Abstract

We present an extensive experimental study of microwave scattering by a fully characterized complex aggregate. We measured the full amplitude scattering matrix (amplitude and phase of the four elements) for a wide range of configurations. The presented results are of special interest to the light scattering community. Our experiments offer the possibility to validate numerical methods against experiments, since the geometrical and dielectric properties of the complex target are known to a high degree of precision, a situation difficult to attain in the optical regime. We analyze in detail the behaviour of amplitude and phase as a function of the scattering angle and target orientation. Furthermore, we compare different computational methods for a specific experimental configuration.

© 2010 Optical Society of America

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2009 (2)

C. Eyraud, A. Litman, A. Herique, and W. Kofman, "Microwave imaging from experimental data within a bayesian framework with realistic random noise," Inverse Problems 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 (2009).
[CrossRef]

2008 (1)

B. Stout, J. C. Auger, and A. Devilez, "Recursive t matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations," J. Opt. Soc. Am. A 25, 2549 (2008).
[CrossRef]

2007 (1)

M. Yurkin and A. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

2006 (2)

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

M. I. Mishchenko, "Scale invariance rule in electromagnetic scattering," J. Quant. Spectrosc. Radiat. Transf. 101, 411-415 (2006).
[CrossRef]

2005 (2)

J. E. Thomas-Osip, B. A. S. Gustafson, L. Kolokolova, and Y.-L. Xu, "An investigation of titan’s aerosols using microwave analog measurements and radiative transfer modeling," Icarus 179, 511-522 (2005).
[CrossRef]

O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
[CrossRef]

2004 (1)

M. Mishchenko, G. Videen, V. Babenko, N. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by partciles and its applications: a comprehensive reference database," J. Quant. Spectrosc. Radiat. Transf. 88, 357-406 (2004).

2003 (2)

F. M. Kahnert, "Numerical methods in electromagnetic scattering theory," J. Quant. Spectrosc. Radiat. Transf. 79-80, 775-824 (2003).
[CrossRef]

J. Auger and B. Stout, "A recursive centered t-matrix algorithm to solve the multiple scattering equation: numerical validation," J. Quant. Spectrosc. Radiat. Transf. 79, 533-547 (2003).
[CrossRef]

2001 (3)

C. M. Sorensen, "Light scattering by fractal aggregates: A review," Aerosol Sci. Technol. 35, 648 (2001).

Y.-L. Xu and B. A. S. Gustafson, "A generalized multiparticle mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transf. 70, 395-419 (2001).
[CrossRef]

L. Kolokolova and B. A. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories," J. Quant. Spectrosc. Radiat. Transf. 70, 611-625 (2001).
[CrossRef]

1998 (1)

Y.-L. Xu and R. T. Wang, "Electromagnetic scattering by an aggregate of spheres: Theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58, 3931-3948 (1998).
[CrossRef]

1996 (2)

B. A. S. Gustafson, "Microwave analog to light scattering measurements: a modern implementation of a proven method to achieve precise control." J. Quant. Spectrosc. Radiat. Transf. 55, 663-672 (1996).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, "Calculation of the t matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A 13, 2266-2278 (1996).
[CrossRef]

1995 (1)

P. van den Berg, M. Cote, and R. Kleinman, ""blind" shape reconstruction from experimental data," Antennas and Propagation, IEEE Transactions on 43, 1389-1396 (1995).
[CrossRef]

1994 (2)

B. Draine and P. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

D. Mackowski, "Calculation of total cross sections of multiple-sphere clusters," J. Opt. Soc. Am. A 11, 2851 (1994).
[CrossRef]

1993 (2)

R. H. Zerull, B. Gustafson, K. Schulz, and E. Thiele-Corbach, "Scattering by aggregates with and without an absorbing mantle: Microwave analog experiments," Appl. Opt. 32, 4088-4100 (1993).
[PubMed]

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti - wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

1987 (1)

R. A. Dobbins and C. M. Megaridis, "Morphology of flame-generated soot as determined by thermophoretic sampling," Langmuir 3, 254-259 (1987).
[CrossRef]

1980 (1)

W. J. Wiscombe, "Improved mie scattering algorithms," Appl. Opt. 19, 1505-1509 (1980).
[CrossRef] [PubMed]

1961 (1)

J. M. Greenberg, N. E. Pedersen, and J. C. Pedersen, "Microwave analog to the scattering of light by nonspherical particles," J. Appl. Phys. 32, 233-242 (1961).
[CrossRef]

1951 (1)

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287 (1951).
[CrossRef]

Auger, J.

