Abstract

A new approach for quantitative electromagnetic imaging of scatterers located in free space from phaseless data is proposed and discussed. The procedure splits the problem into two steps. In the first one, we solve a phase-retrieval problem for the total field, thus estimating the amplitude and phase of the scattered field. Careful analysis of properties and possible representations of both scattered and incident fields allow us to introduce a criterion for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step by use of the estimated scattered field. Numerical examples are provided to check the whole chain in the presence of noise-corrupted data.

© 2004 Optical Society of America

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  1. D. Colton, P. Monk, “The detection and monitoring of leukemia using electromagnetic waves: mathematical theory,” Inverse Probl. 10, 1235–1251 (1994).
    [CrossRef]
  2. P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
    [CrossRef] [PubMed]
  3. O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
    [CrossRef]
  4. D. J. Daniels, “Surface-penetrating radar,” IEEE Electron. Commun. Eng. J. 8, 165–182 (1996).
    [CrossRef]
  5. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3–13 (1984).
    [CrossRef]
  6. M. Moghaddam, W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
    [CrossRef]
  7. E. Wolf, “Determination of the amplitude and the phase of scattered fields by holography,” J. Opt. Soc. Am. 60, 18–20 (1970).
    [CrossRef]
  8. G. W. Faris, H. M. Hertz, “Tunable differential interferometer for optical tomography,” Appl. Opt. 28, 4662–4667 (1989).
    [CrossRef] [PubMed]
  9. O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
    [CrossRef]
  10. M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 10, 1356–1363 (1992).
    [CrossRef]
  11. M. H. Maleki, A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithms from optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
    [CrossRef]
  12. T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
    [CrossRef]
  13. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988), pp. 203–273.
  14. T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “Role of the support and zero locations in phase retrieval by a quadratic approach,” J. Opt. Soc. Am. A 16, 1845–1856 (1999).
    [CrossRef]
  15. I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.
  16. T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
    [CrossRef]
  17. T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
    [CrossRef]
  18. L. Crocco, T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Probl. 17, 1573–1583 (2001).
    [CrossRef]
  19. O. M. Bucci, N. Cardace, L. Crocco, T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
    [CrossRef]
  20. O. M. Bucci, L. Crocco, T. Isernia, “A step-wise approach to inverse scattering problems,” in Proceedings of XXIV General Assembly of the International Union of Radio Science (URSI) (URSI, Ghent, Belgium, 2002; on CD-ROM).
  21. D. Colton, R. Krees, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlang, Berlin, Germany, 1992).
  22. R. Barakat, G. Newsam, “Necessary conditions for an unique solution to two-dimensional phase recovery,” J. Math. Phys. 25, 3190–3193 (1984).
    [CrossRef]
  23. J. L. C. Sanz, T. S. Huang, “Unique reconstruction of a band-limited multidimensional signal from its phase or magnitude,” J. Opt. Soc. Am. 73, 1446–1450 (1983).
    [CrossRef]
  24. P. Debye, “Das Verhalten von Lichtwellen in der Nahe eines Brenpunktes oder einer Brennlinie,” Ann. P. Physik 4, 30–57 (1909).
  25. O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
    [CrossRef]
  26. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
    [CrossRef]
  27. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform pairs from noisy data using a support constraint,” J. Opt. Soc. Am. A 4, 118–124 (1987).
    [CrossRef]
  28. R. Barakat, G. Newsam, “Algorithms for reconstruction of partially known, band-limited Fourier transform pairs from noisy data II. The non-linear problem of phase retrieval,” J. Integr. Eq. 9 (suppl.), 77–125 (1985).
  29. M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D 19, 301–317 (1986).
    [CrossRef]
  30. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).
    [CrossRef]
  31. R. Harrison, “Phase retrieval in crystallography,” J. Opt. Soc. Am. A 7, 1046–1055 (1990).
  32. D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
    [CrossRef]
  33. J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).
  34. O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
    [CrossRef]
  35. T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
    [CrossRef]
  36. R. G. Yaccarino, Y. Rahmat-Samii, “Phaseless bi-polar planar near-field measurements and diagnostics of array antennas,” IEEE Trans. Antennas Propag. 47, 574–583 (1999).
    [CrossRef]
  37. F. Las-Heras, T. K. Sarkar, “A direct optimization approach for source reconstruction and NF–FF transformation using amplitude-only data,” IEEE Trans. Antennas Propag. 50, 500–510 (2002).
    [CrossRef]
  38. W. Chalodhorn, D. R. DeBoer, “Uses of microwave lenses in phase retrieval microwave holography of reflector antennas,” IEEE Trans. Antennas Propag. 50, 1274–1284 (2002).
    [CrossRef]
  39. J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. 47, 334–341 (1964).
  40. O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
    [CrossRef]
  41. P. M. van den Berg, R. E. Kleinman, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
    [CrossRef]

