1 Surface scattering Chris Allen Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

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

3 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

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

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

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) cos n (  ) 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  < 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 Davies H; "The reflection of electromagnetic waves from a rough surface," Proc. IEE, 101(part IV), pp , 1954 Ruck GT; Barrick DE; Stuart WD; Kirchbaum CK; Radar Cross Section, Vol. 2, 1970