Abstract

Optical diffraction tomography (ODT) is examined experimentally by reconstruction of a cross section of a transparent, cylindrical object with known geometry and refractive index. The object is immersed in three liquids of different refractive index to produce varying degrees of weak scattering. In each case the reconstructed size, shape, and refractive index are in good agreement with the known characteristics. This shows that quantitative images of transparent, cylindrical objects can be obtained by ODT. The images obtained from experimental data were also shown to be in good agreement with those obtained from computer-simulated data, thus verifying our computer simulations.

© 1995 Optical Society of America

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References

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  1. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).
  2. 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 UFFC-38, 370–379 (1991).
    [CrossRef]
  3. N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).
  4. L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
    [CrossRef]
  5. M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
    [CrossRef]
  6. 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]
  7. T. C. Wedberg, “Quantitative phase microscopy by two-dimensional optical diffraction tomography,” Ph.D. dissertation (University of Bergen, Bergen, Norway, 1994).
  8. T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. (to be published).
  9. I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
    [CrossRef]
  10. 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, 1991), Vol. 18, pp. 401–411.
    [CrossRef]
  11. 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]
  12. A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
    [CrossRef]
  13. A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
    [CrossRef] [PubMed]
  14. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

1994 (1)

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

1993 (1)

1992 (2)

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[CrossRef]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[CrossRef]

1991 (2)

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[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 UFFC-38, 370–379 (1991).
[CrossRef]

1989 (1)

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

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,” Ultrason. Imag. 4, 336–350 (1982).

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]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[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,” Ultrason. Imag. 4, 336–350 (1982).

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, 1991), Vol. 18, pp. 401–411.
[CrossRef]

Gelius, L.-J.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[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 UFFC-38, 370–379 (1991).
[CrossRef]

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[CrossRef]

Johansen, I.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[CrossRef]

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[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 UFFC-38, 370–379 (1991).
[CrossRef]

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, 1991), Vol. 18, pp. 401–411.
[CrossRef]

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]

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.

Schatzberg, A.

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]

Spjelkavik, B.

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[CrossRef]

Sponheim, N.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[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 UFFC-38, 370–379 (1991).
[CrossRef]

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[CrossRef]

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, 1991), Vol. 18, pp. 401–411.
[CrossRef]

Stamnes, J. J.

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[CrossRef]

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[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 UFFC-38, 370–379 (1991).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. (to be published).

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

Wedberg, T. C.

T. C. Wedberg, “Quantitative phase microscopy by two-dimensional optical diffraction tomography,” Ph.D. dissertation (University of Bergen, Bergen, Norway, 1994).

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. (to be published).

Acoust. Imag. (1)

I. Johansen, L.-J. Gelius, B. Spjelkavik, N. Sponheim, J. J. Stamnes, “Exact and approximate scattering data for testing the filtered backpropagation (FBP) and a hybrid FBP reconstruction algorithm,” Acoust. Imag. 19, 17–22 (1992).
[CrossRef]

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 UFFC-38, 370–379 (1991).
[CrossRef]

J. Acoust. Soc. Am. (1)

L.-J. Gelius, I. Johansen, N. Sponheim, J. J. Stamnes, “A generalized diffraction tomography algorithm,” J. Acoust. Soc. Am. 89, 523–528 (1991).
[CrossRef]

J. Opt. Soc. Am. A (2)

Phys. Rev. Lett. (1)

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

Ultrason. Imag. (2)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).

N. Sponheim, L.-J. Gelius, I. Johansen, J. J. Stamnes, “Ultrasonic tomography of biological tissue,” Ultrason. Imag. 16, 19–32 (1994).

Other (4)

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, 1991), Vol. 18, pp. 401–411.
[CrossRef]

T. C. Wedberg, “Quantitative phase microscopy by two-dimensional optical diffraction tomography,” Ph.D. dissertation (University of Bergen, Bergen, Norway, 1994).

T. C. Wedberg, J. J. Stamnes, “Comparison of phase-retrieval methods for optical diffraction tomography,” Pure Appl. Opt. (to be published).

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

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Figures (10)

Fig. 1
Fig. 1

Classical scan configuration.

Fig. 2
Fig. 2

Experimental setup used for ODT.

Fig. 3
Fig. 3

Recorded relative intensity distributions for a refractive index in the immersion medium of (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was n = 1.546.

Fig. 4
Fig. 4

Real part of the reconstructed refractive index for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was n = 1.546.

Fig. 5
Fig. 5

Diametrical sections of the real part of the reconstructed refractive index for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was n = 1.546.

Fig. 6
Fig. 6

Imaginary parts of the reconstructed refractive index for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was n = 1.546.

Fig. 7
Fig. 7

Real part of the refractive index reconstructed from Born data for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was n = 1.546.

Fig. 8
Fig. 8

Real part of the refractive index reconstructed from simulated data for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was assumed to be n = 1.546.

Fig. 9
Fig. 9

Diametrical sections of the real part of refractive index reconstructed from simulated data for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was assumed to be n = 1.546.

Fig. 10
Fig. 10

Imaginary parts of the refractive index reconstructed from simulated data for (a) n0 = 1.493, (b) n0 = 1.521, and (c) n0 = 1.557. The refractive index of the object was assumed to be n = 1.546.

Tables (1)

Tables Icon

Table 1 Comparison of the FWHM Value d0, the Average Refractive Index n ¯ re, and the rms Error Δnre Obtained from Experimental and Simulated Images for Various n0

Equations (2)

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D ( r ) = 1 i k ln U ( r ) U 0 ( r ) .
Δ n re = { 1 N r A [ n ¯ re - n re ( r ) ] 2 } 1 / 2 ,

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