The cross-range or azimuth resolution of a scanning real-beam radar is determined by the product of the range and the antenna beamwidth in radians (this beamwidth is one wavelength divided by the antenna width measured perpendicular to the boresight). On the ground, the spaceborne or airborne radar beam spreads out over a large area. Thus, to attain high resolution, the radar would need a large antenna, or aperture, to obtain a narrower beam. The required aperture is typically so large that it cannot be formed with an actual physical antenna.
Synthetic-aperture radars (SARs) synthesize a large aperture by coherently integrating the returned signal pulse-to-pulse as the radar moves. The azimuth resolution attained in this manner is half a wavelength divided by the change in viewing angle (in radians) during the aperture formation process (twice that which would be achieved with a real aperture of the same size). Thus, if the same change in viewing angle is maintained, there is no loss in resolution upon moving to a higher altitude.
The formation of synthetic apertures and associated processing is most easily understood from the standpoint of Doppler processing. Consider a fixed radar pointing at a target on a rotating turntable, where both the radar and the target lie on the same plane. Targets moving toward the radar source will exhibit a positive Doppler shift, while those moving away will exhibit a negative Doppler shift, proportional to their distance from the center, or hub, of the turntable. Thus, subsequent to range compression, azimuth compression is efficiently achieved simultaneously for all targets at a given range by Doppler processing with a fast Fourier transform. In a spaceborne or airborne application, however, the radar moves while the target remains fixed. In this case, the data must first undergo motion compensation to drive the range rate from the radar to a fixed motion-compensation point on the ground (the effective hub) to zero. The data then correspond to the case of a fixed radar illuminating a surface rotating about the motion-compensation point.
For stretch waveforms (employing a long pulse that progresses linearly in frequency), both range and azimuth compression may be performed efficiently with fast Fourier transforms; however, for higher resolutions, depth of field becomes increasingly important. The depth of field denotes the horizontal and vertical space over which fast Fourier transforms can be employed for range and azimuth compression without loss of resolution and geometric distortion. One way to overcome a limitation in the depth of field is to generate an image from pieces that are assembled into a complete picture. When depth of field becomes a serious issue, a "polar" transformation is usually applied to the data prior to compression. This linearizes the phase histories in range and azimuth so a two-dimensional fast Fourier transform will properly compress the data from a region typically orders of magnitude larger.