Principles of Modern Radar - Volume 2 1891121537

348 CHAPTER 8 Interferometric SAR and Coherent Exploitationformed at nominal range R can be expressed as( ) Rφ = φ G + φ ρ + φ R = φ G + φ ρ − 4πλ(8.10)where R should be considered the slant range to the pixel at the center of the syntheticaperture, φ G is the phase shift due to the complex gain of the radar receiver and the imageformation processor, φ ρ is the net phase of the composite reflectivity of the scattererscontributing to the pixel, and φ R =−4πR/λ is the deterministic phase shift due to thetwo-way path length to the pixel center [13,14]. For the sidelooking configuration assumedhere, R is the slant range in the y–z plane as shown in Figure 8-4.Let φ a and φ b be the pixel phases measured at the same ground range position (x 0 ,y 0 )in the SAR images formed by sensors a and b in Figure 8-4. We assume the φ G and φ ρterms are nearly equal in both images. 7 It follows from equations (8.4) and (8.10) that( ) δRφ ab ≡ φ a − φ b =−4πλ≈− 4π Bλcos(ψ + β) (8.11)Equation (8.11) applies when the radars at locations a and b are completely separate;each has its own transmitter and receiver, so that the two-way path lengths for the rangemeasurements differ by δR. An important variation exists in the form of systems that useonly one transmitter, say at location b, with two receivers at a and b. That is, the radarat b is an active system, whereas the radar at a is a passive radar receiver. In this event,the difference in the two-way path length observed at a and b is δR/2. Both cases can becombined into a single expression by replacing equation (8.11) with( ) δR 2π pBφ ab =−2π p ≈− cos(ψ + β) (8.12)λ λwhere p = 2 when each sensor has its own transmitter, and p = 1 when one sensor servesas the transmitter for both. Operational scenarios that give rise to these cases are discussedin Section 8.4.1The depression angle can now be estimated as(ψ = cos −1 −λ )2π pB φ ab − β (8.13)The quantity φ ab , called the interferometric phase difference (IPD), is a very sensitiveindicator of range differences and thus of depression angle and elevation. The accuracyof IPD measurements is treated in Section 8.6, but after filtering for noise reductionthe precision (standard deviation) is typically a few tens of degrees or better [15–17].Therefore, φ ab can be used to measure differential range with precisions of fractionsof a radio frequency (RF) wavelength and thus enable much better elevation estimationaccuracy. For example, a precision of 20 ◦ in φ ab corresponds to a precision in measuringδR of λ/36, which is only about 8.3 mm at L band (1 GHz).Once the elevation ĥ of the scatterer imaged at ground range y 0 has been estimated,the actual ground range y 1 of the scatterer can also be determined from the geometry in7 This is a good assumption for φ G but might seem questionable for φ ρ , particularly in repeat-pass InSAR(see Section 8.4.1). Variation of φ ρ is one source of coherence loss, discussed in Section 8.6.1.