A Study of Polarization Features in Bistatic
Scattering from Rough Surfaces
IGARSS 2011
Joel T. Johnson
Department of Electrical and Computer Engineering
ElectroScience Laboratory
The Ohio State University
Vancouver, Canada
26th July 2011
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Motivation

Increasing interest in bistatic microwave sensing (including out-of-plane
geometries) motivates renewed examination of scattering effects

Full hemisphere integration of NRCS required for brightness temperature
studies also motivates understanding bistatic properties

Out-of-plane geometries in particular have received little consideration in the
literature with a few exceptions:
Papa et al, IEEE Trans. Ant. Prop, Oct 1986 , Hauck et al, IEEE Ant. Prop. Mag, Feb ’98, Hsieh&
Chang, J. Marine Sci. Tech, vol. 12, 2004, Nashashibi & Ulaby, IEEE TGRS, June 2007,
Pierdicca et al, TGRS, Oct 2008, Brogioni et al, Int’l J. Rem Sens, Aug 2010



Pierdicca et al suggest some bistatic configurations for sensing soil moisture

Scattering effects that differ with polarization can be useful

Basic properties of scattering features investigated here analytically
Approach: investigate polarization properties of complete hemisphere bistatic
pattern vs. incidence angle/surface roughness/permittivity
Rough surface only considered here: expand in the future to include
volume scattering media
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Outline

Bistatic pattern properties from analytical methods
– SPM
– PO
– SSA/RLCA

Comparison of analytical and numerical models

Further investigation of pattern properties

Summary
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Bistatic Pattern Properties with Analytical Methods:
SPM

The Small Perturbation Method (SPM) is applicable for scattering from surfaces
of small rms height compared to the EM wavelength and small slopes

Produces a perturbation series for scattered fields: first order only most typical

Fields at first order have the form (incident pol b, scattered pol a ):
 ab (ks )  hk k gab (ks , ki )
s
i
Field scattered Bragg Fourier
in direction k s Coefficient from
surface roughness

gVV 
SPM kernel function: depends only on
polarization, incident-scattering angle, and
surface permittivity (not roughness)
Kernel functions capture all polarization effects for slight roughness; explore as
function of scattered polar (qs) and azimuth (fs) angles (0 inc. azimuth angle)
 sin q S sin q I    sin 2 q S   sin 2 q I cos fS
( cos q S    sin q S )
cos(fs )
2
g HH 
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(cos q s    sin 2 q s )
gVH 
g HV 
sin( fs )
(cos q s    sin 2 q s )
sin( fs )   sin 2 q s
( cos q s    sin 2 q s )
Bistatic Pattern Properties with Analytical Methods:
SPM


Things to Notice:
– HH always vanishes in the cross-plane (i.e. fs=90o)
– VH/HV always vanish in plane (i.e. fs=0o or 180o)
– VV has a more complicated dependence on fs
2
Writing
k02  sin q S sin q I
gVV  A  cos fS with A 
*
2
 k1zI k1zS
it can be shown that gVV has a minimum in azimuth at cos fS  Re( A)
2
2
and that gVV at the minimum is proportional to Im( A)

Consequences:
– VV goes to zero if A is real: real valued permittivities or
approximately for large permittivity amplitude
– Does not go to zero for A complex, but has a minimum vs. azimuth
– “Null” locations trace out a curve in (kxs,kys) space that depends on
incidence angle and permittivity
 Approximately a shifted circle for large permittivity amplitude
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SPM Examples

qi=20o, =10+i0.05, h=l/20, L=l/2, Gaussian correlation function

qi=40o, =10+i0.05, h=l/20, L=l/2, Gaussian correlation function
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SPM Examples
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qi=40o h=l/20, L=l/2, Gaussian correlation function, vs permittivity
=3

=10+i0.05
=50+i40
Same case, cuts vs. azimuth at qS=40o
VV min
location
and depth
vary
with 
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HH min
location
and depth
fixed
with 
Bistatic Pattern Properties with Analytical Methods:
PO

PO applicable for larger heights so long as slopes small (i.e. large
scale features in surface), better near specular

PO polarization and permittivity dependence approximated at
stationary phase point; NRCS then decouples roughness and
polarization/permittivity effects in a product form

Influence of permittivity through reflection coefficients makes
determination of minima in PO NRCS difficult; differs from SPM

