Franchois, Ann

Van den Bulcke, Sara

English

Ghent University Academic Bibliography

Modelling 3D Mm-wave Scattering From Human Body Under GaussianBeam Illumination With A 2.5D VIE SolverS. Van den Bulcke and A. FranchoisDepartment of Information TechnologyGhent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgiumsara.vandenbulcke@ugent.be, ann.franchois@ugent.beAbstract: In this paper, a two-and-a-half dimensional exact forward solver, based on a volume integralequation, is used to simulate three-dimensional millimeter wave scattering of a dielectric object hidden un-der clothing. Since a three-dimensional Gaussian beam only illuminates a spatially limited region of thehuman body, we can assume invariance of the electromagnetic properties of the abdomen in the longitudinaldirection (vertical for a standing person). This way, the human body can be modelled as an infinitely longinhomogeneous (lossy) dielectric cylinder with arbitrary cross-sectional shape. A complex source formu-lation is used to implement this three-dimensional Gaussian beam, which may be oblique, and the humanbody is further reduced to a simple model, containing four different layers: clothing, air, human skin andbody fat.Keywords: 2.5D scattering, millimeter waves, contrast source integral equation, 3D Gaussian beam, simplehuman body model.1. IntroductionFor security applications, the detection of hidden objects under clothing is an important research area [1]-[3]. Millimeter waves (mm-waves) have ideal characteristics for this purpose since they are non-ionizingand penetrate clothing, while being absorbed and reflected by the human skin [4]. Moreover, the relativelysmall wavelength yields good resolution possibilities. For the development of such systems it is importantto study the mm-wave scattering behavior of the human body. This could be done by full three dimensional(3D) electromagnetic simulation tools [5], but since the dimensions of the hidden object and the human bodyare several to many wavelengths and a fine discretization is needed due to the relatively high permittivityof the skin, this would yield a huge amount of unknowns. However, when mm-waves are used in activeimaging systems, the incident field is usually a 3D Gaussian beam which only illuminates a spatially limitedregion. Since the size of the illuminated body region is only a few centimeter in the longitudinal direction(vertical for a standing person), it follows that we can assume invariance of the electromagnetic properties ofthe human abdomen along this direction. Therefore it can be modelled as an infinitely long inhomogeneous(lossy) dielectric cylinder with arbitrary cross-sectional shape.For such configurations, we use a 2.5D full-wave forward solver [6], based on a Volume Integral Equation(VIE), to calculate the 3D electromagnetic scattered field. This way, objects with cross-sectional dimensionsof several to many wavelengths can be handled with a reasonable computational effort, while maintaining24th Annual Review of Progress in Applied Computational Electromagnetics March 30 - April 4, 2008 - Niagara Falls, Canada  '2008 ACES63the full 3D character of the incident field. A similar technique is proposed in [7] for modeling geophysicallow-frequency (diffusive) electromagnetic scattering in cross-well logging.In this paper, we use a simple model for the cross-section of the human body to compare the mm-wavescattering behavior of the human body with and without hidden dielectric object. In section 2, the 2.5Dforward solver is presented, as well as the implementation of the 3D Gaussian beam. Section 3 deals withthe obtained simulation results.2. 