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

[CrossRef]
[PubMed]

See, for example, H. A. Hauptman, “The phase problem of X-ray crystallography,” Phys. Today 42(11), 24–29 (1990); R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).

[CrossRef]

S. Kawata, O. Nakamura, T. Noda, H. Ooki, K. Ogino, Y. Kuroiwa, S. Minami, “Laser computed-tomography microscope,” Appl. Opt. 29, 3805–3809 (1990).

[CrossRef]
[PubMed]

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).

[CrossRef]

J. S. Jaffe, R. Fricke, “Constrained reconstruction of complex waveforms,” J. Opt. Soc. Am. A 4, 216–220 (1987).

[CrossRef]

I. H. Lira, C. M. Vest, “Refraction correction in holographic interferometry and tomography of transparent objects,” Appl. Opt. 26, 3919–3928 (1987).

[CrossRef]
[PubMed]

M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D 19, 301–317 (1986).

[CrossRef]

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).

[CrossRef]

S. X. Pan, A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1262–1275 (1983).

[CrossRef]

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

L. S. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. AP-29, 386–391 (1981).

[CrossRef]

J. F. Greenleaf, R. C. Bah, “Clinical imaging with transmissive ultrasonic computerized tomography,” IEEE Trans. Biomed. Eng. BME-28, 496–505 (1981).

[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. Inst. Electr. Eng. 67, 567–587 (1979).

[CrossRef]

A. C. Kak, “Computerized tomography with x-ray emission and ultrasound sources,” Proc. IEEE 67, 1245–1272 (1979).

[CrossRef]

A. F. Fercher, H. Bartelt, H. Becker, E. Wiltschko, “Image formation by inversion of scattered field data: experiments and computational simulation,” Appl. Opt. 18, 2427–2439 (1979).

[CrossRef]
[PubMed]

J. M. Tribolet, “A new phase unwrapping algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-26, 170–177 (1977).

[CrossRef]

K. Iwata, R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov approximation,” Jpn J. Appl. Phys. 14(Suppl. 14-1), 379–383 (1975).

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).

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).

[CrossRef]

J. F. Greenleaf, R. C. Bah, “Clinical imaging with transmissive ultrasonic computerized tomography,” IEEE Trans. Biomed. Eng. BME-28, 496–505 (1981).

[CrossRef]

H. Lipson, W. Cochran, The Determination of Crystal Structures (Cornell U. Press, Ithaca, N.Y, 1966).

D. Colton, P. Monk, “The inverse scattering problem for acoustic waves in an inhomogeneous medium,” in Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, W. Rundell, eds. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).

J. M. Cowley, Diffraction Physics, 2nd rev. ed. (North-Holland, New York, 1981).

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).

[CrossRef]

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

A. Schatzberg, A. J. Devaney, “An optical microscope for imaging three dimensional semi-transparent structures,” Final Project Rep. Small Business Innovation Research Phase I National Science Foundation grant ISI-8960413 (National Science Foundation, Washington, D.C., 1990).

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.

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]

M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D 19, 301–317 (1986).

[CrossRef]

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).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. F. Greenleaf, R. C. Bah, “Clinical imaging with transmissive ultrasonic computerized tomography,” IEEE Trans. Biomed. Eng. BME-28, 496–505 (1981).

[CrossRef]

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

See, for example, H. A. Hauptman, “The phase problem of X-ray crystallography,” Phys. Today 42(11), 24–29 (1990); R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).

[CrossRef]

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

K. Iwata, R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov approximation,” Jpn J. Appl. Phys. 14(Suppl. 14-1), 379–383 (1975).

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.

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

S. X. Pan, A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1262–1275 (1983).

[CrossRef]

A. C. Kak, “Computerized tomography with x-ray emission and ultrasound sources,” Proc. IEEE 67, 1245–1272 (1979).

[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. Inst. Electr. Eng. 67, 567–587 (1979).

[CrossRef]

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

H. Lipson, W. Cochran, The Determination of Crystal Structures (Cornell U. Press, Ithaca, N.Y, 1966).

D. Colton, P. Monk, “The inverse scattering problem for acoustic waves in an inhomogeneous medium,” in Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, W. Rundell, eds. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. Inst. Electr. Eng. 67, 567–587 (1979).

[CrossRef]

K. Iwata, R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov approximation,” Jpn J. Appl. Phys. 14(Suppl. 14-1), 379–383 (1975).

S. X. Pan, A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1262–1275 (1983).

[CrossRef]

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).

