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Electric Field Equation

A Refined Polarization Response, and Object Detection with Radar Polarimetry Using Dual-Frequency and Dual Aspect Angle Observations Teemu Tares and Martti Hallikainen Laboratory of Space Technology, Helsinki University of Technology Espoo, FINLAND. Electric Field Equation.

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Electric Field Equation

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  1. A Refined Polarization Response, andObject Detection with Radar Polarimetry UsingDual-Frequency and Dual Aspect Angle ObservationsTeemu Tares and Martti HallikainenLaboratory of Space Technology, Helsinki University of TechnologyEspoo, FINLAND

  2. Electric Field Equation Backscattered field as a function of incident field Jones vectors of incident and backscattered waves Sinclair matrix S describing the scatterer

  3. Electric Field Ratio R = Polarization

  4. Polarization Equation Scattered polarization as a function of transmit polarization

  5. Power Equation Scattered power as a function of transmit polarization

  6. Polarization Match Similarity of polarization states R1 and R2 1 = same polarizations 0 = orthogonal polarizations

  7. Poincaré Sphere

  8. Polarization Response

  9. Vertical cylinder Max. Power Min. Power V LCP RCP H

  10. Horizontal cylinder Max. Power Min. Power V LCP RCP H

  11. R-Helix Max. Power Min. Power V LCP RCP H

  12. L-Helix Max. Power Min. Power V LCP RCP H

  13. V Max. Power H LCP RCP Min. Power Power responses appear similarly • Vertical/horizontal • cylinder • Right-/left-handed • helix

  14. Random Random type of scatterer Max. Power Min. Power V LCP RCP

  15. Polarization Response • Power depends on: • Cos (R, Rmax) • Max. backscatter Pmax • Min. backscatter Pmin

  16. Polarization Response • Power depends on: • Min. backscatter Pmin • Max. backscatter Pmax • Pol. match to Rmax • Power Eq. optimization: • Max. pol.  (Pmax, Rmax) • Min. pol.  (Pmin, Rmin) • Rmin orthogonal to Rmax

  17. Maxxpower, minpower, maxpol match to H, HIS PCA MaxPower (4th root) MinPower (4th root) IHS = PC2(max,min) PC1(max,min) PC2(max,etah) MaxPol. H-Match

  18. ESAR/Landsat

  19. airphoto

  20. Field Measurements

  21. Calibration

  22. Building Detection Airphoto

  23. +-45 Two linear polarizations: +45 (red) and –45 (green)

  24. R/LCP Circular polarizations: RCP (red) and LCP (green)

  25. HHVV Two linear polarizations: HH (red) and VV (green)

  26. H vs. V Two linear polarizations: H (red) and V (green)

  27. Maxpol Maximum power and polarization Intensity=Power Red = H Cyan = V E-SAR (L) Kirkkonummi 31.8.2000

  28. Best Single-Channel Detection Result (H pol.) Green = detected Red = non-detected Blue = false alarm

  29. Building detection False detection (%) Total Power H Transmit V Transmit HH VV HV Max. Power Buildings detected (%)

  30. Dual-Frequency & Dual Aspect Correlations

  31. Conclusion • According to our studies … • Polarization response can be simplified. • Detecting buildings, H is best and HV not a good channel. • Polarimetric channels are more correlated than • frequency channels and aspect channels, especially.

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