Principles of Modern Radar - Volume 2 1891121537

600 CHAPTER 13 Introduction to Radar PolarimetryFIGURE 13-5(a) Polarizationstates on one octantof the Poincarésphere.(b) Rectangularprojection of thePoincaré sphereshowing full range ofpolarization states(From Kraus [32].With permission.).The propagationdirection is out ofthe page.(a)xzLeft Circular Polarization τ = 45°Left Elliptical Polarizationψ = 45°, τ = 22½°Linear Polarizationψ = 45°, τ = 0°yLinear Polarizationψ = 22½°, τ = 0°Linear Polarizationψ = 0°, τ = 0°Left Circular Polarizationτ = 45°τ = 22½°τ = 0°Ellipticalψ= −90° ψ= −45° ψ = 0° ψ= 45° ψ= 90°Right Ellipticalτ = −22½°Polarizationτ = −45°Right Circular Polarization(b)LeftPolarizationLinear Polarizationand (τ,ψ) = (0,π/2) yields a vertically polarized state located on the negative x-axis.For ease of visualization, a rectangular projection of the various polarizations states onthe Poincaré sphere is shown in Figure 13-5 [32].Case 13.2: Circular PolarizationFor τ =±π/4, the wave is circularly polarized and the polarization state is located at thepoles of the Poincaré sphere, with the North Pole representing left circular polarizationand the South Pole representing right circular polarization. Note that the tilt angle, ψ, isundefined in the case of circular polarization.Case 13.3: Elliptical PolarizationIn general, the wave is elliptically polarized, with the polarization state located at a pointon the upper hemisphere for the left-handed sense and at a point on the lower hemispherefor the right-handed sense. The two limiting cases pertain to circular polarization at thepoles and linear polarization on the equator. Several elliptical states of polarization areshown in Figure 13-5 by ellipses with appropriate tilt angle ψ and ellipticity angle τ drawnat points on the Poincaré sphere. As an example, for (τ,ψ) = (π/8,π/8), we obtain the