Abstract

We introduce a hybrid tomographic method, based on recent investigations concerning the connection between computed tomography and diffraction tomography, that allows direct reconstruction of scattering objects from intensity measurements. This technique is noniterative and is intuitively easier to understand and easier to implement than some other methods described in the literature. The manner in which the new method reduces to computed tomography at short wavelengths is discussed. Numerical examples of reconstructions are presented.

© 2002 Optical Society of America

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  1. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
  2. G. T. Herman, Image Reconstruction from Projections (Academic, Orlando, Fla., 1980).
  3. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  4. E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.
  5. Some of the earliest work is described in G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2001 (2)

2000 (2)

1999 (1)

1997 (1)

1996 (1)

1995 (1)

1994 (1)

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

1993 (2)

1992 (1)

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

1983 (1)

1973 (1)

Some of the earliest work is described in G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

Agarwal, G. S.

Anastasio, M. A.

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985).

Beck, M.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Carney, P. S.

Cheng, J.

Datta, G. K.

Devaney, A. J.

M. H. Maleki, A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
[CrossRef]

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging, Part 2, W. M. Boerner, ed. (Reidel, Boston, Mass., 1985), pp. 1107–1135.

Fuks, B. A.

B. A. Fuks, Introduction to the Theory of Analytic Functions of Several Complex Variables (American Mathematical Society, Providence, R.I., 1963).

Gbur, G.

Gori, F.

Guattari, G.

Gureyev, T. E.

Han, S.

Herman, G. T.

G. T. Herman, Image Reconstruction from Projections (Academic, Orlando, Fla., 1980).

Hounsfield, G. N.

Some of the earliest work is described in G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

Iaconis, C.

Jayshree, N.

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Maleki, M. H.

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

McAlister, D. F.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

Messiah, A.

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1964), Vol. 1.

Nugent, K. A.

Pan, X.

Raymer, M. G.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

Roberts, A.

Santarsiero, M.

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Teague, M. R.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vasu, R. M.

Vdovin, G.

Walmsley, I. A.

Webb, S.

A historical account of the medical development of computerized tomography is given in S. Webb, From the Watching of Shadows (Hilger, Bristol, UK, 1990).

Wolf, E.

G. Gbur, E. Wolf, “Relation between computed tomography and diffraction tomography,” J. Opt. Soc. Am. A 18, 2132–2137 (2001).
[CrossRef]

P. S. Carney, E. Wolf, G. S. Agarwal, “Diffraction tomography using power extinction measurements,” J. Opt. Soc. Am. A 16, 2643–2648 (1999).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

Appl. Opt. (2)

Br. J. Radiol. (1)

Some of the earliest work is described in G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

IEEE Trans. Image Process. (1)

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

Other (11)

A historical account of the medical development of computerized tomography is given in S. Webb, From the Watching of Shadows (Hilger, Bristol, UK, 1990).

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985).

B. A. Fuks, Introduction to the Theory of Analytic Functions of Several Complex Variables (American Mathematical Society, Providence, R.I., 1963).

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1964), Vol. 1.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging, Part 2, W. M. Boerner, ed. (Reidel, Boston, Mass., 1985), pp. 1107–1135.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

G. T. Herman, Image Reconstruction from Projections (Academic, Orlando, Fla., 1980).

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.

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