J. Auger and B. Stout, "A recursive centered t-matrix algorithm to solve the multiple scattering equation: numerical validation," J. Quant. Spectrosc. Radiat. Transf. 79, 533-547 (2003).
[CrossRef]

Auger, J. C.

B. Stout, J. C. Auger, and A. Devilez, "Recursive t matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations," J. Opt. Soc. Am. A 25, 2549 (2008).
[CrossRef]

Babenko, V.

M. Mishchenko, G. Videen, V. Babenko, N. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by partciles and its applications: a comprehensive reference database," J. Quant. Spectrosc. Radiat. Transf. 88, 357-406 (2004).

Cote, M.

P. van den Berg, M. Cote, and R. Kleinman, ""blind" shape reconstruction from experimental data," Antennas and Propagation, IEEE Transactions on 43, 1389-1396 (1995).
[CrossRef]

Devilez, A.

B. Stout, J. C. Auger, and A. Devilez, "Recursive t matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations," J. Opt. Soc. Am. A 25, 2549 (2008).
[CrossRef]

Dobbins, R. A.

R. A. Dobbins and C. M. Megaridis, "Morphology of flame-generated soot as determined by thermophoretic sampling," Langmuir 3, 254-259 (1987).
[CrossRef]

Draine, B.

B. Draine and P. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

Draine, B. T.

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti - wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

Eyraud, C.

C. Eyraud, A. Litman, A. Herique, and W. Kofman, "Microwave imaging from experimental data within a bayesian framework with realistic random noise," Inverse Problems 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 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

Flatau, P.

B. Draine and P. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

Geffrin, J.-M.

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 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

Giovannini, H.

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

Goodman, J.

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti - wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

Greenberg, J. M.

J. M. Greenberg, N. E. Pedersen, and J. C. Pedersen, "Microwave analog to the scattering of light by nonspherical particles," J. Appl. Phys. 32, 233-242 (1961).
[CrossRef]

Gustafson, B.

R. H. Zerull, B. Gustafson, K. Schulz, and E. Thiele-Corbach, "Scattering by aggregates with and without an absorbing mantle: Microwave analog experiments," Appl. Opt. 32, 4088-4100 (1993).
[PubMed]

Gustafson, B. A. S.

J. E. Thomas-Osip, B. A. S. Gustafson, L. Kolokolova, and Y.-L. Xu, "An investigation of titan’s aerosols using microwave analog measurements and radiative transfer modeling," Icarus 179, 511-522 (2005).
[CrossRef]

Y.-L. Xu and B. A. S. Gustafson, "A generalized multiparticle mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transf. 70, 395-419 (2001).
[CrossRef]

L. Kolokolova and B. A. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories," J. Quant. Spectrosc. Radiat. Transf. 70, 611-625 (2001).
[CrossRef]

B. A. S. Gustafson, "Microwave analog to light scattering measurements: a modern implementation of a proven method to achieve precise control." J. Quant. Spectrosc. Radiat. Transf. 55, 663-672 (1996).
[CrossRef]

Herique, A.

C. Eyraud, A. Litman, A. Herique, and W. Kofman, "Microwave imaging from experimental data within a bayesian framework with realistic random noise," Inverse Problems 25, 024005 (2009).
[CrossRef]

Hoekstra, A.

M. Yurkin and A. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

Kahnert, F. M.

F. M. Kahnert, "Numerical methods in electromagnetic scattering theory," J. Quant. Spectrosc. Radiat. Transf. 79-80, 775-824 (2003).
[CrossRef]

Khlebtsov, N.

M. Mishchenko, G. Videen, V. Babenko, N. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by partciles and its applications: a comprehensive reference database," J. Quant. Spectrosc. Radiat. Transf. 88, 357-406 (2004).

Kleinman, R.

P. van den Berg, M. Cote, and R. Kleinman, ""blind" shape reconstruction from experimental data," Antennas and Propagation, IEEE Transactions on 43, 1389-1396 (1995).
[CrossRef]

Kofman, W.

C. Eyraud, A. Litman, A. Herique, and W. Kofman, "Microwave imaging from experimental data within a bayesian framework with realistic random noise," Inverse Problems 25, 024005 (2009).
[CrossRef]

Kolokolova, L.

