Surface scattering Chris Allen callen eecs ku edu Course

Surface scattering Chris Allen (callen@eecs. ku. edu) Course website URL people. eecs. ku. edu/~callen/823/EECS 823. htm 1

Outline Factors affecting scattering Simple models More complex models Where to find more information 2

Factors affecting surface scattering The scattering characteristics of a surface are represented by the scattering coefficient, For surface scattering, several factors affect Dielectric contrast Large contrast at boundary produces large reflection coefficient Air ( r = 1), Ice ( r ~ 3. 2), (Rock (4 r 9), Soil (3 r 10), Vegetation (2 r 15), Water (~ 80), Metal ( ) Surface roughness (measured relative to ) RMS height and correlation length used to characterize roughness Incidence angle, ( ) Surface slope Skews the ( ) relationship Polarization VV HH » HV VH 3

Factors affecting surface scattering Surface roughness (measured relative to ) RMS height and correlation length used to characterize roughness is the surface height standard deviation ℓ is the surface correlation length 4

Surface roughness and scattering Rayleigh criteria for “smoothness” Phase difference between two reflected rays < /2 Which leads to the following constraint on RMS height Frauenhofer criteria for “smoothness” Phase difference between two reflected rays < /8 Which leads to the following constraint on RMS height 5

Surface roughness and scattering The Rayleigh criterion states that if the phase difference (due to propagation) between two reflected rays shown (see Fig. 2. 1) is less than /2 radians, then the surface may be considered smooth. From the geometry we know (eqn 1) which, if set < /2, leads to the Rayleigh criterion for a surface to be considered smooth, that is (eqn 2) Derive the Rayleigh criterion from the information provided. Show all of the steps leading to eqns (1) and (2) 6

Surface roughness and backscatter Backscatter is the special case where o = s, o = s 7

Backscatter from bare soil Note: At 1. 1 GHz, = 27. 3 cm 8

Simple models For purposes of radar system design, simple models for the backscattering characteristics from terrain can be used. A variety of models have been developed. Below are some of the more simple models that may be useful. ( ) = (0) cosn( ) where is the incidence angle and n is a roughness-dependent variable. n = 0 for a very rough (Lambertian) surface [ ( ) = (0)] n = 1 for a moderately rough surface [ ( ) = (0) cos ( )] n = 2 for a moderately smooth surface [ ( ) = (0) cos 2 ( )] or ( ) = (0) e – / o where is the incidence angle and o is a roughness-dependent angle. In both model types (0) depends on the target characteristics 9

More complex models Less simple backscattering models A is the illuminated area k is the wavenumber, k = 2 / ℓ is the surface correlation length r is the permittivity of medium 2 relative to medium 1 r is the permeability of medium 2 relative to medium 1 (0) is the 2 nd derivative of correlation coefficient at the origin is the incidence angle is the surface height standard deviation 2| (0)| is the mean-squared surface slope Backscattering assumed throughout, unless specified otherwise o = s, o = s r = 1 also assumed 10

More complex models Small-perturbation model – or – Incoherent scattering from a slightly rough surface constraints: rough surface-height standard deviation << incident wavelength k < 0. 3 or < 0. 048 average surface slope the standard deviation times the wavenumber rms slope < 0. 3 or < 0. 21ℓ 11

More complex models Small-perturbation model – or – Incoherent scattering from a slightly rough surface 12

More complex models Coherent reflection coefficients for rough planar surface Incoherent scattering from a very rough planar surface constraints: radius of curvature >> , isotropic roughness, ℓ << A shadowing and multiple scattering ignored where s = 4 2 / ℓ 2 13

More complex models Incoherent scattering from a very rough planar surface 14

More complex models Incoherent Kirchhoff surface scattering – or – Geometric optics model constraints: ℓ > 1. 6 ℓ 2 > 2. 76 > 0. 25 shadowing and multiple scattering ignored where p and q represent the transmit and receive polarizations, hence pp represents co-polarized backscattering (hh or vv) and pq represents cross-polarized backscattering (vh or hv) 15

More complex models Incoherent Kirchhoff surface scattering – or – Geometric optics model 2| (0)| is the mean-squared surface slope – or – 2| (0)| = m 2 16

Where to find more information Ulaby FT; Moore RK; Fung AK; Microwave Remote Sensing, Vol. 2, Artech House, 1982 Fung AK; "Review of random surface scatter models, " Proc. SPIE, vol. 358, Applications of Mathematics in Modern Optics, pp. 87 -98 1982 Davies H; "The reflection of electromagnetic waves from a rough surface, " Proc. IEE, 101(part IV), pp. 209 -214, 1954 Ruck GT; Barrick DE; Stuart WD; Kirchbaum CK; Radar Cross Section, Vol. 2, 1970 17