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Comments on Compact Polarimetry

Comments on Compact Polarimetry. R. Keith Raney Johns Hopkins University Applied Physics Laboratory k.raney@ieee.org With contributions from T. Ainsworth (USA), P. Dubois-Fernandez (France), T. Misra (India), E. Pottier (France), and J.-C. Souyris (France). Orthogonal Tx pols

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Comments on Compact Polarimetry

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  1. Comments on Compact Polarimetry R. Keith Raney Johns Hopkins University Applied Physics Laboratory k.raney@ieee.org With contributions from T. Ainsworth (USA), P. Dubois-Fernandez (France), T. Misra (India), E. Pottier (France), and J.-C. Souyris (France) CCRS, Ottawa, Canada, 19 March 2008

  2. Orthogonal Tx pols Coherent Dual Rx Pseudo 3x3 scattering matrix One Tx Pol, Coherent Dual Rx Symmetry assumptions 2x2 coherency matrix No symmetry assumptions 2 magnitudes & co-pol phase Two Tx pols Two Rx pols 2 magnitudes 2 magnitudes One polarization Magnitude Polarimetric Imaging Radar Hierarchy Nomenclature Result Processing Radar 4x4 scattering matrix No assumptions Full polarization Reciprocity & symmetry Quadrature polarization 3x3 scattering matrix Compact polarization 2 orthogonal Like-pol images & CPD 2 orthogonal Like-pol images Dual polarization Like- and Cross-pol images Mono-polarization Real image CCRS, Ottawa, Canada, 19 March 2008

  3. Context and Motivation • Objective: Strive toward quadrature-polarization performance while transmitting on only one polarization • Benefits: Simpler radar, twice the swath width, half of the data volume (per pixel), half of the average transmit power, all in contrast to quad-pol • Disadvantage: Fewer degrees of freedom for image decomposition, compared to full-pol or quad-pol • Comment: Excellent alternative mode for a full-pol SAR, and a major improvement (at small marginal cost) over a basic two-channel (incoherent) dual-polarized radar CCRS, Ottawa, Canada, 19 March 2008

  4. Quad-Pol: First-Order “Cost” Net data volume is comparable: 2x data per pixel AND half as many pixels Courtesy, P. Dubois-Fernandez, ONERA CCRS, Ottawa, Canada, 19 March 2008

  5. Example: ALOS PalSAR Modes Courtesy, P. Dubois-Fernandez, ONERA CCRS, Ottawa, Canada, 19 March 2008

  6. Compact Polarimetry Compact (Partial) Polarimetry SAR Precedents • First papers: Imbo and Souyris (2000) and Lee et al. (2001) • Various combinations of linear polarizations (e.g. HH and VV ) • Full polarization “better”, but partial pol => certain advantages • Pi/4 mode defined in Souyris and Mingot (2002) • Transmit linear polarization at 45-degree orientation, & receive two orthogonal linear H and V polarizations (“Pi/4”) • Rotational variance noted wrt dipole or dihedral backscatterers • Pi/4 mode expanded by Souyris et al. (2005) • Alternative compact modes (2006) • Stacy: Transmit circular; receive like and opposite circular (“CC”) • Raney: Transmit circular; receive linears (“CL”) CCRS, Ottawa, Canada, 19 March 2008

  7. Compact Polarimetry Schemes Compared CCRS, Ottawa, Canada, 19 March 2008

  8. L-0 L-1 Transmitter & waveform 90o L-0 |H| HV* Timing and control H V |V| S1 S2 S3 S4 H H Rx channel LNA H X V V* L-1 V Rx channel LNA H V Antenna H V CL Hybrid-Polarity Architecture* Transmit CP (note the 90o hybrid) Receive (coherently) linear (H & V) Primary data product: 2x2 covariance (or coherency) matrix of the observed field, or (equivalently) the 4-element Stokes vector *MiniSAR on Chandrayaan-1 is the first such orbital radar CCRS, Ottawa, Canada, 19 March 2008