2002

F. Las-Heras, T. K. Sarkar, “A direct optimization approach for source reconstruction and NF–FF transformation using amplitude-only data,” IEEE Trans. Antennas Propag. 50, 500–510 (2002).
[CrossRef]

W. Chalodhorn, D. R. DeBoer, “Uses of microwave lenses in phase retrieval microwave holography of reflector antennas,” IEEE Trans. Antennas Propag. 50, 1274–1284 (2002).
[CrossRef]

2001

O. M. Bucci, N. Cardace, L. Crocco, T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

L. Crocco, T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Probl. 17, 1573–1583 (2001).
[CrossRef]

2000

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

1999

R. G. Yaccarino, Y. Rahmat-Samii, “Phaseless bi-polar planar near-field measurements and diagnostics of array antennas,” IEEE Trans. Antennas Propag. 47, 574–583 (1999).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “Role of the support and zero locations in phase retrieval by a quadratic approach,” J. Opt. Soc. Am. A 16, 1845–1856 (1999).
[CrossRef]

1998

O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
[CrossRef]

1997

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
[CrossRef]

1996

D. J. Daniels, “Surface-penetrating radar,” IEEE Electron. Commun. Eng. J. 8, 165–182 (1996).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
[CrossRef]

1995

P. M. van den Berg, R. E. Kleinman, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

1994

D. Colton, P. Monk, “The detection and monitoring of leukemia using electromagnetic waves: mathematical theory,” Inverse Probl. 10, 1235–1251 (1994).
[CrossRef]

1993

1992

M. Moghaddam, W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 10, 1356–1363 (1992).
[CrossRef]

1990

R. Harrison, “Phase retrieval in crystallography,” J. Opt. Soc. Am. A 7, 1046–1055 (1990).

J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).
[CrossRef]

1989

1987

1986

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

1985

R. Barakat, G. Newsam, “Algorithms for reconstruction of partially known, band-limited Fourier transform pairs from noisy data II. The non-linear problem of phase retrieval,” J. Integr. Eq. 9 (suppl.), 77–125 (1985).

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

1984

J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3–13 (1984).
[CrossRef]

R. Barakat, G. Newsam, “Necessary conditions for an unique solution to two-dimensional phase recovery,” J. Math. Phys. 25, 3190–3193 (1984).
[CrossRef]

1983

1973

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

1970

1964

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. 47, 334–341 (1964).

1909

P. Debye, “Das Verhalten von Lichtwellen in der Nahe eines Brenpunktes oder einer Brennlinie,” Ann. P. Physik 4, 30–57 (1909).

Anderson, A. P.

J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).

Barakat, R.

R. Barakat, G. Newsam, “Algorithms for reconstruction of partially known, band-limited Fourier transform pairs from noisy data II. The non-linear problem of phase retrieval,” J. Integr. Eq. 9 (suppl.), 77–125 (1985).

R. Barakat, G. Newsam, “Necessary conditions for an unique solution to two-dimensional phase recovery,” J. Math. Phys. 25, 3190–3193 (1984).
[CrossRef]

Bucci, O. M.

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

O. M. Bucci, N. Cardace, L. Crocco, T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
[CrossRef]

O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
[CrossRef]

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, “A step-wise approach to inverse scattering problems,” in Proceedings of XXIV General Assembly of the International Union of Radio Science (URSI) (URSI, Ghent, Belgium, 2002; on CD-ROM).

Cardace, N.

Catapano, I.

I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.

Chalodhorn, W.

W. Chalodhorn, D. R. DeBoer, “Uses of microwave lenses in phase retrieval microwave holography of reflector antennas,” IEEE Trans. Antennas Propag. 50, 1274–1284 (2002).
[CrossRef]

Chew, W. C.

M. Moghaddam, W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

Colton, D.

D. Colton, P. Monk, “The detection and monitoring of leukemia using electromagnetic waves: mathematical theory,” Inverse Probl. 10, 1235–1251 (1994).
[CrossRef]

D. Colton, R. Krees, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlang, Berlin, Germany, 1992).

Crocco, L.

O. M. Bucci, N. Cardace, L. Crocco, T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

L. Crocco, T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Probl. 17, 1573–1583 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, “A step-wise approach to inverse scattering problems,” in Proceedings of XXIV General Assembly of the International Union of Radio Science (URSI) (URSI, Ghent, Belgium, 2002; on CD-ROM).

