TUTORIAL ON SAR POLARIMETRY

Estimation of surface characteristics 4. ESTIMATION OF SURFACE CHARACTERISTICS 4.1 The problem : separating roughness and moisture dependence 4.2 Model based moisture and surface roughness estimation 4.2.1.1 Inverting Oh-Model The inversion of the Oh-Model is based on the solution of relations introduced in the former paragraph. In the absence of an analytic solution, ks and ′have to be estimated by an εiterative procedure. In a first step, Γ° is evaluated from 1Γ°2θ q    (1)1 + p −1 = 0    π 0.23 Γ°   Using the measured co- and cross-polarised ratios, Γ° can be estimated from (1) using an iterative technique. In this study, the Newton iteration approach was applied. Accordingly, the n-th Newton iteration for Γ° is given by 2()xn−13a()1− b⋅ x + cn−1 x = 2n (x ) (2)n−12⋅ x n−1 3⋅lna ⋅(1− b⋅ x )− b an−1 3 Where 1 2θ qx := , a := , b := , c := p −1 (3)0 π 0.23Γ2 1 0 10In a second step, from the approximated value , Γ is extracted as and used  x := Γ =  0 xΓ  n to retrieve directly from Eq. (11.26) the real part of the dielectric constant 01 + Γ ′ε = (4)01 − Γ0The obtained values for ε′ are converted into m values after TOPP et al. (1980). Finally, Γ is vused again in Eq. (11.58) to derive the surface roughness value ks as © I. Hajnsek, K. Papathanassiou. January 2005. 1 Estimation of surface characteristics    ()p + 1 ks = ln  (5)1 0 3Γ2θ    π  The iterative procedure converges rather ...