Synthetic aperture radar

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The surface of Venus, as imaged by the Magellan probe using SAR
The surface of Venus, as imaged by the Magellan probe using SAR

Synthetic-aperture radar (SAR) is a form of radar in which sophisticated post-processing of radar data is used to produce a very narrow effective beam. By its nature it requires that data be taken using multiple receive and/or transmit antenna positions. Therefore, it can only be used by moving instruments over relatively immobile targets (providing multiple monostatic radar waveform captures) or when multiple antennas are placed over a relatively large area (providing many combinations of monostatic and bistatic radar waveform captures for a given target area). It has seen wide applications in remote sensing and mapping.

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[edit] Basic operation

NASA's AirSAR instrument is attached to the side of a DC-8
NASA's AirSAR instrument is attached to the side of a DC-8

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 requires significant computational resources. It is normally done at a ground station after the observation is complete, using Fourier transform techniques. The result is a map of radar reflectivity (including both amplitude and phase). 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.

Before rapid computers were available, the processing stage was done using holographic techniques. This was one of the first effective analogue optical computer systems. A scale hologram interference pattern was produced directly from the analogue radar data (for example 1:1,000,000 for 0.6 meters radar). Then laser light with the same scale (in the example 0.6 micrometers) passing through the hologram would produce a terrain projection. This works because SAR is fundamentally very similar to holography with microwaves instead of light.

[edit] The SAR algorithm

The SAR algorithm, in its simplest form, does the following:

A three-dimensional array (a volume) is defined which will represent the volume of space within which targets exist. Each element of the array is a cubical voxel representing the probability (a "density") of a solid object being at that location in space. (Note that two-dimensional SARs are also possible--in order to show only a top-down view of the target area).

Initially, the SAR algorithm gives each voxel a density of zero.

Then, for each captured waveform, the entire volume is iterated. For a given waveform and voxel, the distance from the position represented by that voxel to the antenna(s) used to capture that waveform is calculated. That distance represents a time delay into the waveform. The sample value at that position in the waveform is then added to the voxel's density value. This represents a possible echo from a target at that position. Note that there are several optional approaches here, depending on the precision of the waveform timing, among other things. For example, if phase cannot be accurately known, then only the envelope magnitude (with the help of a Hilbert transform) of the waveform sample might be added to the voxel. If polarization and phase are known in the waveform, and are accurate enough, then these values might be added to a more complex voxel that holds such measurements separately.

After all waveforms have been iterated over all voxels, the basic SAR processing is complete.

What remains, in the simplest approach, is to decide what voxel density value represents a solid object. Voxels whose density is below that threshold are ignored. Note that the threshold level chosen must at least be higher than the peak energy of any single wave--otherwise that wave peak would appear as a sphere (or ellipse, in the case of multistatic operation) of false "density" across the entire volume. Thus to detect a point on a target, there must exist at least two different antenna waveforms that contain an echo from that point. Consequently there is typically a need for large numbers of antenna positions in order to well characterize a target area.

Finally, the voxels that passed the threshold criteria are visualized in 2D or 3D. Optionally, added visual quality can sometimes be had by use of a surface detection algorithm like marching cubes.

[edit] More complex operation

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.

[edit] Multistatic operation

SAR requires that echo waveform captures be taken at multiple antenna positions. The more waveform captures taken (at different antenna locations) the more reliable the target characterization.

Multiple waveform captures can be obtained by moving a single antenna to different locations, by placing multiple stationary antennas at different locations, or combinations thereof.

The advantage of a single moving antenna is that it can be easily placed in any number of positions in order to provide any number of monostatic waveforms. For example, an antenna mounted on an airplane takes many captures per second as the plane travels.

The principle advantages of multiple static antennas are that a moving target can be characterized (assuming the capture electronics is fast enough), that no vehicle or motion machinery is necessary, and that antenna positions need not be derived from other, sometimes unreliable, information. (One problem in a SAR taken by airplane is knowing precise antenna positions as the plane travels).

For multiple static antennas, all combinations of monostatic and multistatic radar waveform captures are possible. Note, however, that it is not advantageous to capture a waveform for each of both transmission directions for a given pair of antennas, because those waveforms will be identical. When multiple static antennas are used, the total number of unique echo waveforms that can be captured is:

NumWaveforms = \frac{N^2 + N}{2}

Where:

NumWaveforms is the number of unique waveforms that can be captured.

N is the number of unique antenna positions.

[edit] Polarimetry

SAR image of Death Valley colored using polarimetry
SAR image of Death Valley colored using polarimetry

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 RX-TX polarizations (HH-pol, VV-pol, VH-pol) are used as the three color channels in a synthesized image. This is what has been done in the picture at left. Interpretation of the resulting colors requires significant testing of known materials.

