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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

qq

f

)sincos(

sin)sin(2

2

ss

ssVHg

qq

qf

)sin(cos)sin(

2ss

sHVg

qqf

)sincos(

cossinsinsinsin2

22

SS

SISISVVg

qq

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

qq

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)