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In a typical SAR application, a single radar antenna will be attached to the side of an aircraft. A single pulse from the antenna will be rather broad (several degrees) because diffraction requires a large antenna to produce a narrow beam. The pulse will also be broad in the vertical direction; often it will illuminate the terrain from directly beneath the aircraft out to the horizon. However, if the terrain is approximately flat, the time at which echoes return allows points at different distances from the flight track to be distinguished. Distinguishing points along the track of the aircraft is difficult with a small antenna. However, if the amplitude and phase of the signal returning from a given piece of ground are recorded, and if the aircraft emits a series of pulses as it travels, then the results from these pulses can be combined. Effectively, the series of observations can be combined just as if they had all been made simultaneously from a very large antenna; this process creates a synthetic aperture much larger than the length of the antenna (and in fact much longer than the aircraft itself).
Combining the series of observations is done using Fast Fourier Transform techniques; it requires significant computational resources, and is normally done at a ground station after the observation is complete. The result is a map of radar reflectivity (including both amplitude and phase) on the ground. The phase information is, in the simplest applications, discarded. The amplitude information, however, contains information about ground cover, in much the same way that a black-and-white picture does. Interpretation is not simple, but a large body of experimental results has been accumulated by flying test flights over known terrain.
The basic design of a synthetic aperture radar system can be enhanced in various ways to collect more information. Most of these methods use the same basic principle of combining many pulses to form a synthetic aperture, but they may involve additional antennas or significant additional processing.
Radar waves have a polarization. Different materials reflect radar waves with different intensities, but anisotropic materials such as grass often reflect different polarizations with different intensities. Some materials will also convert one polarization into another. By emitting a mixture of polarizations and using receiving antennas with a specific polarization, several different images can be collected from the same series of pulses. Frequently three such images are used as the three color channels in a synthesized image. This is what has been done in the picture above. Interpretation of the resulting colors requires significant testing of known materials.
Rather than discarding the phase information, information can be extracted from it. If two observations of the same terrain from very similar positions are available, a great deal of interesting information can be extracted. This technique is called interferometric SAR or InSAR.
If the two samples are obtained simultaneously (perhaps by placing two antennas on the same aircraft, some distance apart), then any phase difference will contain information about the angle from which the radar echo returned. Combining this with the distance information, one can determine the position in three dimensions of the image pixel. In other words, one can extract terrain altitude as well as radar reflectivity, producing a digital elevation map with a single airplane pass. One aircraft application at the Canada Center for Remote Sensing produced digital elevation maps with a resolution of 5 m and altitude errors also on the order of 5 m.
If the two samples are separated in time, perhaps from two different flights over the same terrain, then there are two possible sources of phase shift. The first is terrain altitude, as discussed above. The second is terrain motion: if the terrain has shifted between obervations, it will return a different phase. The amount of shift required to cause a significant phase difference is on the order of the wavelength used. This means that if the terrain shifts by centimeters, it can be seen in the resulting image (A digital elevation map must be available in order to separate the two kinds of phase difference; a third pass may be necessary in order to produce one).
This second method offers a powerful tool in geology and geography. Glacier flow can be mapped with two passes. Maps showing the land deformation after a minor earthquake or after a volcanic eruption (showing the shrinkage of the whole volcano by several centimeters) have been published.