Principles of Modern Radar - Volume 2 1891121537

8.3 Estimating Elevation Profiles Using Radar Echo Phase 357Cross-range (m)20015010050−50−100Cross-range (m)200150100500 0−50−100FIGURE 8-10(a) Simplifiedreflectivity image ofnotional elevationmodel withoutforeshortening.(b) Same image withforeshortening.−150−200−200 −150 −100 −50 0 50 100 150 200Range (m)(a)−150−200−200 −150 −100 −50 0 50 100 150 200Range (m)(b)highlighted on sloped terrain. A ground observer and two airborne observers image thescene and project it into the ground plane. The ground observer A observes the true groundranges of the scene. Airborne observer B measures the scatterers to be at longer rangesdue to the platform altitude. Because the LOS is below the normal to the terrain slope inthe vicinity of scatterers 1, 2, and 3, they are imaged as occurring in the correct order, butwith their spacing compressed. This compression of range, while maintaining the correctordering of features, is called foreshortening. Airborne observer C images the scene froma higher altitude, with an LOS above the terrain normal. The apparent ranges are longerstill, but now the scatterers are imaged in reverse order. That is, a plane wave propagatingalong the LOS will strike scatterer 3 first because it is actually closer to the radar thanscatterer 2, and so forth. The term layover refers to this reversal of apparent range. Layoveris particularly evident when imaging vertical walls, such as the sides of buildings in urbanareas, where the radar is always above the (horizontal) normal to the wall surface.In sidelooking operation, the sole case considered here, foreshortening or layoveroccurs only in the range coordinate. In squinted operation, it occurs in both range andcross-range; details are given in [14,20].Figure 8-10 illustrates foreshortening on the notional example of Figure 8-6. Figure8-10a is a simplified image of the scene without accounting for foreshortening. Thebrightness of a pixel is determined by the relative reflectivity of that pixel, which is modeledwith a constant gamma area reflectivity [12,21]. 8 Recall that the radar is located 5 kmto the left of the image center and is elevated 2 km. The S-shaped hill has the highestreflectivity (brightest pixels) at its beginning and end, when the hill side is oriented towardthe radar and presents a clutter surface closer to normal to the radar line of sight. Thereflectivity is lower in the middle of the hill, where the radar line of sight strikes it at moreof an angle. The image is also quite bright at the plateau edge, which presents a nearlyorthogonal face to the radar LOS. This brightening of facing slopes is quite common inSAR imagery. Of course, the hill also casts a shadow, which is more elongated at the endof the hill due to its greater elevation there.8 The effect of range on clutter reflectivity is not accounted for in this simple illustration; the range variesless than 10% across the image.