Abstract

This paper focuses on the role of polarization—and more specifically, the effect of its selection—in 3D quantitative imaging obtained from scattered field measurements. Although polarization is now commonly used in linear imaging procedures (when unknowns are linked by a linear relationship to the measured signal), the influence of polarization choice is generally ignored in nonlinear imaging problems. In this paper, we propose a formulation to obtain the 3D permittivity map, by a nonlinear imaging procedure, from the scattering matrix. This allows one to select, from the same data set, the desired polarization case as input data for the imaging algorithm. We present a study of the influence of the input data polarization choice on the reconstructed permittivity map. This work shows that a suitable basis choice for the description of the scattering matrix and an appropriate selection of the element of this scattering matrix can greatly improve imaging results.

© 2019 Optical Society of America

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References

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    [Crossref]
  16. A. Litman and L. Crocco, “Guest editor introduction: testing inversion algorithms against experimental data: 3D targets,” Inverse Probl. 25, 020201 (2009).
    [Crossref]
  17. J.-M. Geffrin and P. Sabouroux, “Fresnel database continuation: experimental setup and improvements for 3d scattering measurements,” Inverse Probl. 25, 024001 (2009).
    [Crossref]
  18. 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).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  28. C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, and A. Litman, “Validation of a 3d bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
    [Crossref]
  29. 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, RS003837 (2009).
    [Crossref]
  30. C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, “Drift correction for scattering measurements,” Appl. Phys. Lett. 89, 244104 (2006).
    [Crossref]
  31. C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
    [Crossref]
  32. H. Saleh, “Analogie microonde appliquée à l’étude de la diffraction par des arbres, par des particules atmosphérqiues et des micros-organismes,” Ph.D. thesis (Aix Marseille Université, 2017).
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    [Crossref]

2018 (1)

X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

2017 (2)

2016 (1)

2015 (2)

M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23, 14391–14406 (2015).
[Crossref]

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

2013 (1)

2012 (1)

C. Eyraud, J.-M. Geffrin, A. Litman, and J.-P. Spinelli, “A large 3d target with small inner details: a difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry,” Radio Sci. 47, 1–9 (2012).
[Crossref]

2011 (1)

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]

2010 (1)

2009 (5)

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, RS003837 (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]

A. Litman and L. Crocco, “Guest editor introduction: testing inversion algorithms against experimental data: 3D targets,” Inverse Probl. 25, 020201 (2009).
[Crossref]

J.-M. Geffrin and P. Sabouroux, “Fresnel database continuation: experimental setup and improvements for 3d scattering measurements,” Inverse Probl. 25, 024001 (2009).
[Crossref]

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107, 884–890 (2009).
[Crossref]

2008 (1)

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

2006 (3)

2005 (2)

K. Belkebir and M. Saillard, “Special section on testing inversion algorithms against experimental data: inhomogeneous targets,” Inverse Probl. 21, S1–S3 (2005).
[Crossref]

J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental setup and measurement precision,” Inverse Probl. 21, S117–S130 (2005).
[Crossref]

2003 (1)

B. Toh, R. Cahill, and V. Fusco, “Understanding and measuring circular polarization,” IEEE Trans. Educ. 46, 313–318 (2003).
[Crossref]

2002 (1)

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

2001 (1)

B. E. Barrowes, L. F. Teixeira, and J. A. Kong, “Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices in 3-d scattering,” Microw. Opt. Technol. Lett. 31, 28–32 (2001).
[Crossref]

1997 (1)

O. M. 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]

Alexander, P.

G. Emmons and P. Alexander, “Polarization scattering matrices for polarimetric radar,” (1983).

Barrowes, B. E.

B. E. Barrowes, L. F. Teixeira, and J. A. Kong, “Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices in 3-d scattering,” Microw. Opt. Technol. Lett. 31, 28–32 (2001).
[Crossref]

Belkebir, K.

A. Litman and K. Belkebir, “Inverse profiling using phaseless data,” J. Opt. Soc. Am. A 23, 2737–2746 (2006).
[Crossref]

K. Belkebir and M. Saillard, “Special section on testing inversion algorithms against experimental data: inhomogeneous targets,” Inverse Probl. 21, S1–S3 (2005).
[Crossref]

Boffety, M.

Bohren, G.

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

Bucci, O. M.

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

Cahill, R.

B. Toh, R. Cahill, and V. Fusco, “Understanding and measuring circular polarization,” IEEE Trans. Educ. 46, 313–318 (2003).
[Crossref]

Chaumet, P.

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

Chenault, D.

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]

Crocco, L.

A. Litman and L. Crocco, “Guest editor introduction: testing inversion algorithms against experimental data: 3D targets,” Inverse Probl. 25, 020201 (2009).
[Crossref]

de Erausquin, I.

