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Synthetic Aperture Radar

Synthetic Aperture Radar (SAR) refers to a technique for producing fine resolution images from an intrinsically resolution-limited radar system. The wavelengths, λ, that are used for radar remote sensing of the earth’s surface are typically in the range of a few to tens of centimeters. At these wavelengths, the energy radiated from a radar antenna of dimension D disperses quickly at a rate that is equivalent to the beam width λ/D of the antenna. For a typical spaceborne SAR configuration with wavelengths of ~10 cm and an antenna of 10 m size, this beam width is 1/100 radians, or about 0.6 degrees. If we are in space observing the Earth 1000 km below, the beam size on the ground is then 1000 λ/D = 10 km. This intrinsic resolution of the radar system is insufficient for many applications and practical solutions for improving the resolution needed to be found.

SAR techniques exploit the motion of the radar in orbit to synthesize a typically about 10 km long antenna in the flight direction (see figure). While the radar is traveling along its path, it is sweeping the antenna’s footprint across the ground while it is continuously transmitting and receiving radar pulses. In this scenario, every given point in the “radar swath” is imaged many times by the moving radar platform under constantly changing yet predictable observation geometries. In SAR systems, this change in observation geometry, resulting in a constant change of the distance from the radar to the point on the ground, is precisely encoded in the phase of the observed radar response. The “phase history” for any point on the ground located at a constant distance parallel to the flight track is the same. By compensating the phase history of each pulse that is affecting a particular point on the ground, it is possible to focus the energy across the 10 km synthetic aperture and create an image of vastly improved resolution. The theoretically achievable synthetic aperture resolution can be calculated from D/2, is independent of the range or wavelength, and corresponds to D/2=5 m for the previously outlined spaceborne scenario.

Through the outlined principles, SAR defeats the intrinsic resolution limits of radar antennas in the along-track direction. In the cross-track or range direction, orthogonal to the satellite path, the resolution is not defined by the antenna beam width, but rather the width of the transmitted pulse. This is because the transmitted pulse intersects the imaged surface as it propagates in the beam. After a two-way trip of a transmitted pulse from sensor to the ground and back, two objects can be distinguished if they are spatially separated by more than half the pulse width. Hence, range resolution is controlled by the transmitted waveform that is generated by the radar and not the size of the antenna footprint on the ground. Wider bandwidth signals generate finer resolution images in range.

For most purposes, the transmitted signal can be thought of as a single frequency sinusoid with a well-defined amplitude and phase. Thus the image constructed from the SAR processing is a complex image – each resolution element, or pixel, has an amplitude and phase associated with it. Once calibrated, the amplitude is proportional to the reflectance of the surface. The phase is proportional to the distance the wave traveled between the radar and the ground, any propagation phase delays due to the atmosphere or ionosphere, and any phase contribution imparted by the reflectance from the surface.