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©DCNS all rights reserved / tous droits réservés Scattering of electromagnetic waves from rough surfaces at very low grazing angles. Ph. SPIGA, North American Radio Science Meeting, URSI /07/2007 M. SAILLARD G. SORIANO Ph. SPIGA

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2 | 23/07/2007 | North American Radio Science Meeting CONTENTS 1.Analytical results 2.Numerical model 3.Approximate models 4.The ocean surface

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3 | 23/07/2007 | North American Radio Science Meeting Scattering at low-grazing angles q0q0 q x z Surface S: z = f(x,y) Plane wave Mean plan (z = 0) Homogeneous medium The local perturbation of the plane model Beam x Source point or beam around grazing Reality

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4 | 23/07/2007 | North American Radio Science Meeting Fresnel coefficients Brewster Dirichlet (r=-1) Neumann (r=+1) The Neumann model should not be used for reflexion over finite conductivity materials around and beyond the Brewster angle

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5 | 23/07/2007 | North American Radio Science Meeting Scattering of scalar waves at LGA Tatarskii, Charnotskii, Barrick, Fuks, Voronovich, Ishimaru The scattering amplitude S(q,q 0 ) The backscattering cross section (q) Dirichlet Neumann

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6 | 23/07/2007 | North American Radio Science Meeting Scattering of 3D electromagnetic waves at LGA Spiga, Soriano, Saillard Perfect Electrical conductorby reflexion on the mean plane Horizontal (TE) Vertical (TM) M 0 and P 0 are the linear integral operator of the boundary integral formalism Locally perturbated plane under plane wave illumination Low-grazing incidence angle

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7 | 23/07/2007 | North American Radio Science Meeting Scattering of 3D electromagnetic waves at LGA Spiga, Soriano, Saillard Low-grazing scattering angle? Reciprocity scattered incident polarization Polarization PEC HH PEC HV PEC VH PEC VV Transmission Conclusion Fresnel+Reciprocity PEC only valid in HH at LGA

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8 | 23/07/2007 | North American Radio Science Meeting CONTENTS 1.Analytical results 2.Numerical model 3.Approximate models 4.The ocean surface

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9 | 23/07/2007 | North American Radio Science Meeting THE GRAZING ISSUE i becomes very large grazing incidence: With present model, the number of unknowns is numerically untractable. Backscattering energy is very weak at small grazing angles numerical accuracy is required. i Numerical solution of the rigorous problem

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10 | 23/07/2007 | North American Radio Science Meeting The Grazing Model The roughness is a local perturbation of a plane. The problem is bounded. A plane wave can be used. The size of the problem is independent of the incidence More precise for backscattering.

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11 | 23/07/2007 | North American Radio Science Meeting The scattered field Theoretical results x z S+S+ Extinction theorem S - = 0 Numerical results

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12 | 23/07/2007 | North American Radio Science Meeting Surface waves SPW radiate in upper and lower half-space as a sinc function. Surface size is finite

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13 | 23/07/2007 | North American Radio Science Meeting The scattered field The behavior of the scattered field is enforced, the truncated SPW contribution has been cancelled. the truncated SPW contribution = S - S diff = S + - S -

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14 | 23/07/2007 | North American Radio Science Meeting CONTENTS 1.Analytical results 2.Numerical model 3.Approximate models 4.The ocean surface

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15 | 23/07/2007 | North American Radio Science Meeting Comparisons with approximate methods on moderately rough surfaces Geometrical Optics Physical Optics Small Perturbation Method : Perturbative expansion of the scattering amplitude Small height, rms< /20 Small Slope Approximation (by Voronovich): Based on the fundamental properties of the scattering amplitude Physical Optics integral with polarization dependence Coincide with SPM at the small height limit Small slope (rms< 0.15 ) + moderate height

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16 | 23/07/2007 | North American Radio Science Meeting Comparisons with SPM1 and SSA1 Perfect conducting Gaussian surface, rms = /12 and lc = /2

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17 | 23/07/2007 | North American Radio Science Meeting Conclusion and future works A rigorous model is well adapted for the grazing angle The number of unknowns is independent of the incidence angle Deterioration of the results of SPM1 and SSA1 at low grazing backward angles Failure of SPM1 and SSA1 at low grazing incidence angle for Gaussian surface Compare other approximate models, more advanced or Low grazing angle oriented (WCA, Ishimaru, …), with the Grazing boundary integral The dielectric and impedance cases

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18 | 23/07/2007 | North American Radio Science Meeting CONTENTS 1.Analytical results 2.Numerical model 3.Approximate models 4.The ocean surface

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19 | 23/07/2007 | North American Radio Science Meeting The high-frequency part of the ocean wave spectrum wave < 15 x EM 80°89° Error in backscattering X band X f=10GHZ =3cm

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20 | 23/07/2007 | North American Radio Science Meeting Two-scale model for ocean scattering Combining GO for long waves and SPM or SSA for short waves Surface model Tilted rough facets Facets slopes and small-scale roughness are independent The Shadowing issue Local shadowing cannot enforce zero limit at grazing Non-local shadowingshadowing functions (65 Beckmann 67 Wagner 67 Smith 02 Bourlier) gives the probability that a point on a rough surface doesnt lie in shadow when the surface is illuminated with a parallel beam of given incidence.

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21 | 23/07/2007 | North American Radio Science Meeting The shadowing function for grazing incident and scattering angles Non-local shadowing functions (65 Beckmann 67 Wagner 67 Smith 02 Bourlier) gives the probability that a point on a rough surface doesnt lie in shadow when the surface is illuminated with a parallel beam of given incidence. The Scattering Cross Section is corrected by a multiplicative factor, the shadow- ing function F(q,q 0 )

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22 | 23/07/2007 | North American Radio Science Meeting The shadowing function for grazing incident and scattering angles The shadow function evaluation may turn very tricky when the correlation function between height and slope is taken into account. All shadowing functions rely on ray tracing. They may be derived from the second order Kirchhoff approximation for vector waves, with a high-frequency assumption. The Kirchhoff approximation is mainly designed for near-specular scattering. In that sense, LGA backscattering is obvious out of its validity domain. Note that on the ocean surface, shadowing starts around 80-85°, depending on the wind speed. All the shadowing functions share the same behaviour at LGA With as a consequence a supplementary q multiplicative factor over the backscattering cross section

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