Principles of Modern Radar - Volume 2 1891121537

350 CHAPTER 8 Interferometric SAR and Coherent ExploitationAnother alternate form is obtained in terms of the angular baseline δψ B (see Figure 8-4),which satisfies B ⊥ ≈ R · δψ B so thatα IF =− λ cos ψ2π p · δψ B(8.18)Typical values of δψ B are quite small. For the earlier SRTM example, δψ B ≈ 177 μrador about 0.01 ◦ . For a typical airborne InSAR case with B ⊥ = 1 m and R = 7 km, δψ B ≈143 μrad or about 0.008 ◦ .Equation (8.16) states that a change in the elevation of the scatterer relative to thezero-elevation reference plane can be estimated by multiplying the measured change in theinterferometric phase difference relative to the zero-elevation IPD by the interferometricscale factor.To take advantage of this relationship, we first need the IPD map that results from azero-elevation scene. Recasting equation (8.12) in terms of elevation and ground range,the IPD for a scatterer at zero elevation and ground range y becomes2π pBφ ab (x,y) ≈− cos [ψ (y) + β]λ( [cos −12π pB=− cosλ2π pB=−λy√H2+ y 2 )+ β⎡ ⎛⎞ ⎤cos⎣cos −1 1⎝√1 + ( H / y ) ⎠ + β2](h(x,y) = 0)⎦ ≡ φab FE (x,y) (8.19)This ground plane IPD is called the flat earth IPD, here denoted as φab FE . If we considerδφ ab as the difference between the actual IPD and the flat earth IPD, then δh will be thedifference between zero elevation and the actual elevation of the scatterer (i.e., h). Theactual elevation of the scatterer producing the pixel at location (x,y) in the SAR imagescan therefore be estimated asĥ(x,y) ≈ α IF[φab (x,y) − φ FEab (x,y)] (8.20)In using this equation, it is important to realize that the interferometric scale factor is afunction of ψ and thus of ground range y. The value of α IF must be updated for eachground range bin.We now have a second InSAR DEM algorithm, defined by the following procedure.InSAR DEM Algorithm 21. Using the two SAR images, measure the IPD φ ab (x,y) at each ground plane pixellocation (x,y).2. Compute φab FE (x,y) using equation (8.19).3. For each ground plane image coordinate (x,y), compute the range R to a scatterer ofelevation zero at that location using equation (8.1).4. Estimate the depression angle ψ of the scatterer imaged at each (x,y) ground coordinateusing equation (8.13).