2.5D Forward SolverA. Contrast Source Integral EquationConsider an inhomogeneous, possibly lossy, dielectric cylinder with arbitrary cross-sectional shape andwith axis along the z-direction in a 3D cartesian coordinate system ρ = r + zuz, with r = xux + yuy the 2Dposition vector. This object is surrounded with free space and has a complex permittivity ǫ(r) = ǫr(r)ǫ0.We formulate the problem in the frequency domain and omit the time dependence exp(−iωt) . The scat-tering object is illuminated with a 3D incident field Ei(r, z) and the resulting scattered field is defined asEs(r, z) = E(r, z) − Ei(r, z), with E(r, z) the total field.A contrast source integral equation (CSIE) in the 2D space-spatial frequency domain (r; kz) is obtained fromperforming a spatial Fourier transform with respect to the z-coordinate, defined as gˆ(r, kz) =∫ ∞−∞g(r, z)e−ikzzdz,on the Maxwell equations:Êi(r, kz) = D̂(r, kz)ǫ(r) −(k20I + ∇̂∇̂)· Âs(r, kz). (1)The electric flux density D(r, z) is chosen as the unknown of the scattering problem [5] and the vectorpotential Âs(r, kz) is defined asÂs(r, kz) = 1ǫ0∫SĜ(r, r′; kz)χ(r′)D̂(r′, kz)dr′, (2)where ∇̂ = (∂x, ∂y, ikz) andχ(r) = ǫ(r) − ǫ0ǫ(r) (3)is the normalized permittivity contrast. Because of this contrast, the integration in (2) can be limited to theobject domain S , where the permittivity of the object ǫ(r) differs from ǫ0. The Green’s function is given byĜ(r, r′; kz) = i4 H(1)0(√k20 − k2z |r − r′|). (4)We discretize the object domain S in square cells with cell size ∆ and expand the 3D fields using rooftopbasis functions. The complex permittivity takes a constant value within each cell. A Method of Momentswith Galerkin weighting is applied to discretize the CSIE and the resulting linear set of equations is solvediteratively with a stabilized biconjugate gradient Fast Fourier Transform method.24th Annual Review of Progress in Applied Computational Electromagnetics March 30 - April 4, 2008 - Niagara Falls, Canada  '2008 ACES64B. 3D Gaussian Beam As Incident FieldThe implementation of a Fourier transformed 3D Gaussian beam, under the paraxial approximation, is basedon the complex-source beam formulation proposed in [8] for a beam-type wave object which correspondswith the classic formulation within the paraxial approximation. We consider a beam that is propagating alonga ui-direction, with the beam center located at ρ0 = (x0, y0, z0) and beam waist w0. A 3D complex sourcebeam is obtained by evaluating the 3D Greens’ function, G(s) = 1sexp(ik0s), with respect to a complexsource-point ρc = ρ0 + ibui. This complex source point is a combination of the real source point ρ0 — thebeam waist center — on the one hand, and beam parameters, as the beam collimation distance b = w20k0/2and the beam direction ui on the other hand. A complex distance function s(r) is defined ass(r) = ((x − xc)2 + (y − yc)2 + z2c)1/2, (5)with Im (s(r)) ≤ 0. We obtain the Fourier transform of this beam by replacing the 3D Greens’ function withthe 2.5D Greens’ function:Êi(r, kz) = Ĝ(s; kz)upol = i4 H(1)0(√k20 − (kc − kz)2 s)upol, (6)where kc = k0 ui · uz.3. Scattering Of Objects Hidden On A Human BodyThe 2.5D solver described above is used to study mm-wave scattering from a quasi-2D object that is hiddenon an adult human body and which is illuminated by a 3D TM-polarized incident Gaussian beam — upol =uz — at 100 GHz. A simple model for the human body cross-section is shown is Fig. 1, where the limitedpenetration of mm-waves into the human body [4] as well as the finiteness of the illuminated region in thex-direction has allowed us to consider only a small part of the abdomen cross-section. The 3D Gaussianbeam is propagating along the y-axis with a waist w0 = 8 mm and its beam center r0 is chosen at the exteriorsurface of the skin in x = y = 0.In this restricted model we distinguish 4 layers: clothing, air, dry skin and fat. The thickness d and relativepermittivity ǫr for each layer are chosen as follows: d = 2 mm and ǫr = 4.0 + i 0.1 for clothing [4], d = 3mm and ǫr = 1 for air, d = 2 mm and ǫr = 5.60+ i 7.09 for dry skin [9] and d = 10 mm and ǫr = 2.89+ i 0.64for fat [9]. A rectangular dielectric object with width 15 mm, thickness 2.5 mm and relative permittivityǫob j = 2, representing certain explosives, is placed between the clothing and skin. The computational domainhas dimensions of 110 mm in the x-direction and 40 mm in the