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Applied Optics

Applied Optics


  • Vol. 27, Iss. 16 — Aug. 15, 1988
  • pp: 3433–3436

Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments

Kazuichi Ichikawa, Adolf W. Lohmann, and Mitsuo Takeda  »View Author Affiliations

Applied Optics, Vol. 27, Issue 16, pp. 3433-3436 (1988)

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Experimental demonstrations of deterministic phase retrieval based on the Teague-Streibl irradiance transport equation are presented. A new technique is proposed, in which the transport equation is solved by the Fourier transform method for a periodic boundary condition with high spatial carrier frequency, which is created by making a light beam with unknown phase distribution pass through a grating. Quantitative phase measurements were performed by experiments without recourse to interferometry, and the results were found to be in good agreement with theory.

© 1988 Optical Society of America

Original Manuscript: February 1, 1988
Published: August 15, 1988

Kazuichi Ichikawa, Adolf W. Lohmann, and Mitsuo Takeda, "Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments," Appl. Opt. 27, 3433-3436 (1988)

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  1. For a review of various phase retrieval schemes see, for example, H. A. Ferwerda, “The Phase Reconstruction Problems for Wave Amplitudes and Coherence Functions,” in Inverse Source Problems in Optics, H. P. Baltes, Ed. (Springer-Verlag, Heidelberg, 1978), p. 13; J. R. Fienup, “Phase Retrieval Algorithms: A Comparison,” Appl. Opt. 21, 2758 (1982). [CrossRef] [PubMed]
  2. M. R. Teague, “Irradiance Moments: Their Propagation and Use for Unique Retrieval of Phase,” J. Opt. Soc. Am. 72, 1199 (1982). [CrossRef]
  3. M. R. Teague, “Deterministic Phase Retrieval: a Green’s Function Solution,” J. Opt. Soc. Am. 73, 1434 (1983). [CrossRef]
  4. N. Streibl, “Phase Imaging by the Transport Equation of Intensity,” Opt. Commun. 49, 6 (1984). [CrossRef]
  5. N. Streibl, “Phase Imaging Based on the Transport Equation of Intensity,” in ICO-13 Conference Digest, 352 (1984).
  6. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982). [CrossRef]
  7. M. Takeda, S. Kobayashi, “Lateral Aberration Measurements with a Digital Talbot Interferometer,” Appl. Opt. 23, 1760 (1984). [CrossRef] [PubMed]
  8. M. Takeda, K. Mutoh, “Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes,” Appl. Opt. 22, 3977 (1983). [CrossRef] [PubMed]

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