The following considerations apply also to real-aperture terrain-imaging radars, but are more consequential when resolution in range is matched to a cross-beam resolution that is available only from a SAR.
The two dimensions of a radar image are range and cross-range. Radar images of limited patches of terrain can resemble oblique photographs, but not ones taken from the location of the radar. This is because the range coordinate in a radar image is perpendicular to the vertical-angle coordinate of an oblique photo. The apparent entrance-pupil position (or camera center) for viewing such an image is therefore not as if at the radar, but as if at a point from which the viewer's line of sight is perpendicular to the slant-range direction connecting radar and target, with slant-range increasing from top to bottom of the image.
Because slant ranges to level terrain vary in vertical angle, each elevation of such terrain appears as a curved surface, specifically a hyperbolic cosine one. Verticals at various ranges are perpendiculars to those curves. The viewer’s apparent looking directions are parallel to the curve’s “hypcos” axis. Items directly beneath the radar appear as if optically viewed horizontally (i.e., from the side) and those at far ranges as if optically viewed from directly above. These curvatures are not evident unless large extents of near-range terrain, including steep slant ranges, are being viewed.
When viewed as specified above, fine-resolution radar images of small areas can appear most nearly like familiar optical ones, for two reasons. The first reason is easily understood by imagining a flagpole in the scene. The slant-range to its upper end is less than that to its base. Therefore the pole can appear correctly top-end up only when viewed in the above orientation. Secondly, the radar illumination then being downward, shadows are seen in their most-familiar "overhead-lighting" direction.
Note that the image of the pole’s top will overlay that of some terrain point which is on the same slant range arc but at a shorter horizontal range (“ground-range”). Images of scene surfaces which faced both the illumination and the apparent eyepoint will have geometries that resemble those of an optical scene viewed from that eyepoint. However, slopes facing the radar will be foreshortened and ones facing away from it will be lengthened from their horizontal (map) dimensions. The former will therefore be brightened and the latter dimmed.
Returns from slopes steeper than perpendicular to slant range will be overlaid on those of lower-elevation terrain at a nearer ground-range, both being visible but intermingled. This is especially the case for vertical surfaces like the walls of buildings. Another viewing inconvenience that arises when a surface is steeper than perpendicular to the slant range is that it is then illuminated on one face but “viewed” from the reverse face. Then one “sees”, for example, the radar-facing wall of a building as if from the inside, while the building’s interior and the rear wall (that nearest to, hence expected to be optically visible to, the viewer) have vanished, since they lack illumination, being in the shadow of the front wall and the roof. Some return from the roof may overlay that from the front wall, and both of those may overlay return from terrain in front of the building. The visible building shadow will include those of all illuminated items. Long shadows may exhibit blurred edges due to the illuminating antenna's movement during the "time exposure" needed to create the image.
Surfaces that we usually consider rough will, if that roughness consists of relief less than the radar wavelength, behave as smooth mirrors, showing, beyond such a surface, additional images of items in front of it. Those mirror images will appear within the shadow of the mirroring surface, sometimes filling the entire shadow, thus preventing recognition of the shadow.
An important fact that applies to SARs but not to real-aperture radars is that the direction of overlay of any scene point is not directly toward the radar, but toward that point of the SAR's current path direction that is nearest to the target point. If the SAR is "squinting" forward or aft away from the exactly broadside direction, then the illumination direction, and hence the shadow direction, will not be opposite to the overlay direction, but slanted to right or left from it. An image will appear with the correct projection geometry when viewed so that the overlay direction is vertical, the SAR's flight-path is above the image, and range increases somewhat downward.
Objects in motion within a SAR scene alter the Doppler frequencies of the returns. Such objects therefore appear in the image at locations offset in the across-range direction by amounts proportional to the range-direction component of their velocity. Road vehicles may be depicted off the roadway and therefore not recognized as road traffic items. Trains appearing away from their tracks are more easily properly recognized by their length parallel to known trackage as well as by the absence of an equal length of railbed signature and of some adjacent terrain, both having been shadowed by the train. While images of moving vessels can be offset from the line of the earlier parts of their wakes, the more recent parts of the wake, which still partake of some of the vessel's motion, appear as curves connecting the vessel image to the relatively quiescent far-aft wake. In such identifiable cases, speed and direction of the moving items can be determined from the amounts of their offsets. The along-track component of a target's motion causes some defocus. Random motions such as that of wind-driven tree foliage, vehicles driven over rough terrain, or humans or other animals walking or running generally render those items not focusable, resulting in blurring or even effective invisibility.
These considerations, along with the speckle structure due to coherence, take some getting used to in order to correctly interpret SAR images. To assist in that, large collections of significant target signatures have been accumulated by performing many test flights over known terrains and cultural objects.
Read more about this topic: Synthetic Aperture Radar
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