A. Schatzberg, A. J. Devaney, “An optical microscope for imaging three dimensional semi-transparent structures,” Final Project Rep. Small Business Innovation Research Phase I National Science Foundation grant ISI-8960413 (National Science Foundation, Washington, D.C., 1990).

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. 28.

[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, 1990), Vol. 18.

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

L. S. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. AP-29, 386–391 (1981).

[CrossRef]

J. M. Tribolet, “A new phase unwrapping algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-26, 170–177 (1977).

[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. Inst. Electr. Eng. 67, 567–587 (1979).

[CrossRef]

E. Wolf, “Determination of the amplitude and the phase of the scattered field by holography,” J. Opt. Soc. Am. 60, 18–20 (1970).

[CrossRef]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).

[CrossRef]

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]

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

D. W. Sweeney, C. M. Vest, “Reconstruction of three-dimensional refractive index fields from multidimensional interferometric data,” Appl. Opt. 12, 2649–2664 (1973).

[CrossRef]
[PubMed]

W. H. Carter, P.-C. Ho, “Reconstruction of inhomogeneous scattering objects from holograms,” Appl. Opt. 13, 162–172 (1974); A. Gretzula, W. H. Carter, “Structural measurements by inverse scattering in the Rytov approximation,” J. Opt. Soc. Am. A 2, 1958–1960 (1985).

[CrossRef]
[PubMed]

A. F. Fercher, H. Bartelt, H. Becker, E. Wiltschko, “Image formation by inversion of scattered field data: experiments and computational simulation,” Appl. Opt. 18, 2427–2439 (1979).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

I. H. Lira, C. M. Vest, “Refraction correction in holographic interferometry and tomography of transparent objects,” Appl. Opt. 26, 3919–3928 (1987).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

S. Kawata, O. Nakamura, T. Noda, H. Ooki, K. Ogino, Y. Kuroiwa, S. Minami, “Laser computed-tomography microscope,” Appl. Opt. 29, 3805–3809 (1990).

[CrossRef]
[PubMed]

J. M. Tribolet, “A new phase unwrapping algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-26, 170–177 (1977).

[CrossRef]

S. X. Pan, A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1262–1275 (1983).

[CrossRef]

L. S. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. AP-29, 386–391 (1981).

[CrossRef]

J. F. Greenleaf, R. C. Bah, “Clinical imaging with transmissive ultrasonic computerized tomography,” IEEE Trans. Biomed. Eng. BME-28, 496–505 (1981).

[CrossRef]

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

[CrossRef]
[PubMed]

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).

[CrossRef]

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]

E. Wolf, “Determination of the amplitude and the phase of the scattered field by holography,” J. Opt. Soc. Am. 60, 18–20 (1970).

[CrossRef]

M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D 19, 301–317 (1986).

[CrossRef]

K. Iwata, R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov approximation,” Jpn J. Appl. Phys. 14(Suppl. 14-1), 379–383 (1975).

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).

[CrossRef]

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).

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

[CrossRef]
[PubMed]

See, for example, H. A. Hauptman, “The phase problem of X-ray crystallography,” Phys. Today 42(11), 24–29 (1990); R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).

[CrossRef]

A. C. Kak, “Computerized tomography with x-ray emission and ultrasound sources,” Proc. IEEE 67, 1245–1272 (1979).

[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. Inst. Electr. Eng. 67, 567–587 (1979).

[CrossRef]

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

H. Lipson, W. Cochran, The Determination of Crystal Structures (Cornell U. Press, Ithaca, N.Y, 1966).

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]

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

J. M. Cowley, Diffraction Physics, 2nd rev. ed. (North-Holland, New York, 1981).

The radius of the Ewald limiting circle differs from its value of 2kin x-ray crystallography because only forward-scattered radiation is measured in DT.

J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, E. H. Wood, “Algebraic reconstruction of spatial distributions of acoustic absorption in tissues from their two-dimensional acoustic projections,” in Acoustical Holography, P. S. Green, ed. (Plenum, New York, 1974), Vol. 5, 591–603.

[CrossRef]

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. 28.

[CrossRef]

A. Schatzberg, A. J. Devaney, “An optical microscope for imaging three dimensional semi-transparent structures,” Final Project Rep. Small Business Innovation Research Phase I National Science Foundation grant ISI-8960413 (National Science Foundation, Washington, D.C., 1990).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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.

D. Colton, P. Monk, “The inverse scattering problem for acoustic waves in an inhomogeneous medium,” in Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, W. Rundell, eds. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).

The intensity profile for this fiber was also computed with an exact eigenfunction-based method and was found to coincide almost exactly with that computed with the hybrid method.