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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 10, Iss. 5 — May. 1, 1993
  • pp: 1086–1092

Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography

Mohammad H. Maleki and Anthony J. Devaney  »View Author Affiliations

JOSA A, Vol. 10, Issue 5, pp. 1086-1092 (1993)

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We compare two methods of reconstructing the complex index-of-refraction distribution of a scattering object from optical scattering data obtained in a set of scattering experiments employing incident monochromatic plane waves. The first method generates an approximate reconstruction directly from the far-field intensity, which is measured as a function of scattering angle for each incident plane wave. The second method uses an iterative phase-retrieval algorithm to extract the phase of the scattered field over any given plane from the measurement of the intensity of the total field over that plane and from a priori object-support information. The reconstruction is then performed from the scattered field that is so determined by using the filtered backpropagation algorithm of diffraction tomography. We compare the performance of the two procedures on computer-simulated and experimental scattering data.

© 1993 Optical Society of America

Original Manuscript: March 16, 1992
Revised Manuscript: August 31, 1992
Manuscript Accepted: September 8, 1992
Published: May 1, 1993

Mohammad H. Maleki and Anthony J. Devaney, "Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography," J. Opt. Soc. Am. A 10, 1086-1092 (1993)

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  1. N. Sponheim, I. Johansen, A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, H. Lee, G. Wade, eds. (Plenum, New York, 1990), Vol. 18.
  2. W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chommelous, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Prob. 4, 305–331 (1988). [CrossRef]
  3. R. B. Pratt, M. H. Worthington, “The application of diffraction tomography to cross-hole seismic data,” Geophysics 53, 1284–1294 (1988). [CrossRef]
  4. M. A. Fiddy, “Inversion of optical scattered field data,”J. Phys. D 19, 301–317 (1986). [CrossRef]
  5. E. Wolf, “Determination of the amplitude and the phase of the scattered field by holography,”J. Opt. Soc. Am. 60, 18–20 (1970). [CrossRef]
  6. R. Snyder, L. Hesselink, “High speed optical tomography for flow visualization,” Appl. Opt. 24, 4046–4051 (1985). [CrossRef] [PubMed]
  7. M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992). [CrossRef]
  8. A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Prob. 2, 161–183 (1986). [CrossRef]
  9. V. T. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  10. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imag. 4, 336–350 (1982).
  11. A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983). [CrossRef]
  12. See J. R. Shewell, E. Wolf, “Inverse diffraction and a new reciprocity theorem,”J. Opt. Soc. Am. 58, 1596–1603 (1968); G. C. Sherman, “Diffracted wave fields expressible by plane-wave expansions containing only homogeneous waves,”J. Opt. Soc. Am. 59, 697–711 (1969). [CrossRef]
  13. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  14. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]
  15. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  16. A. Levi, H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984). [CrossRef]
  17. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,”J. Phys. D 6, L6–L9 (1973). [CrossRef]
  18. R. Rolleston, N. George, “Image reconstruction from partial Fresnel zone information,” Appl. Opt. 25, 178–183 (1986). [CrossRef] [PubMed]
  19. G. Liu, P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4, 159–165 (1987). [CrossRef]
  20. L. Wang, B. Dong, G. Yang, “Phase retrieval from two intensity measurements in an optical system involving nonunitary transformation,” Appl. Opt. 29, 3422–3427 (1990). [CrossRef] [PubMed]
  21. A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963). [CrossRef]
  22. 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). [CrossRef]
  23. M. Nieto-Vesperinas, “Inverse scattering problems: a study in terms of the zeros of entire functions,”J. Math. Phys. 25, 2109–2115 (1984). [CrossRef]
  24. L. S. Taylor, “The phase retrieval problem,”IEEE Trans. Antennas Propag. AP-29, 386–391 (1981). [CrossRef]
  25. R. E. Burge, M. A. Fiddy, A. H. Greenway, G. Ross, “The application of dispersion relations (Hilbert transforms) to phase retrieval,”J. Phys. D 7, L65–L68 (1974). [CrossRef]
  26. R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in 1980 Intl. Optical Computing Conf. I, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.231, 130–141 (1980). [CrossRef]

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