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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5550–5560

Through-focus phase retrieval and its connection to the spatial correlation for propagating fields

O. El Gawhary, A. Wiegmann, N. Kumar, S. F. Pereira, and H. P. Urbach  »View Author Affiliations

Optics Express, Vol. 21, Issue 5, pp. 5550-5560 (2013)

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Through-focus phase retrieval methods aim to retrieve the phase of an optical field from its intensity distribution measured at different planes in the focal region. By using the concept of spatial correlation for propagating fields, for both the complex amplitude and the intensity of a field, we can infer which planes are suitable to retrieve the phase and which are not. Our analysis also reveals why all techniques based on measuring the intensity at two Fourier-conjugated planes usually lead to a good reconstruction of the phase. The findings presented in this work are important for aberration characterization of optical systems, adaptive optics and wavefront metrology.

© 2012 OSA

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval
(350.5500) Other areas of optics : Propagation

ToC Category:
Image Processing

Original Manuscript: November 1, 2012
Revised Manuscript: December 12, 2012
Manuscript Accepted: December 13, 2012
Published: February 27, 2013

O. El Gawhary, A. Wiegmann, N. Kumar, S. F. Pereira, and H. P. Urbach, "Through-focus phase retrieval and its connection to the spatial correlation for propagating fields," Opt. Express 21, 5550-5560 (2013)

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  1. R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
  2. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart)35, 237–246 (1972).
  3. J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
  4. H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004). [CrossRef] [PubMed]
  5. H. M. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy103153–164 (2005). [CrossRef] [PubMed]
  6. 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,” Nature400342–344 (1999). [CrossRef]
  7. J. A. Rodrigo, T. Alieva, G. Cristbal, and M. L. Calvo, “Wavefield imaging via iterative retrieval based on phase modulation diversity,” Opt. Express1918621–18635 (2011). [CrossRef] [PubMed]
  8. M. R. Teague, “Image formation in terms of the transport equation,” J. Opt. Soc. Am. A2, 2019–2026 (1985). [CrossRef]
  9. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express17624 – 639 (2009). [CrossRef] [PubMed]
  10. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982). [CrossRef]
  11. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A15, 1662–1669 (1998). [CrossRef]
  12. B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett.28, 801–803 (2003). [CrossRef] [PubMed]
  13. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987). [CrossRef] [PubMed]
  14. M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2007), 883–891.

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