and biotechnology : Coded aperture imaging
(340.7430) X-ray optics : X-ray coded apertures

ToC Category:
Image Processing

History
Original Manuscript: June 7, 2012
Manuscript Accepted: July 3, 2012
Published: August 15, 2012

Citation
Albert Fannjiang and Wenjing Liao, "Phase retrieval with random phase illumination," J. Opt. Soc. Am. A 29, 1847-1859 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-9-1847


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References

  1. R. P. Millane, “Phase retrieval in crystallography and optics” J. Opt. Soc. Am. A 7, 394–411 (1990). [CrossRef]
  2. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.
  3. 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,” Nature 400, 342–344 (1999). [CrossRef]
  4. M. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process 30, 140–154 (1982). [CrossRef]
  5. M. Hayes, “Reducible polynomials in more than one variables,” Proc. IEEE 70, 197–198 (1982). [CrossRef]
  6. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986). [CrossRef]
  7. 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]
  8. 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 19, 1334–1345 (2002). [CrossRef]
  9. S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007). [CrossRef]
  10. A. Fannjiang, “Absolute uniqueness of phase retrieval with random illumination,” Inverse Probl. 28, 075008 (2012).
  11. T. A. Pitts and J. F. Greenleaf, “Fresnel transform phase retrieval from magnitude,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035–1045 (2003). [CrossRef]
  12. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
  13. P. F. Almoro, G. Pedrine, P. N. Gundu, W. Osten, and S. G. Hansom, “Enhanced wavefront reconstruction by random phase modulation with a phase diffuser,” Opt. Lasers Eng. 49, 252–257 (2011). [CrossRef]
  14. A. Anand, G. Pedrini, W. Osten, and P. Almoro, “Wavefront sensing with random amplitude mask and phase retrieval,” Opt. Lett. 32, 1584–1586 (2007). [CrossRef]
  15. E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” preprint, August 2011.
  16. J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A 56, 596–605 (2000). [CrossRef]
  17. J. Miao, J. Kirz, and D. Sayre, “The oversampling phasing method,” Acta Crystallogr. Sect. D 56, 1312–1315 (2000). [CrossRef]
  18. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
  19. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef]
  20. 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 (1972).
  21. A. Levi and H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. 1, 932–943 (1984). [CrossRef]

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