Abstract

We compare the filtered backpropagation algorithm with the filtered backprojection algorithm for reconstructing the complex refractive-index distribution of semitransparent, cylindrical objects. Before reconstruction, the recorded scattered light is propagated back to the reconstruction area by inverse diffraction. Our comparison is based on computer-simulated data, and experimental optical data obtained from fibers with step-index, graded-index, and uniform-index distributions. The results show that both the filtered backpropagation algorithm and the filtered backprojection algorithm can produce accurate reconstructions of the complex refractive-index distribution as long as the weak-scattering approximation is valid. The good agreement between the results obtained from these two reconstruction algorithms indicates that the errors introduced by the assumption of straight-line propagation inside the object are negligible compared with those introduced by the weak-scattering approximation.

© 1995 Optical Society of America

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1995 (3)

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross-sectional complex refractive index of semitransparent, birefringent fibers,” J. Microsc. 177, 53–67 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4, 39–54 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
[CrossRef]

1993 (3)

1992 (1)

1991 (1)

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

1990 (2)

1989 (2)

G. W. Faris, H. Hertz, “Tunable differential interferometer for optical tomography,” Appl. Opt. 28, 4662–4667 (1989).
[CrossRef] [PubMed]

A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

1985 (2)

R. Snyder, L. Hesselink, “High speed optical tomography for flow visualization,” Appl. Opt. 24, 4046–4051 (1985).
[CrossRef] [PubMed]

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

1984 (1)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

1983 (1)

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[CrossRef]

1982 (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

1979 (1)

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

1970 (1)

Brenner, K.-H.

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, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
[CrossRef] [PubMed]

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[CrossRef]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, Vol. 18, H. Lee, G. Wade, eds. (Plenum, New York, 1991).

Faris, G. W.

Gelius, L.-J.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

Hertz, H.

Hertz, H. M.

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

Hesselink, L.

Johansen, I.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, Vol. 18, H. Lee, G. Wade, eds. (Plenum, New York, 1991).

Kak, A. C.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Kaveh, M.

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Kawata, S.

Kobayashi, T.

Kuroiwa, Y.

Larsen, L. E.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Maleki, M. H.

Minami, S.

Mueller, R. K.

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Nakamura, O.

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986), Chap. 5.

Noda, T.

Ooki, H.

Sasaki, O.

Singer, W.

Slaney, M.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Snyder, R.

Sponheim, N.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, Vol. 18, H. Lee, G. Wade, eds. (Plenum, New York, 1991).

Stamnes, J. J.

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4, 39–54 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
[CrossRef]

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

T. C. Wedberg, J. J. Stamnes, “Quantitative imaging by optical diffraction tomography,” in Proceedings of the ICO Topical Meeting on Optics (International Commission on Optics, Kyoto, Japan, 1995), Opt. Rev. 2.

T. C. Wedberg, J. J. Stamnes, “Quantitative microscopy of phase objects by optical diffraction tomography,” in Microscopy, Holography, and Interferometry in Biomedicine, A. F. Fercher, A. Lewis, H. Podbielska, H. Schneckenburger, T. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2083, 168–173 (1993).

T. C. Wedberg, J. J. Stamnes, “Analytical and numerical examination of the quantitative imaging properties of optical diffraction tomography,” J. Mod. Opt. (to be published).

Tatarski, V. T.

V. T. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.

Wade, G.

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Wedberg, T. C.

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross-sectional complex refractive index of semitransparent, birefringent fibers,” J. Microsc. 177, 53–67 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4, 39–54 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Quantitative imaging by optical diffraction tomography,” in Proceedings of the ICO Topical Meeting on Optics (International Commission on Optics, Kyoto, Japan, 1995), Opt. Rev. 2.

T. C. Wedberg, J. J. Stamnes, “Quantitative microscopy of phase objects by optical diffraction tomography,” in Microscopy, Holography, and Interferometry in Biomedicine, A. F. Fercher, A. Lewis, H. Podbielska, H. Schneckenburger, T. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2083, 168–173 (1993).

T. C. Wedberg, J. J. Stamnes, “Analytical and numerical examination of the quantitative imaging properties of optical diffraction tomography,” J. Mod. Opt. (to be published).

Wedberg, W. C.

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross-sectional complex refractive index of semitransparent, birefringent fibers,” J. Microsc. 177, 53–67 (1995).
[CrossRef]

Wolf, E.

Appl. Opt. (7)

IEEE Trans. Biomed. Eng. (1)

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

J. Microsc. (1)

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross-sectional complex refractive index of semitransparent, birefringent fibers,” J. Microsc. 177, 53–67 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

Phys. Rev. Lett. (1)

A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Pure Appl. Opt. (1)

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4, 39–54 (1995).
[CrossRef]

Ultrasonic Imaging (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

Other (6)

V. T. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.

T. C. Wedberg, J. J. Stamnes, “Analytical and numerical examination of the quantitative imaging properties of optical diffraction tomography,” J. Mod. Opt. (to be published).

T. C. Wedberg, J. J. Stamnes, “Quantitative microscopy of phase objects by optical diffraction tomography,” in Microscopy, Holography, and Interferometry in Biomedicine, A. F. Fercher, A. Lewis, H. Podbielska, H. Schneckenburger, T. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2083, 168–173 (1993).

T. C. Wedberg, J. J. Stamnes, “Quantitative imaging by optical diffraction tomography,” in Proceedings of the ICO Topical Meeting on Optics (International Commission on Optics, Kyoto, Japan, 1995), Opt. Rev. 2.

F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986), Chap. 5.

N. Sponheim, I. Johansen, A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, Vol. 18, H. Lee, G. Wade, eds. (Plenum, New York, 1991).

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