New developments in polarimetry also include utilizing the changes in the random polarization returns of some surfaces (such as grass or sand), between two images of the same location at different points in time to determine where changes not visible to optical systems occurred. Examples include subterranean tunneling, or paths of vehicles driving through the area being imaged.

[edit] Interferometry

Main article: Interferometric synthetic aperture radar

Rather than discarding the phase data, information can be extracted from it. If two observations of the same terrain from very similar positions are available, aperture synthesis can be performed to provide the resolution performance which would be given by a RADAR system with dimensions equal to the separation of the two measurements. 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 model (DEM) with a single airplane pass. One aircraft application at the Canada Centre for Remote Sensing produced digital elevation maps with a resolution of 5 m and altitude errors also on the order of 5 m. This method was used in 2000 by the IFSAR team to map many regions of the Earth's surface with unprecedented accuracy from the Space Shuttle.

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 observations, 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.

[edit] Differential Interferometry

Differential interferometry (D-InSAR) requires taking at least two images with addition of a DEM. The DEM can be either produced by GPS measurements or could be generated by interferometry as long as the time between acquisition of the image pairs is short, which guarantees minimal distortion of the image of the target surface. In principle, 3 images of the ground area with similar image acquisition geometry is often adequate for D-InSar. The principle for detecting ground movement is quite simple. One interferogram is created from the first two images; this is also called the reference interferogram or topographical interferogram. A second interferogram is created that captures topography + distortion. Subtracting the latter from the reference interferogram can reveal differential fringes, indicating movement. The described 3 image D-InSAR generation technique is called 3-pass or double-difference method.

Differential fringes which remain as fringes in the differential interferogram are a result of SAR range changes of any displaced point on the ground from one interferogram to the next. In the differential interferogram, each fringe is directly proportional to the SAR wavelength, which is about 5.6 cm for ERS and RADARSAT single phase cycle. Surface displacement away from the satellite look direction causes an increase in path (translating to phase) difference. Since the signal travels from the SAR antenna to target and back again, the measured displacement is twice the unit of wavelength. This means in differential interferometry one fringe cycle -pi to +pi or one wavelength corresponds to a displacement relative to SAR antenna of only half wavelength (2.8 cm). There are various publications on measuring subsidence movement, slope stability analysis, land slide, glacier movement, etc tooling D-InSAR. Further advancement to this technique whereby differential interferometry from satellite SAR ascending pass and descending pass can be used to estimate 3-D ground movement. Research in this area has shown accurate measurements of 3-D ground movement with accuracies comparable to GPS based measurements can be achieved.

[edit] Ultra-wideband SAR

Conventional radar systems emit bursts of radio energy with a fairly narrow range of frequencies. A narrow-band channel, by definition, does not allow rapid changes in modulation. Since it is the change in a received signal that reveals the time of arrival of the signal (obviously an unchanging signal would reveal nothing about "when" it reflected from the target), a signal with only a slow change in modulation cannot reveal the distance to the target as well as can a signal with a quick change in modulation.

Ultra-wideband (UWB) refers to any radio transmission that uses a very large bandwidth - which is the same as saying it uses very rapid changes in modulation. Although there is no set bandwidth value that qualifies a signal as "UWB", systems using bandwidths greater than a sizable portion of the baseband frequency (typically about ten percent, or so) are most often called "UWB" systems. A typical UWB system might use a bandwidth of one-third to one-half of its center frequency. For example, some systems use a bandwidth of about 1 GHz centered around 3 GHz.

There are as many ways to increase the bandwidth of a signal as there are forms of modulation - it is simply a matter of increasing the rate of that modulation. However, the two most common methods used in UWB radar, including SAR, are very short-lived pulses and high-bandwidth chirping. A general description of chirping appears elsewhere in this article; simply note that the bandwidth of a chirped system can be as narrow or as wide as the designers desire. Pulse-based UWB systems, being the more common method associated with the term "UWB radar", are described here.

A pulse-based radar system transmits very short pulses of electromagnetic energy, typically comprised of only a few waves or less. A very short pulse is, of course, a very rapidly changing signal, and thus occupies a very wide bandwidth. This allows far more accurate measurement of distance, and thus resolution.

