OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 20 — Jul. 10, 2002
  • pp: 4133–4139

Phase Retrieval from Experimental Far-Field Intensities by Use of a Gaussian Beam

Nobuharu Nakajima and Masaomi Watanabe  »View Author Affiliations


Applied Optics, Vol. 41, Issue 20, pp. 4133-4139 (2002)
http://dx.doi.org/10.1364/AO.41.004133


View Full Text Article

Acrobat PDF (246 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The noniterative phase-retrieval method by use of Gaussian filtering is applied to the reconstruction of phase objects from experimental far-field intensities. In this method, the complex amplitude of transmitted light through an object is reconstructed from three far-field intensities, which are measured with the modulation of the object by laterally shifted and unshifted Gaussian filters. In the experiment, the amplitude of a Gaussian beam illuminating objects is utilized as a Gaussian filter, and, as the phase objects, a converging lens with a small exit pupil and a plastic fiber immersed in optical adhesive are used. The experimental results show that the Gaussian beam of a laser is capable of retrieving the phases of those objects with the accuracy of the range from ~1/10 to 1/4 of the laser’s wavelength.

© 2002 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.5070) Image processing : Phase retrieval

Citation
Nobuharu Nakajima and Masaomi Watanabe, "Phase Retrieval from Experimental Far-Field Intensities by Use of a Gaussian Beam," Appl. Opt. 41, 4133-4139 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-20-4133


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. H. A. Ferwerda, “The phase reconstruction problem for wave amplitudes and coherence functions,” in Inverse Source Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 13–39.
  2. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978).
  3. G. Ross, M. A. Fiddy, and M. Nieto-Vesperinas, “The inverse scattering problem in structural determinations,” in Inverse Scattering Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1980), pp. 15–71.
  4. M. H. Hayes, “The unique reconstruction of multidimensional sequences from Fourier transform magnitude or phase,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 195–230.
  5. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.
  6. A. Levi and H. Stark, “Restoration from phase and magnitude by generalized projections,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 277–320.
  7. M. A. Fiddy, “The role of analyticity in image recovery,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 499–529.
  8. N. Nakajima, “Phase retrieval using the properties of entire functions,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Vol. 93(Academic, New York, 1995), pp. 109–171.
  9. 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).
  10. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
  11. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. 4, 118–123 (1987).
  12. J. G. Walker, “Computer simulation of a method for object reconstruction from stellar speckle interferometry data,” Appl. Opt. 21, 3132–3137 (1982).
  13. W. Kim, “Two-dimensional phase retrieval using a window function,” Opt. Lett. 26, 134–136 (2001).
  14. R. W. Gonsalves, “Small-phase solution to the phase retrieval problem,” Opt. Lett. 26, 684–685 (2001).
  15. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
  16. M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am. 72, 1199–1209 (1982).
  17. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
  18. T. E. Gureyev, A. Roberts, and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials,” J. Opt. Soc. Am. A 12, 1932–1941 (1995).
  19. T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13, 1670–1682 (1996).
  20. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
  21. S. Bajt, A. Barty, K. A. Nugent, M. MaCartney, M. Wall, and D. Paganin, “Quantitative phase-sensitive imaging in a transmission electron microscope,” Ultramicroscopy 83, 67–73 (2000).
  22. B. E. Allman, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).
  23. N. Nakajima, “Phase retrieval system using a shifted Gaussian filter,” J. Opt. Soc. Am. A 15, 402–406 (1998).
  24. N. Nakajima, “Phase retrieval from Fresnel zone intensity measurements by use of Gaussian filtering,” Appl. Opt. 37, 6219–6226 (1998).
  25. T. Iwai and H. Masui, “Application of the phase retrieval method to the refractive-index profiling of an optical fiber,” Opt. Commun. 72, 195–201 (1989).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited