Principles of Modern Radar - Volume 2 1891121537

354 CHAPTER 8 Interferometric SAR and Coherent Exploitationδφ ab = 2π in equation (8.16). This fringe height or ambiguous height ish amb = 2π|α IF | =λR cos ψpB ⊥(8.28)Note that since ψ and thus α IF vary with ground range across the scene, so does the fringeelevation.Figure 8-7 illustrates the wrapped version of the IPD of Figure 8-6b. For this exampleh amb = 26.93 m in the center of the image. By counting the places where the patternwraps from almost black back to white, we can see that there are about six and one-thirdfringes or fringe cycles across the image, consistent with the approximately 40 radians ofIPD variation. The height variation in this image is 73.6 m, and |α IF | is about 4.28 at thecenter and varies only about 10% across the scene. Equation (8.16) then suggests an IPDvariation of only 17.2 radians. The remaining variation in IPD is due to the flat earth IPD,which varies 32.2 radians across the scene. (The total IPD variation is less than the sum ofthese two contributions because the maximum variation due to topography does not occurat the same range as the maximum flat earth IPD.)If the IPD is not unwrapped, then an InSAR elevation profile obtained using the secondInSAR method will produce a wrapped elevation map, with the estimated elevation varyingonly over a range of h amb meters before wrapping. A similar problem exists with the firstInSAR method. Using the wrapped phase implicitly assumes choosing a particular valueof k in equation (8.27), restricting the range of depression angles and thus the range ofelevations that can be represented. In either case, the restricted range imposed on h isoften much smaller than the actual elevation variations to be mapped, so the phase mustbe unwrapped to produce a useful profile.8.3.5 Spatial Baseline Effect on Accuracy and Fringe HeightEquation (8.28) shows that the fringe elevation is inversely proportional to the baselinelength as projected orthogonal to the LOS, B ⊥ , which in turn is proportional to the baselineB. A smaller value of B thus allows a larger elevation variation before the IPD wraps.Because it is generally easier and less error-prone to perform phase unwrapping whenthere are fewer fringes in the IPD, this relationship suggests that smaller values of B aredesirable.On the other hand, equation (8.16) implies that for a given change in elevation, alarger value of B results in a larger change in the IPD. That is, larger baselines enablegreater sensitivity in measuring height changes. Conversely, if δφ ab is interpreted as anerror in measuring the IPD, then a larger baseline reduces the contribution of the IPD errorto the height error. Thus, a trade-off is required in the choice of baseline length betweenincreasing IPD sensitivity to height changes (long baseline), reducing the effect of IPDerrors on height estimates (long baseline), and reducing the number of fringe cycles to beunwrapped (short baseline).8.3.6 Estimating Elevation Relative to a Reference ProfileIt is often the case that some information is already known regarding the elevation profileof a scene. For example, a coarse-resolution, low-accuracy (perhaps DTED 1) DEM profileh ref (x,y) of an area may be available, and the intent of the InSAR system is to produce afiner resolution, higher accuracy (perhaps DTED 3) profile estimate h(x,y). ⌢ Define the