Abstract

In tomography algorithms, the complex amplitude scattering matrix corresponds to the input parameter. When considering 3D targets, the scattering matrix now contains vectorial information. Thus, this scattering matrix might be calculated with various polarization projections. Moreover, when dealing with experimental data, we are almost every time faced with truncated data. We focus here on the impact of selecting parts of the amplitude scattering matrix elements versus others and in particular on the influence of the polarization choices on the imaging results. In order to better apprehend the physical content associated to each polarization term, the study is conducted with a simple vectorial-induced current reconstruction algorithm allowing reconstruction of qualitative maps of the scene. This algorithm is applied on scaled models of aggregates combined with experimental scattered fields acquired in the microwave frequency range.

© 2013 Optical Society of America

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  1. O. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
    [CrossRef]
  2. J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
    [CrossRef]
  3. S. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
    [CrossRef]
  4. A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
    [CrossRef]
  5. S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
    [CrossRef]
  6. M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  7. O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
    [CrossRef]
  8. G. Videen, Y. Yatskiv, and M. Mishchenko, “Photopolarimetry in remote sensing,” in Proceedings of the NATO Advanced Study Institute (2003).
  9. C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
    [CrossRef]
  10. R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
    [CrossRef]
  11. O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
    [CrossRef]
  12. G. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  13. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).
  14. D. Zwillinger, CRC Standard Mathematical Tables and Formulae (Chapman and Hall, 2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
    [CrossRef]
  21. C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
    [CrossRef]
  22. C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
    [CrossRef]
  23. W. Wang, J. Li, and F. Niu, “A revisit to the validity of Born approximation in high frequency scattering problems,” Microw. Opt. Technol. Lett. 54, 2792–2797 (2012).
    [CrossRef]
  24. C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
    [CrossRef]

2013 (1)

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

2012 (1)

W. Wang, J. Li, and F. Niu, “A revisit to the validity of Born approximation in high frequency scattering problems,” Microw. Opt. Technol. Lett. 54, 2792–2797 (2012).
[CrossRef]

2011 (3)

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

2010 (1)

2009 (5)

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, and M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef]

J.-M. Geffrin and P. Sabouroux, “Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements,” Inverse Probl. 25, 024001 (2009).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
[CrossRef]

C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
[CrossRef]

2008 (1)

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

2006 (1)

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

2001 (1)

2000 (1)

1997 (1)

O. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

1996 (1)

S. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[CrossRef]

1995 (1)

P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
[CrossRef]

Arnaubec, A.

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

Badizadegan, K.

Bellez, S.

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

Bohren, G.

G. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bucci, O.

O. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

Castelli, J.

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

Chaumet, P. C.

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

Cheraly, A.

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

Choi, W.

Cloude, S.

S. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[CrossRef]

Coté, M. G.

P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
[CrossRef]

Dahon, C.

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

Dasari, R.

Devaney, A.

A. Devaney, Mathematical Foundations of Imaging, Tomography and Wavefield Inversion (Cambridge University, 2012).

Dubois-Fernandez, P.-C.

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

Eyraud, C.

C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
[CrossRef]

C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

Fang-Yen, C.

Feld, M.

Geffrin, J.-M.

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

J.-M. Geffrin and P. Sabouroux, “Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements,” Inverse Probl. 25, 024001 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

Giovannini, H.

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

Gurg, G.

Hérique, A.

C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
[CrossRef]

Huffman, D.

G. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Isernia, T.

O. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

Kak, A.

A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).

Kleinman, R. E.

P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
[CrossRef]

Kofman, W.

C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
[CrossRef]

Lacis, A.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lacroix, B.

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

Li, J.

W. Wang, J. Li, and F. Niu, “A revisit to the validity of Born approximation in high frequency scattering problems,” Microw. Opt. Technol. Lett. 54, 2792–2797 (2012).
[CrossRef]

Litman, A.

C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
[CrossRef]

C. Eyraud, A. Litman, A. Hérique, and W. Kofman, “Microwave imaging from experimental data within a Bayesian framework with realistic random noise,” Inverse Probl. 25, 024005 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

Merchiers, O.

