High Precision Object Phase Reconstruction with Modified Phase Retrieval

  • Sandro Förster
  • Herbert Gross

The recovering of phase information out of intensity measurements through focus image stacks is an interesting topic for a long time. This so called phase retrieval avoids expensive and environmental sensitive direct phase measurement. The method is applicable to the imaging of phase objects [1], to the layout and optimization of phase structures for desired illumination distributions in beam shaping setups [2] and for metrology of systems [3]. The reconstruction of the phase is a nonlinear inverse problem and the corresponding computation is critical concerning convergence and accuracy. In the past a large variety of algorithms is proposed in the literature to deal with this problem [4], [5], [6], [7]. Usually, the performance of the algorithms can be improved, if several images are taken into account, which are diversified by at least one parameter. The most prominent and easiest choice to get information out of the system is to gather the images in several defocussed planes.


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  1. 1.
    Fienup, J.R. (1978) Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3:27-29CrossRefGoogle Scholar
  2. 2.
    Wu,R., Shu, F., Zhang, W., Zhang, X., Li, Y. (2007) Extended algorithm for the design of diffractive optical elements around the focal plane. Appl. Opt. 46:5779-5783CrossRefGoogle Scholar
  3. 3.
    Möller,B., Gross,H. (2005) Characterization of complex optical systems based on wavefront retrieval from point spread function. Proc. SPIE 5905.Google Scholar
  4. 4.
    Marchesini, S. (2007) A unified evaluation of iterative projection algorithms for phase retrieval. Rev. of Sci. Inst. 78:011301Google Scholar
  5. 5.
    Brady, G.R., Fienup, J.R. (2006) Nonlinear optimization algorithm for retrieving the full complex pupil function. Opt. Express 14:474-486CrossRefGoogle Scholar
  6. 6.
    Fienup,J.R., Wackerman, C.C. (1986) Phase-retrieval stagnation problems and solutions. JOSA A 3:1897-1907CrossRefGoogle Scholar
  7. 7.
    Fienup,J.R. (1982) Phase retrieval algorithms: a comparison. Appl. Opt. 21:2758-2769CrossRefGoogle Scholar
  8. 8.
    Gerchberg G. W., W. O. Saxon, D. (1972) Practical algorithm for the determination of phase from image and diffraction plane pictures. Optik (Stuttgart) 35, 237–246Google Scholar
  9. 9.
    Dean, B., Bowers, C.W. (2003) Diversity selection for phase-diverse phase retrieval. JOSA A 20:1490-1504CrossRefGoogle Scholar
  10. 10.
    Brady, G. R., Guizar-Sicairos, M., Fienup, J. R. (2009) Optical wavefront measurement using phase retrieval with transverse translation diversity. Opt. Express 17:624-639CrossRefGoogle Scholar
  11. 11.
    Nakajima, N. (2005) Phase retrieval from diffraction intensities by use of a scanning slit aperture. Appl. Opt. 44:6228-6234CrossRefGoogle Scholar
  12. 12.
    Guizar-Sicairos, M., Fienup, J.R. (2008) Phase retrieval with transverse translation diversity: a nonlinear optimization aproach. Opt. Express 16:7264-7278CrossRefGoogle Scholar
  13. 13.
    Soldovieri, F., Leone, G., Pierri, R. (2008) A novel phase retrieval technique based on propagation diversity via a dielectric slab. Opt. Express 16:7418-74427CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sandro Förster
    • 1
  • Herbert Gross
    • 1
  1. 1.Carl Zeiss AGOberkochenGermany

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