Edmiston, C.

Emmons, G.

G. Emmons and P. Alexander, “Polarization scattering matrices for polarimetric radar,” (1983).

Eyraud, C.

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

C. Eyraud, R. Vaillon, A. Litman, J.-M. Geffrin, and O. Merchiers, “Polarization effects in 3d vectorial-induced polarization effects in 3d vectorial-induced current reconstructions,” J. Opt. Soc. Am. A 30, 1967–1974 (2013).
[Crossref]

C. Eyraud, J.-M. Geffrin, A. Litman, and J.-P. Spinelli, “A large 3d target with small inner details: a difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry,” Radio Sci. 47, 1–9 (2012).
[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, 2056–2075 (2010).
[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]

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, RS003837 (2009).
[Crossref]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, 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]

J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental setup and measurement precision,” Inverse Probl. 21, S117–S130 (2005).
[Crossref]

Fusco, V.

B. Toh, R. Cahill, and V. Fusco, “Understanding and measuring circular polarization,” IEEE Trans. Educ. 46, 313–318 (2003).
[Crossref]

Garcia, M.

Geffrin, J.-M.

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

C. Eyraud, R. Vaillon, A. Litman, J.-M. Geffrin, and O. Merchiers, “Polarization effects in 3d vectorial-induced polarization effects in 3d vectorial-induced current reconstructions,” J. Opt. Soc. Am. A 30, 1967–1974 (2013).
[Crossref]

C. Eyraud, J.-M. Geffrin, A. Litman, and J.-P. Spinelli, “A large 3d target with small inner details: a difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry,” Radio Sci. 47, 1–9 (2012).
[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, 2056–2075 (2010).
[Crossref]

J.-M. Geffrin and P. Sabouroux, “Fresnel database continuation: experimental setup and improvements for 3d scattering measurements,” Inverse Probl. 25, 024001 (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, RS003837 (2009).
[Crossref]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, 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]

J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental setup and measurement precision,” Inverse Probl. 21, S117–S130 (2005).
[Crossref]

Giovannini, H.

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

Gio-vannini, H.

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

Goldstein, D.

Goudail, F.

Gruev, V.

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

Kim, Y.

J. V. Zyl and Y. Kim, Synthetic Aperture Radar Polarimetry (Jet Propulsion Laboratory, 2010).

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]

Kong, J. A.

B. E. Barrowes, L. F. Teixeira, and J. A. Kong, “Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices in 3-d scattering,” Microw. Opt. Technol. Lett. 31, 28–32 (2001).
[Crossref]

Lacis, A.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/staff/mmishchenko/books.html .

Lacroix, B.

Litman, A.

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

C. Eyraud, R. Vaillon, A. Litman, J.-M. Geffrin, and O. Merchiers, “Polarization effects in 3d vectorial-induced polarization effects in 3d vectorial-induced current reconstructions,” J. Opt. Soc. Am. A 30, 1967–1974 (2013).
[Crossref]

C. Eyraud, J.-M. Geffrin, A. Litman, and J.-P. Spinelli, “A large 3d target with small inner details: a difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry,” Radio Sci. 47, 1–9 (2012).
[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]

A. Litman and L. Crocco, “Guest editor introduction: testing inversion algorithms against experimental data: 3D targets,” Inverse Probl. 25, 020201 (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]

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, RS003837 (2009).
[Crossref]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, 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]

A. Litman and K. Belkebir, “Inverse profiling using phaseless data,” J. Opt. Soc. Am. A 23, 2737–2746 (2006).
[Crossref]

Ma, X.

X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

Macdonald, C.

Marinov, R.

Markel, V.

Merchiers, O.

Mishchenko, M.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/staff/mmishchenko/books.html .

Neel, V.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107, 884–890 (2009).
[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]

Sabouroux, P.

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, 2056–2075 (2010).
[Crossref]

J.-M. Geffrin and P. Sabouroux, “Fresnel database continuation: experimental setup and improvements for 3d scattering measurements,” Inverse Probl. 25, 024001 (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, RS003837 (2009).
[Crossref]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, 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]

J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental setup and measurement precision,” Inverse Probl. 21, S117–S130 (2005).
[Crossref]

Saillard, M.

K. Belkebir and M. Saillard, “Special section on testing inversion algorithms against experimental data: inhomogeneous targets,” Inverse Probl. 21, S1–S3 (2005).
[Crossref]

Saleh, H.

H. Saleh, “Analogie microonde appliquée à l’étude de la diffraction par des arbres, par des particules atmosphérqiues et des micros-organismes,” Ph.D. thesis (Aix Marseille Université, 2017).

Salomatina-Motts, E.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107, 884–890 (2009).
[Crossref]

Shaw, J.