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

Michshenko, M.

Mishchenko, M.

G. Videen, Y. Yatskiv, and M. Mishchenko, “Photopolarimetry in remote sensing,” in Proceedings of the NATO Advanced Study Institute (2003).

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Niu, F.

W. Wang, J. Li, and F. Niu, “A revisit to the validity of Born approximation in high frequency scattering problems,” Microw. Opt. Technol. Lett. 54, 2792–2797 (2012).
[CrossRef]

Pottier, E.

S. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[CrossRef]

Refregier, Ph.

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

Roueff, A.

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

Roussel, H.

S. Bellez, H. Roussel, C. Dahon, J. Castelli, and A. Cheraly, “A full polarimetric bistatic radar imaging experiments on sets of dielectric cylinders above a conductive circular plate,” IEEE Trans. Geosci. Remote Sens. 99, 1–13 (2013).
[CrossRef]

Sabouroux, P.

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

J.-M. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, “Optimization of a bistatic microwave scattering measurement setup: from high to low scattering targets,” Radio Sci. 44, RS2007 (2009).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

J.-M. Geffrin and P. Sabouroux, “Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements,” Inverse Probl. 25, 024001 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

Slaney, M.

A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).

Stout, B.

Sung, Y.

Tortel, H.

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel, H. Giovannini, and A. Litman, “Validation of a 3D bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[CrossRef]

Travis, L.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Vaillon, R.

R. Vaillon, J.-M. Geffrin, C. Eyraud, O. Merchiers, P. Sabouroux, and B. Lacroix, “A new implementation of a microwave analog to light scattering measurement device,” J. Quant. Spectrosc. Radiat. Transfer 112, 1753–1760 (2011).
[CrossRef]

O. Merchiers, C. Eyraud, J.-M. Geffrin, R. Vaillon, B. Stout, P. Sabouroux, and B. Lacroix, “Microwave measurements of the full amplitude scattering matrix of a complex aggregate: a database for the assessment of light scattering codes,” Opt. Express 18, 2056 (2010).
[CrossRef]

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

van den Berg, P. M.

P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
[CrossRef]

Videen, G.

G. Videen, Y. Yatskiv, and M. Mishchenko, “Photopolarimetry in remote sensing,” in Proceedings of the NATO Advanced Study Institute (2003).

Wang, W.

W. Wang, J. Li, and F. Niu, “A revisit to the validity of Born approximation in high frequency scattering problems,” Microw. Opt. Technol. Lett. 54, 2792–2797 (2012).
[CrossRef]

Wolf, E.

Yatskiv, Y.

G. Videen, Y. Yatskiv, and M. Mishchenko, “Photopolarimetry in remote sensing,” in Proceedings of the NATO Advanced Study Institute (2003).

Zwillinger, D.

D. Zwillinger, CRC Standard Mathematical Tables and Formulae (Chapman and Hall, 2002).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

O. Merchiers, J.-M. Geffrin, R. Vaillon, P. Sabouroux, and B. Lacroix, “Microwave analog to light scattering measurements on a fully characterized complex aggregate,” Appl. Phys. Lett. 94, 181107 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

A. Roueff, A. Arnaubec, P.-C. Dubois-Fernandez, and Ph. Refregier, “Cramer–Rao lower bound analysis of vegetation height estimation with random volume over ground model and polarimetric SAR interferometry,” IEEE Geosci. Remote Sens. Lett. 8, 1115–1119 (2011).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

C. Eyraud, J.-M. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

P. M. van den Berg, M. G. Coté, and R. E. Kleinman, “Blind shape reconstruction from experimental data,” IEEE Trans. Antennas Propag. 43, 1389–1396 (1995).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

S. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
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[CrossRef]

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[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

Geometrical configuration.

Fig. 2.
Fig. 2.

Ewald sphere using the specified configuration with ϕbT=30°, ϕuT=130°, θbR=θT+50°, and θuR=θT+310° (each point corresponds to a transmitter–receiver couple). (a) 3D visualization and (b)–(d) cross sections.