  9. Stokes Parameters and Hybrid Polarity • Results depend on choice of transmit polarization (circular polarization preferred for several reasons) • Stokes parameter values are independent of the polarization basis of the received field • Therefore, a linear basis on receive is just as good as the classical circular polarity (e.g. Arecibo) CL Hybrid Polarity Circular/circular S1 = < |EH|2 + |EV |2 > = < |EL|2 + |ER|2 > S2 = < |EH|2−|EV|2 > = 2 Re < ELER* > S3 = 2 Re < EHEV*> = 2 Im < ELER* > S4 = − 2 Im < EHEV*> = − < |EL|2−|ER|2 > CCRS, Ottawa, Canada, 19 March 2008

  10. Stokes “Child” Parameters Fundamental; 1:1 mapping wrtEntropyE E ~ (1 – m2)γ, γ~0.74 Degree of polarization m = (S22 + S32 + S42)½ / S1 Indicator of scattering associated with planetary ice deposits or dihedrals: μC > ~0.5 (Generalizes to elliptical pol) Circular polarization ratio μC = (S1 - S4) / (S1 + S4) Sensitive indicator of “double bounce” backscattering, rotationally invariant iff CP Tx Relative phase δ= arctan( S4 / S3 ) Gentle transition from perfect circular polarization to elliptical (near-unity axial ratio) Ellipticity μE = S4 / S1 CCRS, Ottawa, Canada, 19 March 2008

  11. CL-pol 2x2 decomposition: m- method • Decomposition data analysis (a la S. Cloude) starts with a 3x3 coherency matrix (from a quad-pol radar) • ALERT: The canonic data product from a compact-pol radar is (only!) the 2x2 coherency matrix • Consequence: EITHER expand the 2x2 into a 3x3 pseudo-coherency matrix by assuming certain symmetry conditions (e.g. Souyris, Ainsworth, Dubois-Fernandez) OR use the 2x2 matrix (minimal assumptions) • The Stokes Parameters and their “child parameters” are an excellent “2x2” starting point (e.g., m-delta) CCRS, Ottawa, Canada, 19 March 2008

  12. Expected opposite-sense phase signal in response to circularly polarized transmissions, indicating single-bounce (e.g. Bragg) or triple-bounce backscatter +180 90 Relative H-V phase δ (degrees) Phase signal of same-sense circularly-polarized return in response to circularly polarized transmissions, which indicates double bounce (dihedral) or coherent backscatter effect (volumetric water ice) 0 -90 -180 0 Degree of polarizationm 1 Stokes-parameter based transformation from hybrid-polarity SAR image data to m-δ feature space Polarimetric SAR data, Courtesy, JPL RH-Pol Backscatter Decomposition in m-δSpace CCRS, Ottawa, Canada, 19 March 2008

  13. Image Following m-delta Feature Decomposition G (Green) dominantly depolarised backscatter R (Red) dominantly double bounce backscatter B (Blue) dominantly single bounce (or Bragg) backscatter where So = first Stokes parameter, m = the polarization index, and delta = relative H/V phase Acknowledgement, Tapan Misra Space Applications Centre, ISRO Ahmedabad, India CCRS, Ottawa, Canada, 19 March 2008

  14. Result: m/delta CL-pol Decomposition of San Francisco The same methodology is generalizable to other specific applications Credit: Tapan Misra SAC, ISRO Original source: AirSAR C-Band quad-pol data, courtesy JPL CCRS, Ottawa, Canada, 19 March 2008

  15. Calibration “Circular” = Simultaneous Linear Polarizations !!! Transmit: Left-Circular Polarization => EH + jEV, |EH| = |EV| Backscatter (complex) reflectivities: [ shhshv; svhsvv ] Receive:EH = shhEH + jshvEV(gain and loss normalized, EV = svhEH + jsvvEVand |EH| = |EV| = 1) Symmetry conditions: shv = svhand < svvs*vh> = 0 Then: <|EH|2> = <|shh|2> + <|shv|2> <|EV|2> = <|svv |2> + <|shv|2> CCRS, Ottawa, Canada, 19 March 2008