Shen, H.

X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

Silva, A. D.

Spinelli, J.-P.

C. Eyraud, J.-M. Geffrin, A. Litman, and J.-P. Spinelli, “A large 3d target with small inner details: a difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry,” Radio Sci. 47, 1–9 (2012).
[Crossref]

Stout, B.

Teixeira, L. F.

B. E. Barrowes, L. F. Teixeira, and J. A. Kong, “Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices in 3-d scattering,” Microw. Opt. Technol. Lett. 31, 28–32 (2001).
[Crossref]

Toh, B.

B. Toh, R. Cahill, and V. Fusco, “Understanding and measuring circular polarization,” IEEE Trans. Educ. 46, 313–318 (2003).
[Crossref]

Tortel, H.

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, 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), http://www.giss.nasa.gov/staff/mmishchenko/books.html .

Tricoli, U.

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van der Vorst, H. A.

H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems (Cambridge University, 2003).

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X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

Wu, Y.

X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

Yaroslavskaya, A.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107, 884–890 (2009).
[Crossref]

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J. V. Zyl and Y. Kim, Synthetic Aperture Radar Polarimetry (Jet Propulsion Laboratory, 2010).

Appl. Opt. (1)

Appl. Phys. Lett. (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]

IEEE Antennas Wireless Propag. Lett. (1)

C. Eyraud, J.-M. Geffrin, A. Litman, and H. Tortel, “Complex permittivity determination from far-field scattering patterns,” IEEE Antennas Wireless Propag. Lett. 14, 309–312 (2015).
[Crossref]

IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing (1)

X. Ma, P. Wu, Y. Wu, and H. Shen, “A review on recent developments in fully polarimetric SAR image despeckling,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 743–758 (2018).
[Crossref]

IEEE Trans. Antennas Propag. (1)

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]

IEEE Trans. Educ. (1)

B. Toh, R. Cahill, and V. Fusco, “Understanding and measuring circular polarization,” IEEE Trans. Educ. 46, 313–318 (2003).
[Crossref]

IEEE Trans. Geosci. Remote. Sens. (1)

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[Crossref]

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[Crossref]

J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental setup and measurement precision,” Inverse Probl. 21, S117–S130 (2005).
[Crossref]

A. Litman and L. Crocco, “Guest editor introduction: testing inversion algorithms against experimental data: 3D targets,” Inverse Probl. 25, 020201 (2009).
[Crossref]

J.-M. Geffrin and P. Sabouroux, “Fresnel database continuation: experimental setup and improvements for 3d scattering measurements,” Inverse Probl. 25, 024001 (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]

J. Biomed. Opt. (1)

X. Ma, P. Wu, Y. Wu, and H. Shen, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[Crossref]

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Microw. Opt. Technol. Lett. (1)

B. E. Barrowes, L. F. Teixeira, and J. A. Kong, “Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices in 3-d scattering,” Microw. Opt. Technol. Lett. 31, 28–32 (2001).
[Crossref]

Opt. Express (2)

Opt. Spectrosc. (1)

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107, 884–890 (2009).
[Crossref]

Optica (1)

Radio Sci. (4)

C. Eyraud, J.-M. Geffrin, P. Sabouroux, P. Chaumet, H. Tortel, H. Gio-vannini, and A. Litman, “Validation of a 3d bistatic microwave scattering measurement setup,” Radio Sci. 43, RS4018 (2008).
[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, RS003837 (2009).
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[Crossref]

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H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems (Cambridge University, 2003).

G. Emmons and P. Alexander, “Polarization scattering matrices for polarimetric radar,” (1983).

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

H. Saleh, “Analogie microonde appliquée à l’étude de la diffraction par des arbres, par des particules atmosphérqiues et des micros-organismes,” Ph.D. thesis (Aix Marseille Université, 2017).

J. V. Zyl and Y. Kim, Synthetic Aperture Radar Polarimetry (Jet Propulsion Laboratory, 2010).

W.-M. Boener, “Recent advances in radar polarimetry and polarimetric SAR interferometry,” Lecture notes PolSARpro, 2005, https://earth.esa.int/web/polsarpro/polarimetry-tutorial .

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/staff/mmishchenko/books.html .