I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.

D’Elia, G.

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

D’Urso, M.

I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.

Daniels, D. J.

D. J. Daniels, “Surface-penetrating radar,” IEEE Electron. Commun. Eng. J. 8, 165–182 (1996).
[CrossRef]

DeBoer, D. R.

W. Chalodhorn, D. R. DeBoer, “Uses of microwave lenses in phase retrieval microwave holography of reflector antennas,” IEEE Trans. Antennas Propag. 50, 1274–1284 (2002).
[CrossRef]

Debye, P.

P. Debye, “Das Verhalten von Lichtwellen in der Nahe eines Brenpunktes oder einer Brennlinie,” Ann. P. Physik 4, 30–57 (1909).

Devaney, A. J.

M. H. Maleki, A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithms from 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 10, 1356–1363 (1992).
[CrossRef]

Devaney, J.

J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3–13 (1984).
[CrossRef]

Faris, G. W.

Fiddy, M. A.

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

Fienup, J. R.

Gennarelli, C.

O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
[CrossRef]

Harada, H.

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

Harrison, R.

R. Harrison, “Phase retrieval in crystallography,” J. Opt. Soc. Am. A 7, 1046–1055 (1990).

Hartow, A.

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

Hertz, H. M.

Huang, T. S.

Isernia, T.

T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

O. M. Bucci, N. Cardace, L. Crocco, T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

L. Crocco, T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Probl. 17, 1573–1583 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “Role of the support and zero locations in phase retrieval by a quadratic approach,” J. Opt. Soc. Am. A 16, 1845–1856 (1999).
[CrossRef]

O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, “A step-wise approach to inverse scattering problems,” in Proceedings of XXIV General Assembly of the International Union of Radio Science (URSI) (URSI, Ghent, Belgium, 2002; on CD-ROM).

I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.

Junkin, G.

J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988), pp. 203–273.

Kleinman, R. E.

P. M. van den Berg, R. E. Kleinman, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

Krees, R.

D. Colton, R. Krees, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlang, Berlin, Germany, 1992).

Krone, R. K.

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

Las-Heras, F.

F. Las-Heras, T. K. Sarkar, “A direct optimization approach for source reconstruction and NF–FF transformation using amplitude-only data,” IEEE Trans. Antennas Propag. 50, 500–510 (2002).
[CrossRef]

Leone, G.

T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “Role of the support and zero locations in phase retrieval by a quadratic approach,” J. Opt. Soc. Am. A 16, 1845–1856 (1999).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
[CrossRef]

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

Maleki, M. H.

M. H. Maleki, A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithms from 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 10, 1356–1363 (1992).
[CrossRef]

McCormack, J. E.

J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).

Meaney, P. M.

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

Millane, R. P.

Misell, D. L.

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

Moghaddam, M.

M. Moghaddam, W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

Monk, P.

D. Colton, P. Monk, “The detection and monitoring of leukemia using electromagnetic waves: mathematical theory,” Inverse Probl. 10, 1235–1251 (1994).
[CrossRef]

Morris, D.

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

Newsam, G.

R. Barakat, G. Newsam, “Algorithms for reconstruction of partially known, band-limited Fourier transform pairs from noisy data II. The non-linear problem of phase retrieval,” J. Integr. Eq. 9 (suppl.), 77–125 (1985).

R. Barakat, G. Newsam, “Necessary conditions for an unique solution to two-dimensional phase recovery,” J. Math. Phys. 25, 3190–3193 (1984).
[CrossRef]

Pascazio, V.

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

Paulsen, K. D.

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

Pierri, R.

T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “Role of the support and zero locations in phase retrieval by a quadratic approach,” J. Opt. Soc. Am. A 16, 1845–1856 (1999).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
[CrossRef]

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

Rahmat-Samii, Y.

R. G. Yaccarino, Y. Rahmat-Samii, “Phaseless bi-polar planar near-field measurements and diagnostics of array antennas,” IEEE Trans. Antennas Propag. 47, 574–583 (1999).
[CrossRef]

Richmond, J. H.

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. 47, 334–341 (1964).

Sanz, J. L. C.

Sarkar, T. K.

F. Las-Heras, T. K. Sarkar, “A direct optimization approach for source reconstruction and NF–FF transformation using amplitude-only data,” IEEE Trans. Antennas Propag. 50, 500–510 (2002).
[CrossRef]

Savarese, C.

O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
[CrossRef]

Schatzberg, A.

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 10, 1356–1363 (1992).
[CrossRef]

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988), pp. 203–273.

Soldovieri, F.

Takenaka, T.

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

Tanaka, M.