J. E. Thomas-Osip, B. A. S. Gustafson, L. Kolokolova, and Y.-L. Xu, "An investigation of titan’s aerosols using microwave analog measurements and radiative transfer modeling," Icarus 179, 511-522 (2005).
[CrossRef]

L. Kolokolova and B. A. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories," J. Quant. Spectrosc. Radiat. Transf. 70, 611-625 (2001).
[CrossRef]

Lax, M.

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287 (1951).
[CrossRef]

Litman, A.

C. Eyraud, A. Litman, A. Herique, and W. Kofman, "Microwave imaging from experimental data within a bayesian framework with realistic random noise," Inverse Problems 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 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

Mackowski, D.

D. Mackowski, "Calculation of total cross sections of multiple-sphere clusters," J. Opt. Soc. Am. A 11, 2851 (1994).
[CrossRef]

Mackowski, D. W.

D. W. Mackowski and M. I. Mishchenko, "Calculation of the t matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A 13, 2266-2278 (1996).
[CrossRef]

Megaridis, C. M.

R. A. Dobbins and C. M. Megaridis, "Morphology of flame-generated soot as determined by thermophoretic sampling," Langmuir 3, 254-259 (1987).
[CrossRef]

Mishchenko, M.

M. Mishchenko, G. Videen, V. Babenko, N. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by partciles and its applications: a comprehensive reference database," J. Quant. Spectrosc. Radiat. Transf. 88, 357-406 (2004).

Mishchenko, M. I.

M. I. Mishchenko, "Scale invariance rule in electromagnetic scattering," J. Quant. Spectrosc. Radiat. Transf. 101, 411-415 (2006).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, "Calculation of the t matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A 13, 2266-2278 (1996).
[CrossRef]

Moine, O.

O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
[CrossRef]

Pedersen, J. C.

J. M. Greenberg, N. E. Pedersen, and J. C. Pedersen, "Microwave analog to the scattering of light by nonspherical particles," J. Appl. Phys. 32, 233-242 (1961).
[CrossRef]

Pedersen, N. E.

J. M. Greenberg, N. E. Pedersen, and J. C. Pedersen, "Microwave analog to the scattering of light by nonspherical particles," J. Appl. Phys. 32, 233-242 (1961).
[CrossRef]

Sabouroux, P.

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 (2009).
[CrossRef]

C. Eyraud, J.-M. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, "Drift correction for scattering measurements," Appl. Phys. Lett. 89, 244104-3 (2006).
[CrossRef]

Schulz, K.

R. H. Zerull, B. Gustafson, K. Schulz, and E. Thiele-Corbach, "Scattering by aggregates with and without an absorbing mantle: Microwave analog experiments," Appl. Opt. 32, 4088-4100 (1993).
[PubMed]

Sorensen, C. M.

C. M. Sorensen, "Light scattering by fractal aggregates: A review," Aerosol Sci. Technol. 35, 648 (2001).

Stout, B.

B. Stout, J. C. Auger, and A. Devilez, "Recursive t matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations," J. Opt. Soc. Am. A 25, 2549 (2008).
[CrossRef]

O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
[CrossRef]

J. Auger and B. Stout, "A recursive centered t-matrix algorithm to solve the multiple scattering equation: numerical validation," J. Quant. Spectrosc. Radiat. Transf. 79, 533-547 (2003).
[CrossRef]

Thiele-Corbach, E.

R. H. Zerull, B. Gustafson, K. Schulz, and E. Thiele-Corbach, "Scattering by aggregates with and without an absorbing mantle: Microwave analog experiments," Appl. Opt. 32, 4088-4100 (1993).
[PubMed]

Thomas-Osip, J. E.

J. E. Thomas-Osip, B. A. S. Gustafson, L. Kolokolova, and Y.-L. Xu, "An investigation of titan’s aerosols using microwave analog measurements and radiative transfer modeling," Icarus 179, 511-522 (2005).
[CrossRef]

van den Berg, P.

P. van den Berg, M. Cote, and R. Kleinman, ""blind" shape reconstruction from experimental data," Antennas and Propagation, IEEE Transactions on 43, 1389-1396 (1995).
[CrossRef]

Videen, G.

M. Mishchenko, G. Videen, V. Babenko, N. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by partciles and its applications: a comprehensive reference database," J. Quant. Spectrosc. Radiat. Transf. 88, 357-406 (2004).

Wang, R. T.

Y.-L. Xu and R. T. Wang, "Electromagnetic scattering by an aggregate of spheres: Theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58, 3931-3948 (1998).
[CrossRef]

Wiscombe, W. J.

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Figures (11)

Fig. 1.
Fig. 1.