Fig. 3.
Fig. 3.

For a given couple of transmitter and receiver positions [source: (rT=102λ, θT=100°, ϕT=60°), receiver (rR=102λ, θR=150°, ϕR=90°), representation of the basis vectors for the source (red, left) and for the receiver (green, right) (the ki and ks vectors are plotted in black ()] under (a) the spherical convention and (b) the Bohren and Huffman convention.

Fig. 4.
Fig. 4.

Experimental setup: photography of the anechoic chamber.

Fig. 5.
Fig. 5.

Dielectric targets: (a) pyramid of four spheres (sphere diameter, 1.5λ) and (b) aggregate of 74 spheres (sphere diameter, 0.3λ).

Fig. 6.
Fig. 6.

Maps reconstructed at several altitudes using the pyramid of spheres scattered fields in the Sϕϕ polarization. The real sphere boundaries are plotted in black.

Fig. 7.
Fig. 7.

Maps reconstructed at several altitudes using the pyramid of spheres scattered fields in the Sθθ polarization. The real spheres boundaries are plotted in black.

Fig. 8.
Fig. 8.

Maps reconstructed at several altitudes using the pyramid of spheres scattered fields in the Sϕθ polarization. The real spheres boundaries are plotted in black.

Fig. 9.
Fig. 9.

Maps reconstructed at several altitudes using the pyramid of spheres scattered fields in the S element. The real spheres boundaries are plotted in black.

Fig. 10.
Fig. 10.

Maps reconstructed at several altitudes using the pyramid of spheres scattered fields in the S element. The real spheres boundaries are plotted in black.

Fig. 11.
Fig. 11.

3D visualization (in blue) of the reconstructed maps using the S case—the isosurface threshold value is set to 0.2. The real 74 sphere aggregate is overlaid (in green).

Fig. 12.
Fig. 12.

Maps reconstructed at z=0λ using different elements of the scattered fields matrix with the spherical convention. The real aggregate boundaries are plotted in green.

Fig. 13.
Fig. 13.

Maps reconstructed at z=0λ using different elements of the scattered fields matrix with the Bohren and Huffman convention. The real aggregate boundaries are plotted in green.

Fig. 14.
Fig. 14.

Maps of the normalized induced current magnitude in the target zone at altitude z=0.45λ for the pyramid of spheres for a transmitter polarization choice along eϕ. Jn,i corresponds to the component along the ei vector (i{x,y,z}).

Tables (3)

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Table 1. Measurements Used with the Inversion Procedure for the Configuration with ϕbT=30°, ϕuT=130°, θbR=50°, and θuR=310°

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Table 2. Criteria Values for the Pyramid of Spheres

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Table 3. Criteria Values for the Aggregate

Equations (15)

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Es(r)=ΩG(r,r)χ(r)E(r)dr.
k0r1,rr,k0r2r1,rΓ,rΩ,
G(r,r)ejks·(rr)4πr[Ierer],
Es=SEi.
(EθsEϕs)=(SθθSϕθSθϕSϕϕ)(EθiEϕi).
(EsEs)=(SSSS)(EiEi),
Es(r)ejks·r4πr[eθeθ+eϕeϕ]upTΩej(kski)·rJp(r)ejki·rdr.
upT=fprer+fpθeθ+fpϕeϕ,
uqR=gqθeθ+gqϕeϕ,
Sp,q=Es(r)·uqRejks·r4πrupT·uqRΩej(kski)·rJp(r)ejki·rdr.
|Jp,q(r)|A|S˜p,q(K)|upT·uqR,ifupT·uqR0,
Mn=|M|min(|M|)max(|M|)min(|M|).
CL2=MntrueMnrecoL2.
Cc=Cov(Mnreco,Mntrue)Var(Mnreco)Var(Mntrue),
Ccc=r(Mntrue(r+d*))(Mnreco(d*))¯r(Mntrue(r+0))(Mntrue(0))¯,

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