a study of polarization features in bistatic scattering from rough surfaces
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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. Motivation. - PowerPoint PPT PresentationTRANSCRIPT
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A Study of Polarization Features in Bistatic Scattering from Rough Surfaces
IGARSS 2011
Joel T. JohnsonDepartment of Electrical and Computer Engineering
ElectroScience LaboratoryThe Ohio State University
Vancouver, Canada26th 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 ):
Kernel functions capture all polarization effects for slight roughness; explore as function of scattered polar (qs) and azimuth (fs) angles (0 inc. azimuth angle)
),()( iskks kkghkis abab
Field scattered in direction sk
Bragg FourierCoefficient fromsurface roughness
SPM kernel function: depends only onpolarization, incident-scattering angle, andsurface permittivity (not roughness)
)sin(cos
)cos(2
ss
sHHg
f
)sincos(
sin)sin(2
2
ss
ssVHg
qf
)sin(cos)sin(
2ss
sHVg
qqf
)sincos(
cossinsinsinsin2
22
SS
SISISVVg
fqqqq
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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
Writing with
it can be shown that has a minimum in azimuth at and that at the minimum is proportional to
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
SVV Ag fcoszSzI
IS
kkk
A11
*
220 sinsin
2
VVg )Re(cos AS f2
VVg 2)Im(A
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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 qi=40o h=l/20, L=l/2, Gaussian correlation function, vs permittivity
Same case, cuts vs. azimuth at qS=40o
=3 =10+i0.05 =50+i40
VV minlocation and depth vary with
HH minlocation and depth fixed with
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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:
IzsxsI
ysI
xs kkkkkk qqq cotsin2sin2
202
20
Final term
differs from SPM VV large|| limitSame shifted circle as in SPM VV
large || limit
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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
MOM predictions show “minimum” regions similar to SPM
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
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=40o, =10+i0.05, h=l/20, L=l/2
MOM predictions again show “minimum” regions similar to SPM
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
Locations of minimum regions coming closer to PO for HH
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
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
Locations of minimum regions coming closer to PO for HH
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
Cuts in azimuth at qS=20o
SSA captures “filling in” of minima as roughness increases, also transition from SPM-like to PO-like minima locations
Increasingrms height
Increasingrms height
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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)