Introduction of Surface Scattering ModelingIntroduction of Surface Scattering Modeling
• Importance of surface scattering
• Dielectric properties of Soil:
• Surface roughness properties:
• Surface scattering models 1) Small Perturbation Model
2) Physical Optical Model
3) Geometrical Optical Model
4) Integral Equation Model
• Validation of surface scattering model• Numerical Simulations
Dielectric Properties of Soil Dielectric Properties of Soil
Solid Material - 4.7
Water - frequency & temperature
Soil - frequency, moisture, temperature, and texture
Im D
C
Clay 80% & Sand 20%
Clay 20% & Sand 80%
Measurement of Dielectric Properties of Soil
Measurement of Dielectric Properties of Soil
Surface Roughness PropertiesSurface Roughness Properties
• Stationary Random Rough Surface
• Description:• surface rms. Height
• correlation length
• correlation function
correlation function
1/e
GaussExponential
2/122 zzs
1)( el
dxxz
dxxzxz
)(
)()()(
2
Surface Roughness Measurement Surface Roughness Measurement
Surface Roughness Correlation Functions Surface Roughness Correlation Functions
Surface Roughness Measurements at Washita Site
n
l
xx exp)(
power spectral density function
Characteristics:
• Exponential function has higher frequency components
Power spectrum FT surface profile or correlation function
Small Perturbation ModelSmall Perturbation Model
pq = vv or hh
is the fourier transform of the surface correlation function. 0,2 xkW
0),sin(2)(cos82424 kWsk pq
opq
22 ))sin((exp2
10),sin(2 kllkW
5.12
2
))sin(2(120),sin(2
kl
lkW
Exponential
Guass
Validity Condition: ks < 0.3, kl < 3 & rms slope < 0.3
hh
s
( )
(cos sin )
12 2 22
22
)sin(cos
)sin)sin1()(1(
ss
vv
Physical Optical ModelPhysical Optical Model
is nth power of fourier transform of the surface correlation function. 0,2 xn kW
2
22
22
)sincos(
)sincos()(
vvR 2
)()( hhhhR
0),sin(2!
))cos(2())cos(2(exp)()(cos
1
2222 kW
n
ksksRk n
n
n
pqopq
n
kl
n
lkW n
22 ))sin((exp0),sin(2
5.122
2
))sin(2(0),sin(2
kln
nlkW n
Guass
Exponential
Validity Condition: 0.05λ < s < 0.15λ, l > λ, & m < 0.25
Geometric Optical ModelGeometric Optical Model
)(cos)0("2
)0("2)(tanexp)0(
42
2
2
s
sRpq
opq
)0("22 sm
2
1
1)0()0(
hhvv RR
Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7
rms slope - m
Reflectivity
Validity Regions of Classical Surface Backscattering Models
Validity Regions of Classical Surface Backscattering Models
Tradition Backscattering ModelsTradition Backscattering Models
Polorization Magnitude Roughness function
SP
PO
GO
222 )sin(exp)()( klklks
2
2
sincos
sincos
rr
rr
)1()1(rr )
2
tanexp(
2
1 2
mm
n
kl
nn
kl
klkl
n
n
4
)(exp
!
)cos(
)sin(exp)(
2
1
22
22
22
sincos
sin1sin)1(
rr
rr
Measured Co-Polarization Ratio by ScatterometerMeasured Co-Polarization Ratio by Scatterometer
Integral Equation Model (1)Integral Equation Model (1)
!
0,22exp
2
/,cos4)(2
1
222
0
n
kWIk
k
II
xn
n
nppz
ipsspspp s
where kZ = k cos, kX = k sin, and pp = vv or hh,
2
0,0,exp2 22 xppxpp
nz
zppn
znpp
kFkFkkfkI
the symbol is the Fourier transform of the nth power of the surface correlation coefficient.
0,2)(x
n kW
Integral Equation (2)Integral Equation (2)
cos/2cos/2 || RfRf hhvv
22
222||
2
cos
cossin11
cos
1sin20,0,
r
rrr
rxvvxvv
RkFkF
22
2222
cos
cossin11
cos
1sin20,0,
r
rrr
rxhhxhh
RkFkF
where, are the Fresnel reflection coefficients for horizontal and vertical polarization.
RR ,||
Validation ExperimentValidation Experiment
Comparing Models with Different SurfacesComparing Models with Different Surfaces
20°
40°
Smooth Surface
Mixed Surface
Comparing Models with Rough Surface Comparing Models with Rough Surface
40°
20°
40°
Comparing Models with Mixed Surface Comparing Models with Mixed Surface
40° 20°
Comparing IEM Model with SIR-C & AIRSAR Measurements
Comparing IEM Model with SIR-C & AIRSAR Measurements
Polarization & Incidence Sensitivities to Soil Moisture
Polarization & Incidence Sensitivities to Soil Moisture
-- - (VV*HH)^0.5….. VV----- HH 40°
VV ------ 50° - - - - 30°
Sensitivity to Surface Roughness Sensitivity to Surface Roughness
40°Co-function : exp
-- - 50°….. 40°----- 30°
L - - - 20L ….. 15L ----- 10
n - - - 1n ….. 1.2n----- 1.4
n - - - 1n ….. 1.2n----- 1.4
Characteristics of Classical & IEM Surface Backscattering Models
Characteristics of Classical & IEM Surface Backscattering Models
For GO• Co-polarization ratio is unite
For IEM• Dielectric and roughness functions are not independent
Tradition models: Two independent functions • Dielectric and roughness
For SP & PO• co-polarization ratio HH/VV is independent of surface roughness and proportion to dielectric constant and incidence angle
Problems in Roughness MeasurementsProblems in Roughness Measurements
Simulation of Surface RoughnessSimulation of Surface Roughness
Effect of Multi-scale Surface roughness on Backscattering
Effect of Multi-scale Surface roughness on Backscattering
Summary on Surface Scattering ModelsSummary on Surface Scattering Models
• Surface roughness parameters are described by the surface
auto-correlation function, rms height, and correlation length
• Tradition surface scattering models (SP, PO, and GO) are
outside of application range due to restrictions on surface
roughness parameters
• Recently developed IEM model has much wider application
range for surface roughness parameters
• Research is needed for better techniques to describe natural
surface properties
Outline of today’s talkOutline of today’s talk
• Importance of surface scattering
• Dielectric properties of Soil:
• Surface roughness properties:
• Surface scattering models 1) Small Perturbation Model
2) Physical Optical Model
3) Geometrical Optical Model
4) Integral Equation Model
• Validation of surface scattering model• Numerical Simulations