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Surface scattering

Chris Allen (callen@eecs.ku.edu)

Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

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OutlineFactors affecting scattering

Simple models

More complex models

Where to find more information

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Factors affecting surface scatteringThe 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 coefficientAir (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 slopeSkews the () relationship

PolarizationVV HH » HV VH

s0ss00 p,p;,;,

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Factors affecting surface scatteringSurface 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

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Surface roughness and scatteringCriteria for “smoothness”

Phase difference between two reflected rays < /2Which leads to the following constraint on RMS height

cos32

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Surface roughness and backscatterBackscatter is the special case where o = s, o = s

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Backscatter from bare soil

Note: At 1.1 GHz, = 27.3 cm

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Simple modelsFor 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) cos2 ()]

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

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More complex modelsLess 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 2nd 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 otherwiseo = s, o = s

r = 1 also assumed

coso

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More complex modelsSmall-perturbation model – or – Incoherent scattering from a slightly rough surface

constraints:

rough surface-height standard deviation << incident wavelengthk < 0.3 or < 0.048

average surface slope the standard deviation times the wavenumber

rms slope < 0.3 or < 0.21ℓ

2sink24224ohh eRcosk4

2sink

2

22

rr

2r

2

r4224o

vv esincos

sin1sin1cosk4

0ovh

ohv

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More complex modelsSmall-perturbation model – or – Incoherent scattering from a slightly rough surface

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More complex modelsCoherent 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 / ℓ2

]cosk2[expRR 2||

R||

]cosk2[expRR 2R

2

2

2

||2

4ovv

ohh tan

s

1exp0R

s

sec

0ovh

ovh

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More complex modelsIncoherent scattering from a very rough planar surface

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More complex modelsIncoherent Kirchhoff surface scattering – or – Geometric optics model

constraints:

ℓ > 1.6

ℓ2 > 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) andpq represents cross-polarized backscattering (vh or hv)

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02/tan2

ppopp cos02

e0R22

0opq

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More complex modelsIncoherent Kirchhoff surface scattering – or – Geometric optics model

2|(0)| is the mean-squared surface slope

– or –

2|(0)| = m2

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Where to find more informationUlaby 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