1) The document analyzes polarization features in bistatic scattering from rough surfaces using analytical methods like SPM, PO, and SSA/RLCA. 2) SPM predicts nulls in certain polarization configurations depending on permittivity and scattering angles. PO and SSA/RLCA transitions these predictions depending on roughness. 3) Numerical simulations using MOM agree with SSA/RLCA and show the transition of null regions with increasing roughness. 4) Understanding these polarization effects could help design bistatic remote sensing systems or interpret results from previous studies of soil moisture sensing.

1. 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

3. Full hemisphere integration of NRCS required for brightness temperature studies also motivates understanding bistatic properties

4. 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. RemSens, Aug 2010

5. Pierdicca et al suggest some bistatic configurations for sensing soil moisture

6. Scattering effects that differ with polarization can be useful

7. Basic properties of scattering features investigated here analytically

8. Approach: investigate polarization properties of complete hemisphere bistatic pattern vs. incidence angle/surface roughness/permittivity

10. 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 polb, scattered pola ): Kernel functions capture all polarization effects for slight roughness; explore as function of scattered polar (qs) and azimuth (fs) angles (0 inc. azimuth angle) SPM kernel function: depends only onpolarization, incident-scattering angle, and surface permittivity (not roughness) Bragg Fourier Coefficient fromsurface roughness Field scattered in direction

11. 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

12. SPM Examples qi=20o, e=10+i0.05, h=l/20, L=l/2, Gaussian correlation function qi=40o, e=10+i0.05, h=l/20, L=l/2, Gaussian correlation function

13. SPM Examples qi=40o h=l/20, L=l/2, Gaussian correlation function, vspermittivity Same case, cuts vs. azimuth at qS=40o e=3 e=10+i0.05 e=50+i40 HH minlocation and depth fixed withe VV minlocation and depth vary withe

14. 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: Final term differs from SPM VV large |e| limit Same shifted circle as in SPM VV large |e| limit

15. 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 bistaticpol 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

16. 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

17. Comparison of MOM and SSA:qi=20o, e=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

18. Comparison of MOM and SSA:qi=20o, e=10+i0.05, h=l/20, L=l/2 Zoom around “null” region for qS=40o In plane versus qSto examine x-pol “null” region

19. Comparison of MOM and SSA:qi=40o, e=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

20. Comparison of MOM and SSA:qi=20o, e=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

21. Comparison of MOM and SSA:qi=20o, e=10+i0.05, h=l/10, L=l Zoom around “null” region for qS=40o In plane versus qSto examine x-pol “null” region

22. Comparison of MOM and SSA:qi=20o, e=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

23. Variation with roughness from SSA: qi=20o, e=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

24. 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

25. 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) Bistaticpolarimetry has also been explored (not discussed here)