In limit of large permittivity amplitude, HH and VV returns become
identical
– NRCS vanishes for both pols on contour in (kxs,kys) plane:
2
2
 k  k0
  k 2   k0
  k k cot q
 xs



ys
xs zs
I
2
sin
q
2
sin
q
I 
I 


Same shifted circle as in SPM VV
large || limit

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Final term
differs from
SPM VV large
|| limit
Bistatic Pattern Properties with Analytical
Methods: SSA or RLCA

Small Slope Approximation (SSA) or Reduced Local Curvature Approximation
(RLCA) reduce to SPM and PO in appropriate limits
– Here using two field series terms (3 NRCS terms) from these methods
– RLCA/SSA generally similar so only SSA shown in what follows
– Analytic forms not simple; require numerical evaluation to examine

Should expect similar bistatic pol behaviors as SPM at small rms height that
presumably will approach PO behaviors at larger heights


Differences between PO and SPM imply that “minimum” regions should
depend on roughness
– e.g. SPM null in HH at fs=90o apparently “fills in” to no null in PO at larger
roughness
All analytical methods considered in what follows are limited to “smoother”
surfaces (h/L<~ 1/5) and non-grazing incident/scattering angles
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Numerical Method

Since higher order scattering effects may dominate when single scattering
is weak (i.e. in “null” regions), important to compare with any more “exact”
scattering method to verify predictions

Method of moments (MOM) used for this purpose in Monte Carlo simulation
– 3-D surface scattering problem, 64 realizations
– 32 x 32 wavelength surface, 512 x 512 points, 1 million unknowns
– Point matching solution, iterative solver, Canonical grid acceleration
– Run using supercomputing resources at Maui High Performance
Computing Center
– Use new approach by Saillard and Soriano, Waves Random Complex
Media, 2011 to illuminate surface with plane wave without edge
diffraction concerns
– Isotropic Gaussian correlation function surfaces
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Comparison of MOM and SSA:
qi=20o, =10+i0.05, h=l/20, L=l/2
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MOM predictions show “minimum” regions similar to SPM
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Ratio of MOM to SSA NRCS values shows SSA provides good match

;i
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Comparison of MOM and SSA:
qi=20o, =10+i0.05, h=l/20, L=l/2
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Zoom around “null” region for qS=40o
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In plane versus qS to examine x-pol “null” region
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Comparison of MOM and SSA:
qi=40o, =10+i0.05, h=l/20, L=l/2
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MOM predictions again show “minimum” regions similar to SPM
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Ratio again shows SSA provides good match
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Comparison of MOM and SSA:
qi=20o, =10+i0.05, h=0.1l, L=1l
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Locations of minimum regions coming closer to PO for HH
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Larger differences with SSA but minimum regions still similar
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Comparison of MOM and SSA:
qi=20o, =10+i0.05, h=l/10, L=l
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Zoom around “null” region for qS=40o

In plane versus qS to examine x-pol “null” region
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Comparison of MOM and SSA:
qi=20o, =10+i0.05, h=0.3l, L=2l
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Locations of minimum regions coming closer to PO for HH
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Larger differences with SSA but minimum regions still similar
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Variation with roughness from SSA:
qi=20o, =3, L=l, h varies from l/20 to l/4
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Cuts in azimuth at qS=20o
Increasing
rms height

Increasing
rms height
SSA captures “filling in” of minima as roughness increases, also
transition from SPM-like to PO-like minima locations
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Potential Applications

Previous bistatic soil moisture sensing study (Pierdicca et al, 2008)
used AIEM with a “brute force” approach to study soil moisture
sensitivity
– Insights from this work may motivate renewed examination?

Since VV minimum region varies with permittivity, some sensitivity to
permittivity should be expected

Different effects of surface scattering on polarizations may be useful for
separating surface and volume effects
– Like co-pol vs. cross-pol for backscatter but again with permittivity
dependent minimum location
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Conclusions

Analytical properties of “null” regions in bistatic cross sections derived
– SPM at first order:
 HH vanishes in cross-plane, cross-pol vanishes in-plane
 VV has a minimum in a curve in (kxs,kys) space, vanishes on
this curve if permittivity is real or large amplitude
– PO difficult to derive minima locations, but for large permittivity
amplitude both HH and VV vanish on a (kxs,kys) curve distinct
from that of SPM
– SSA/RLCA capture transition between SPM/PO predictions and
“filling in” of minima as roughness increases

MOM comparisons indicate that SSA captures these behaviors
accurately at least for “smooth” surfaces

Insight into these behaviors may be useful in designing bistatic remote
sensing systems (or interpreting insights from previous studies)

Bistatic polarimetry has also been explored (not discussed here)
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