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Figures (16)

Fig. 1.
Fig. 1. Definition of the spherical convention: coordinate (a) and the polarization basis (b).
Fig. 2.
Fig. 2. Definition of the three bases: (a) linear—spherical convention, (b) linear—Bohren and Huffman convention, and (c) circular.
Fig. 3.
Fig. 3. Definition of the left and right circular polarizations with the IEEE convention [20].
Fig. 4.
Fig. 4. Experimental setup.
Fig. 5.
Fig. 5. Circular helix.
Fig. 6.
Fig. 6. 2D cross section in the (y0z) plane at x=0mm of the reconstructed maps in the principal polarization cases from calculated scattered fields for the cube case. The edges of the target are superimposed in cyan.
Fig. 7.
Fig. 7. 2D cross section in the (x0z) plane at y=0mm of the reconstructed maps in the principal polarization cases from calculated scattered fields for the cube case. The edges of the target are superimposed in cyan.
Fig. 8.
Fig. 8. 2D cross section in the (x0y) plane at z=0mm of the reconstructed maps in the principal polarization cases from calculated scattered fields for the cube case. The edges of the target are superimposed in cyan.
Fig. 9.
Fig. 9. 3D view of the reconstructed maps in the different polarization cases from measured scattered fields for the circular helix (the threshold is chosen at 1.1). The real object is superimposed in cyan.
Fig. 10.
Fig. 10. 2D cross section in the (y0z) plane at x=0mm of the reconstructed maps in the principal polarization cases from measured scattered fields for the circular helix.
Fig. 11.
Fig. 11. 2D cross section in the (x0z) plane at y=0mm of the reconstructed maps in the principal polarization cases from measured scattered fields for the circular helix.
Fig. 12.
Fig. 12. 2D cross section in the (x0y) plane at z=0mm of the reconstructed maps in the principal polarization cases from measured scattered fields for the circular helix.
Fig. 13.
Fig. 13. Sum of all the singular values for the cube (left: in spherical basis, middle: in BH basis, and right: in circular basis) (n=1NrλB,pq(n)).
Fig. 14.
Fig. 14. Sum of all the singular values for the circular helix (left: in spherical basis, middle: in BH basis, and right: in circular basis) (n=1NrλB,pq(n)).
Fig. 15.
Fig. 15. Spectra of singular values λB,pq(n) for the cube: full spectra (left) and spectra corresponding to the signal space (right).
Fig. 16.
Fig. 16. Spectra of singular values λB,pq(n) for the circular helix: full spectra (left) and spectra corresponding to the signal space (right).

Tables (5)

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Table 1. Comparison of the Different Reconstruction Cases from the Calculated Scattered Fielda

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Table 2. Comparison of the Different Reconstruction Cases from Calculated Scattered Fielda

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Table 3. Comparison of the Different Reconstruction Cases from the Measured Scattered Fielda

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Table 4. Values of the Quantity QB for Different Polarization Cases

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Table 5. Values of the Quantity AB,p for the Different Illuminations of the Two Linear Bases in the Cube Case

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

[EBs]=[SB][EBi].
(EpsEqs)=(SppSqpSpqSqq)(EpiEqi).
Srr=12[(SS)j(S+S)],Srl=12[(S+S)j(SS)],Slr=12[(S+S)+j(SS)],Sll=12[(SS)+j(S+S)].
FB,pq(n)=12NsNrs=1Nsr=1Nr|SB,pqc(ϵrB,pq(n);rs,rr)SB,pqm(rs,rr)|2,
ϵrB,pq(n+1)(r)=ϵrB,pq(n)(r)+αB,pq(n)dB,pq(n)(r),
Cϵr1,Bcc(d*)=N(ϵrtrue(r+d*)1)(ϵrreco(d*)1)¯N(ϵrtrue(r+0)1)(ϵrtrue(0)1)¯,
CBc=N(ϵrreco(r)ϵrreco¯)(ϵrtrue(r)ϵrtrue¯)N(ϵrreco(r)ϵrreco¯)2N(ϵrtrue(r)ϵrtrue¯)2,
CB=(1CBL2)×Cϵr1,Bcc×CBc.
[SB,pq]=[UB,pq][LB,pq][VB,pq],
Es(rs,rr)=ΩG(rr,r)χ(r)E(r)dr,
Es(rs,rr)·eB,qs=(ΩG(rr,r)χ(r)E(r)dr)·eB,qs.
rΩ,JB,p(r)=χ(r)EB,p(r).
Es(rs,rr).eB,qs[ΩG(rr,r)JB,p(r)dreB,pi].eB,qs.
rrΓ,rΩ,korr1,rrrandkor2rr1,
G(rr,r)ejkorr4πrrejkoeB,qs.r[eθeθ+eϕeϕ].
Es(rs,rr)·eB,qs(ΩJB,p(r)ejkoeB,qs·rdr)g(rr)[eθeθ+eϕeϕ]eB,pi·eB,qs,
QB=1NsNrNsNrqB(ϕs,θs,θsθr),
Spherical basis,AB,p=ASp,p=1N1Nss|JB,p.eB,pi|JB,p,
BHbasis,AB,p=ABH,p=1N1NsNrsr|JB,p.eB,pi|JB,p.

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