  16. <|EH|2> = <|shh|2> + <|shv|2><|EV|2> = <|svv |2> + <|shv|2> Consequences • The mean signal levels in the two receive channels are always similar, differing only by <|svv|2>  <|shh|2> • “Cross-polarized” constituents are always equal • Equality of mean signal power iff |svv|2= |shh|2 • This condition is always true in nadir-viewing incidence, over nominally level random terrain • CL architecture is self-calibrating (for relative gain) without known reference such as a corner reflector • A nadir-viewing mode is advisable for any dual-pol or full-pol radar as an operational capability CCRS, Ottawa, Canada, 19 March 2008

  17. Quantitative Comparison: Compact vs Quad Quad-Pol Data used to Simulate the Compact Polarimetric Modes Pauli Display Red: |HH-VV| Green: |HV| Blue: |HH+VV| Courtesy, T. Ainsworth, NRL L-band data of Oberpfaffenhofen CCRS, Ottawa, Canada, 19 March 2008

  18. CL Hybrid-Pol Mode vs Quad-Pol Entropy (H) and Alpha from pseudo-3x3 scattering matrix Courtesy, T. Ainsworth, NRL CCRS, Ottawa, Canada, 19 March 2008

  19. True Quad-pol Classification L-band Quad-pol Classification, Flevoland Courtesy, T. Ainsworth, NRL CCRS, Ottawa, Canada, 19 March 2008

  20. Pseudo Quad-pol results are biased high, but hybrid-pol mode (left) is generally better than the /4 mode (right) for both entropy and . Compact vs. True Quad-pol Entropy & -angle Entropy (H) and Alpha from pseudo-3x3 scattering matrix Courtesy, T. Ainsworth, NRL CCRS, Ottawa, Canada, 19 March 2008

  21. A Polarimetric Analysis Tool Box* Sponsorship: European Space Agency POLSARPRO Documentation. To read the User Manual, click on a title below. Envisat Spaceborne Data Processing Interface User Manual  Interfaces for the EO Scientific Investigator User Manual       POLSARPRO Display and Viewer v3.0 User Manual       Tools User Manual       POLSARPRO version 3.0 Beta 3.1 Software Technical Documentation * Available (free) on-line: Highly recommended Courtesy, E. Pottier CCRS, Ottawa, Canada, 19 March 2008

  22. Conclusions (1/2) • Compact polarimetry allows free choice of the receiver polarization basis, to optimize the radar design for example • Compact polarization data are sufficient for decomposition strategies (either 2x2 direct approach, or 3x3 pseudo-covariance matrix) • Choice of Transmit (Tx) polarization: The 4-element covariance matrix (or Stokes vector) of the backscattered field is rotationally invariant if and only if the transmit polarization is circular • Hybrid-polarity CL-polarchitecture: Tx circular; Rx H&V coherently (one form of compact polarimetry) • CL hybrid-polarity architecture provides unique advantages for system calibration, including relative gain and phase • CL hybrid-polarity is more robust in response to imperfect transmit polarization, antenna patterns, and dual-channel receiver match CCRS, Ottawa, Canada, 19 March 2008

  23. Conclusions (2/2) • CL hybrid quad-pol architecture minimizes range ambiguities • CL hybrid-pol architecture maximizes cross-channel isolation • A CL hybrid-polarity mode is recommended for any multi-pol SAR • Choice of transmit polarization is application-dependent • Nadir imaging mode is suggested for any multi-pol SAR to provide reference data for calibration against natural random terrain • Any (existing) quad-pol data can be transformed to replicate compact polarimetric data, such as CL hybrid-pol or pi/4 mode • The resulting data sets provide a basis for quantitative comparison of compact vs quad-pol decomposition for a variety of applications CCRS, Ottawa, Canada, 19 March 2008

  24. Suggested References • Proceedings (on line) PolInSAR 2007 • Proceedings, ASAR/CEOS, Vancouver, 2007 • Dubois-Fernandez et al, forthcoming paper on compact polarimetry, TGARS, 2008 • Freeman and Raney, IGARSS 2008 (Range ambiguity suppression in CL Hybrid Quad Pol) • Raney, IGARSS 2008 (CL Hybrid Quad Pol) • (Other recent papers and conference proceedings by the participating/contributing authors) CCRS, Ottawa, Canada, 19 March 2008

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