Abstract

A recently developed inverse scattering algorithm [ A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004) ] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm, in applications employing a limited number of scattering experiments (the so-called limited-view case) and also in cases where multiple scattering occurs between the object being interrogated and the (known) background in which the object is embedded. The new algorithm is compared and contrasted with the filtered backpropagation algorithm in a computer simulation of ODT of weakly inhomogeneous cylindrical objects being interrogated in a limited number of scattering experiments employing incident plane waves. Our study has potential applications in biomedical imaging and tomographic microscopy.

© 2005 Optical Society of America

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  1. A. J. Devaney, M. Maleki, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
    [CrossRef]
  2. 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]
  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]
  4. M. Maleki, A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithm for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
    [CrossRef]
  5. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).
    [CrossRef] [PubMed]
  6. A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. GE- 22, 3–12 (1984).
    [CrossRef]
  7. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  8. A. J. Devaney, M. Dennison, “Inverse scattering in inhomogeneous background media,” Inverse Probl. 19, 855–870 (2003).
    [CrossRef]
  9. M. Dennison, A. J. Devaney, “Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation,” Inverse Probl. 20, 1307–1324 (2004).
    [CrossRef]
  10. J. H. Taylor, Scattering Theory (Wiley, 1972).
  11. T. J. Hall, A. M. Darling, M. A. Fiddy, “Image compression and restoration incorporating prior knowledge,” Opt. Lett. 7, 467–468 (1982).
    [CrossRef] [PubMed]
  12. C. L. Byme, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, A. M. Darling, “Image restoration and resolution enhancement,” J. Opt. Soc. Am. 73, 1481–1487 (1983).
    [CrossRef]
  13. P. Guo, A. J. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004).
    [CrossRef] [PubMed]
  14. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction phase pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  15. R. A. Gonsalves, “Phase retrieval from modulus data,” J. Opt. Soc. Am. 66, 961–964 (1976).
    [CrossRef]
  16. A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. 30, 377–386 (1983).
    [CrossRef] [PubMed]
  17. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

2004 (2)

M. Dennison, A. J. Devaney, “Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation,” Inverse Probl. 20, 1307–1324 (2004).
[CrossRef]

P. Guo, A. J. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004).
[CrossRef] [PubMed]

2003 (1)

A. J. Devaney, M. Dennison, “Inverse scattering in inhomogeneous background media,” Inverse Probl. 19, 855–870 (2003).
[CrossRef]

1995 (2)

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

1993 (1)

1992 (1)

1984 (1)

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. GE- 22, 3–12 (1984).
[CrossRef]

1983 (2)

1982 (2)

T. J. Hall, A. M. Darling, M. A. Fiddy, “Image compression and restoration incorporating prior knowledge,” Opt. Lett. 7, 467–468 (1982).
[CrossRef] [PubMed]

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

1976 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction phase pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Born, M.

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

Byme, C. L.

Darling, A. M.

Dennison, M.

M. Dennison, A. J. Devaney, “Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation,” Inverse Probl. 20, 1307–1324 (2004).
[CrossRef]

A. J. Devaney, M. Dennison, “Inverse scattering in inhomogeneous background media,” Inverse Probl. 19, 855–870 (2003).
[CrossRef]

Devaney, A. J.

M. Dennison, A. J. Devaney, “Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation,” Inverse Probl. 20, 1307–1324 (2004).
[CrossRef]

P. Guo, A. J. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004).
[CrossRef] [PubMed]

A. J. Devaney, M. Dennison, “Inverse scattering in inhomogeneous background media,” Inverse Probl. 19, 855–870 (2003).
[CrossRef]

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

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

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. GE- 22, 3–12 (1984).
[CrossRef]

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

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

Fiddy, M. A.

Fitzgerald, R. M.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction phase pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Gonsalves, R. A.

Guo, P.

Hall, T. J.

Kak, A. C.

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

Maleki, M.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction phase pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Schatzberg, A.

Slaney, M.

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

Stamnes, J. J.

Taylor, J. H.

J. H. Taylor, Scattering Theory (Wiley, 1972).

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

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.

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

IEEE Trans. Biomed. Eng. (1)

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

IEEE Trans. Geosci. Remote Sens. (1)

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. GE- 22, 3–12 (1984).
[CrossRef]

Inverse Probl. (2)

A. J. Devaney, M. Dennison, “Inverse scattering in inhomogeneous background media,” Inverse Probl. 19, 855–870 (2003).
[CrossRef]

M. Dennison, A. J. Devaney, “Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation,” Inverse Probl. 20, 1307–1324 (2004).
[CrossRef]

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. (2)

J. Opt. Soc. Am. A (3)

Opt. Lett. (2)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction phase pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Ultrason. Imaging (1)

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

Other (3)

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

J. H. Taylor, Scattering Theory (Wiley, 1972).

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

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