Computer generated representation of the aggregate using the output of the algorithm (a). Front (b) and side (c) views of the constructed aggregate. In pictures (b) and (c), one can appreciate the polystyrene supports, transparent to microwaves, on which the aggregate rests. The plexiglass spheres are removed after the aggregate has been aligned.

Fig. 2.
Fig. 2.

On the left, a picture of the anechoic chamber and on the right the name conventions for the polarization components of the electric field in the experimental set-up. Here the red dashed line corresponds with the vertical arch and the green dashed one with the receiver positions in our configuration.

Fig. 3.
Fig. 3.

Scattering angle as a function of receiver position. The curve for the OP configuration was obtained for ϕE = 60°.

Fig. 4.
Fig. 4.

Amplitude (a) and phase (b) of S 1 as a function of frequency for a fixed aggregate position. ((oe-18-3-2056-i001) IP simulated, (oe-18-3-2056-i002) OP simulated, (oe-18-3-2056-i003) IP experimental, (oe-18-3-2056-i004) OP experimental).

Fig. 5.
Fig. 5.

Amplitude (a) and phase (b) of S 3 as a function of frequency for a fixed aggregate position. ((oe-18-3-2056-i005) IP simulated, (oe-18-3-2056-i006) OP simulated, (oe-18-3-2056-i007) IP experimental, (oe-18-3-2056-i008) OP experimental).

Fig. 6.
Fig. 6.

Axial rotations of the aggregate seen from above. Figure (c) corresponds with the position of the object in the experiments of section 5.1.

Fig. 7.
Fig. 7.

Amplitude (a) and phase (b) of S 1 for different positions, at a single frequency = 20 GHz. ((oe-18-3-2056-i009) IP simulated, (oe-18-3-2056-i010) OP simulated, (oe-18-3-2056-i011) IP experimental, (oe-18-3-2056-i012) OP experimental).

Fig. 8.
Fig. 8.

Amplitude (a) and phase (b) of S 3 for different positions, at a single frequency = 20 GHz. ((oe-18-3-2056-i013) IP simulated, (oe-18-3-2056-i014) OP simulated, (oe-18-3-2056-i015) IP experimental, (oe-18-3-2056-i016) OP experimental).

Fig. 9.
Fig. 9.

Amplitude (a) and phase (b) of S 1 at 20 GHz in IP configuration. (oe-18-3-2056-i017) Mean value, (oe-18-3-2056-i018) Extremal values.

Fig. 10.
Fig. 10.

Amplitude and phase of S 1 and S 2 matrix elements at 20 GHz in IP configuration. ((oe-18-3-2056-i019) Experiment, (oe-18-3-2056-i020) T-Matrix Mackowski, (oe-18-3-2056-i021) ddscat7.0, (oe-18-3-2056-i022) MoM, (oe-18-3-2056-i023) T-Matrix Stout).

Fig. 11.
Fig. 11.

Amplitude and phase of S 3 and S 4 matrix elements at 20 GHz in IP configuration. ((oe-18-3-2056-i024) Experiment, (oe-18-3-2056-i025) T-Matrix Mackowski, (oe-18-3-2056-i026) ddscat7.0, (oe-18-3-2056-i027) MoM, (oe-18-3-2056-i028) T-Matrix Stout).

Tables (1)

Tables Icon

Table 1. The values of the error function f err for each matrix element and computational method.

Equations (15)

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

N = k 0 ( R g / a ) D f ,
E θ k = E k · e θ ,
E ϕ k = E k · e ϕ ,
ε ( r ) = ε 0 ε r ( r ) + i ε 0 ε i ( r )
E s ( r ) = Ω G 0 r ( r , r ) χ ( r ) E ( r ) dr
E ( r ' ) = E 0 ( r ) + Ω G 00 ( r , r ) χ ( r ) E ( r ) d r
C = i = 0 N r E c , i s E ̄ m , i s i = 0 N r E m , i s E ̄ m , i s
E s E s = e ik ( r z ) ikr S 2 S 3 S 4 S 1 E i E i ,
E θ s E ϕ s = S θθ S θϕ S ϕθ S ϕϕ E θ i E ϕ i ,
M TP = T s 1 · M BH · T i ,
q = k s k i ,
= 4 π λ 1 sin ( θ S / 2 ) ,
I ( q ) ~ 1 1 3 q 2 R g 2 ,
f err = E m s E c s 2 E m s 2 ,
N O , c x e + 4 x e 1 / 3 + 2 ,

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