y-direction and is discretized into 1120×416cells with cell size ∆ = 0.1 mm, yielding a total of 1.397760 million unknowns. The simulation withouthidden object proves that the dimensions of the restricted model are large enough since no remarkable fieldvalues appeared on the upper and lower boundaries of Fig. 1, as well as inside the abdomen. The incidentfield is calculated using the complex-source beam formula for five different kz values.Simulations, with and without hidden object were computed in 2h. 43 min. and 2h. 35 min., respectively.Fig. 2 shows the amplitude and phase of the difference between the total field with and without object andclearly reveals the presence of the hidden object.24th Annual Review of Progress in Applied Computational Electromagnetics March 30 - April 4, 2008 - Niagara Falls, Canada  '2008 ACES65ClothingFree spaceDry skinFatHidden objectEixyFigure 1: Configuration.0.00.1Figure 2: Amplitude (left) and phase (right) of the difference between the total field with hidden dielectricobject and the total field without hidden object.24th Annual Review of Progress in Applied Computational Electromagnetics March 30 - April 4, 2008 - Niagara Falls, Canada  '2008 ACES664. ConclusionWe have used a 2.5D exact forward solver to simulate three-dimensional millimeter wave scattering of ahidden dielectric object on a simplified human body model, which was illuminated by a 3D Gaussian beam.This beam has been implemented using a complex source formulation. Gaussian beam and millimeterwave properties have been used to reduce the abdomen cross-section to the presented simple model. Theintroduction of a hidden dielectric object has led to a noticeable change in the total field, as could be seen ina figure of the difference between the total field with and without object.References[1] D. M. Sheen, D. L. Mc Makin and T. E. Hall, ”Three-Dimensional Millimeter-Wave Imaging forConcealed Weapon Detection”, IEEE Trans. Microw. Theory Tech., vol. 49(9), pp. 1581-1592,September 2001.[2] K. J. Langenberg, K. Mayer, and C. Sklarczyk, ”Wave field imaging for homeland security”, Proc.Int. URSI Comm. B Electromagnetic Theory Symposium (EMTS), 26-28 July 2007, Ottawa, Canada.[3] L. Volkov and J. Stiens, ”US patent 6777684: Systems and methods for millimeter and sub-millimeterwave imaging”, August 2004.[4] O. P. Gandhi and A. Riazi, ”Absorption of millimeter waves by human beings and its biologicalimplications”, IEEE Trans. Microw. Theory Tech., vol.34(2), pp. 228-235, February 1986.[5] P. Zwamborn and P. M. van den Berg, ”The three-dimensional weak form of the conjugate gradientFFT method for solving scattering problems”, IEEE Trans. Microw. Theory Tech., vol. 40(9), pp.1757-1766, September 1992.[6] S. Van den Bulcke and A. Franchois, ”A 2.5D solver to model scattering of long dielectric cylin-ders in an active millimeter wave imaging system”, The 23rd Annual Review of Progress in AppliedComputational Electromagnetics (ACES), 19-23 March 2007, Verona, Italy, pp. 1223-1229.[7] A. Abubakar, P. M. van den Berg, and T. M. Habashy, ”An integral equation approach for 2.5-dimensional forward and inverse electromagnetic scattering”, Geophys. J. Int., vol. 165, pp. 744-762,2006.[8] Felsen E. Heyman and L. B. Felsen, ”Gaussian beam and pulsed beam dynamics: complex-sourceand complex-spectrum formulations within and beyond paraxial asymptotics”, J. Opt. Soc. Am. A,vol.18(7), pp. 1588-1611, July 2001.[9] Website of the Institute for Applied Physics (Italian National research Council):http://niremf.ifac.cnr.it/tissprop/htmlclie/htmlclie.htm.24th Annual Review of Progress in Applied Computational Electromagnetics March 30 - April 4, 2008 - Niagara Falls, Canada  '2008 ACES67

Modelling 3D mm-wave scattering from human body under Gaussian beam illumination with a 2.5D VIE solver

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Modelling 3D mm-wave scattering from human body under Gaussian beam illumination with a 2.5D VIE solver

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