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

van den Berg, P. M.

P. M. van den Berg, R. E. Kleinman, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

Wall, D. J. N.

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

Wolf, E.

Yaccarino, R. G.

R. G. Yaccarino, Y. Rahmat-Samii, “Phaseless bi-polar planar near-field measurements and diagnostics of array antennas,” IEEE Trans. Antennas Propag. 47, 574–583 (1999).
[CrossRef]

Ann. P. Physik

P. Debye, “Das Verhalten von Lichtwellen in der Nahe eines Brenpunktes oder einer Brennlinie,” Ann. P. Physik 4, 30–57 (1909).

Appl. Opt.

IEE Proc. Part H: Microwaves, Antennas Propag.

J. E. McCormack, G. Junkin, A. P. Anderson, “Micro- wave metrology of reflector antennas from a single amplitude,” IEE Proc. Part H: Microwaves, Antennas Propag. 137, 276–284 (1990).

IEEE Electron. Commun. Eng. J.

D. J. Daniels, “Surface-penetrating radar,” IEEE Electron. Commun. Eng. J. 8, 165–182 (1996).
[CrossRef]

IEEE Trans. Antennas Propag.

O. M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Propag. 46, 351–359 (1998).
[CrossRef]

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

O. M. Bucci, G. D’Elia, G. Leone, R. Pierri, “Far-field pattern determination from the near-field amplitude on two surfaces,” IEEE Trans. Antennas Propag. 38, 1772–1779 (1990).
[CrossRef]

T. Isernia, G. Leone, R. Pierri, “Radiation pattern evaluation from near-field intensities on planes,” IEEE Trans. Antennas Propag. 44, 701–710 (1996).
[CrossRef]

R. G. Yaccarino, Y. Rahmat-Samii, “Phaseless bi-polar planar near-field measurements and diagnostics of array antennas,” IEEE Trans. Antennas Propag. 47, 574–583 (1999).
[CrossRef]

F. Las-Heras, T. K. Sarkar, “A direct optimization approach for source reconstruction and NF–FF transformation using amplitude-only data,” IEEE Trans. Antennas Propag. 50, 500–510 (2002).
[CrossRef]

W. Chalodhorn, D. R. DeBoer, “Uses of microwave lenses in phase retrieval microwave holography of reflector antennas,” IEEE Trans. Antennas Propag. 50, 1274–1284 (2002).
[CrossRef]

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. 47, 334–341 (1964).

IEEE Trans. Biomed. Eng.

P. M. Meaney, K. D. Paulsen, A. Hartow, R. K. Krone, “An active microwave imaging system for reconstruction of 2-D electrical property distributions,” IEEE Trans. Biomed. Eng. 42, 1017–1026 (1995).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens.

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information,” IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001).
[CrossRef]

J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3–13 (1984).
[CrossRef]

M. Moghaddam, W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
[CrossRef]

Inverse Probl.

P. M. van den Berg, R. E. Kleinman, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

L. Crocco, T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Probl. 17, 1573–1583 (2001).
[CrossRef]

D. Colton, P. Monk, “The detection and monitoring of leukemia using electromagnetic waves: mathematical theory,” Inverse Probl. 10, 1235–1251 (1994).
[CrossRef]

J. Integr. Eq.

R. Barakat, G. Newsam, “Algorithms for reconstruction of partially known, band-limited Fourier transform pairs from noisy data II. The non-linear problem of phase retrieval,” J. Integr. Eq. 9 (suppl.), 77–125 (1985).

J. Math. Phys.

R. Barakat, G. Newsam, “Necessary conditions for an unique solution to two-dimensional phase recovery,” J. Math. Phys. 25, 3190–3193 (1984).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

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

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

Microwave Opt. Technol. Lett.

T. Takenaka, D. J. N. Wall, H. Harada, M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[CrossRef]

Radio Sci.

O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
[CrossRef]

Other

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988), pp. 203–273.

I. Catapano, L. Crocco, M. D’Urso, T. Isernia, “Advances in microwave tomography: phaseless measurements and layered backgrounds,” in Proceedings of the Second International Workshop on Advanced Ground Penetrating Radar, A. Yarovoy, ed. (International Research Centre for Telecommunications-Transmission and Radar, Delft University of Technology, The Netherlands, 2003), pp. 183–188.

O. M. Bucci, L. Crocco, T. Isernia, “A step-wise approach to inverse scattering problems,” in Proceedings of XXIV General Assembly of the International Union of Radio Science (URSI) (URSI, Ghent, Belgium, 2002; on CD-ROM).

D. Colton, R. Krees, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlang, Berlin, Germany, 1992).

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