The main disadvantage of pulse-based UWB SAR is that the transmitting and receiving front-end electronics are difficult to design for high-power applications. Specifically, the transmit duty cycle is so exceptionally low and pulse time so exceptionally short, that the electronics must be capable of extremely high instantaneous power in order to rival the average power of more conventional radars. (Although it is true that UWB provides a notable gain in link budget over a narrow band signal because of the relationship of bandwidth in the Shannon–Hartley theorem, there is still a notable disparity in link budget because conventional radar might be several orders of magnitude more powerful than a typical pulse-based radar). So pulse-based UWB SAR is typically used in applications requiring average power levels in the microwatt or milliwatt range, and thus is used for scanning smaller, nearer target areas (several tens of meters), or in cases where lengthy integration (over a span of minutes) of the received signal is possible. Note, however, that this limitation is solved in chirped UWB radar systems.

The principle advantages of UWB radar are better resolution (a few millimeters using commercial off-the-shelf electronics) and more spectral information of target reflectivity.

[edit] Doppler-Beam Sharpening

A commonly used technique for SAR systems is called Doppler beam sharpening. Because the real aperture of the RADAR antenna is so small (compared to the wavelength in use), the RADAR energy spreads over a wide area (usually many degrees wide in a direction orthogonal (at right angles) to the direction of the platform (aircraft). Doppler-beam sharpening takes advantage of the motion of the platform in that targets ahead of the platform return a Doppler upshifted signal (slightly higher in frequency) and targets behind the platform return a Doppler downshifted signal (slightly lower in frequency). The amount of shift varies with the angle forward or backward from the ortho-normal direction. By knowing the speed of the platform, target signal return is placed in a specific angle "bin" that changes over time. Signals are integrated over time and thus the RADAR "beam" is synthetically reduced to a much smaller aperture - or more accurately (and based on the ability to distinguish smaller Doppler shifts) the system can have hundreds of very "tight" beams concurrently. This technique dramatically improves angular resolution; however, it is far more difficult to take advantage of this technique for range resolution. (See Pulse-doppler radar).

[edit] Chirped (Pulse Compressed) Radars

A common technique for many RADAR systems (usually also found in SAR systems) is to "chirp" the signal. In a "chirped" radar, the pulse is allowed to be much longer. A longer pulse allows more energy to be emitted, and hence received, but usually hinders range resolution. But in a chirped radar, this longer pulse also has a frequency shift during the pulse (hence the chirp or frequency shift). When the "chirped" signal is returned, it must be correlated with the sent pulse. Classically, in analog systems, it is passed to a dispersive delay line (often a SAW device) that has the property of varying velocity of propagation based on frequency. This technique "compresses" the pulse in time - thus having the effect of a much shorter pulse (improved range resolution) while having the benefit of longer pulse length (much more signal returned). Newer systems use digital pulse correlation to find the pulse return in the signal.

[edit] Data collection

Highly accurate data can be collected by aircraft overflying the terrain in question. In the 1980s, as a prototype for instruments to be flown on the NASA Space shuttles, NASA operated a synthetic-aperture radar on a NASA Convair 990. However, in 1986, this plane caught fire on takeoff. In 1988, NASA rebuilt a C, L, and P-band SAR to fly on the NASA DC-8 aircraft. Called AIRSAR, it flew missions at sites around the world until 2004. Another such aircraft, the Convair 580, was flown by the Canada Center for Remote Sensing until about 1996 when it was handed over to Environment Canada due to budgetary reasons. Most land-surveying applications are now carried out by satellite observation. Satellites such as ERS-1/2, JERS-1, Envisat ASAR, and RADARSAT-1 were launched explicitly to carry out this sort of observation. Their capabilities differ, particularly in their support for interferometry, but all have collected tremendous amounts of valuable data. The Space Shuttle has also carried synthetic-aperture radar equipment during the SIR-A and SIR-B missions during the 1980s, as well as the Shuttle Radar Laboratory (SRL) missions in 1994 and the Shuttle Radar Topography Mission in 2000.

The Venera 15 and Venera 16 followed later by the Magellan space probe mapped the surface of Venus over several years using synthetic-aperture radar.

Synthetic-aperture radar was first used by NASA on JPL's Seasat oceanographic satellite in 1978 (this mission also carried an altimeter and a scatterometer); it was later developed more extensively on the Spaceborne Imaging Radar (SIR) missions on the space shuttle in 1981, 1984 and 1994. The Cassini mission to Saturn is currently using SAR to map the surface of the planet's major moon Titan, whose surface is partly hidden from direct optical inspection by atmospheric haze.

The Mineseeker Project ([1]) is designing a system for determining whether regions contain landmines based on a blimp carrying ultra-wideband synthetic-aperture radar. Initial trials show promise; the radar is able to detect even buried plastic mines.

SAR has been used in radio astronomy for many years to simulate a large radio telescope by combining observations taken from multiple locations using a mobile antenna.

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