thumb|This radar image acquired by the SIR-C/X-SAR radar on board the [[Space Shuttle Endeavour shows the Teide volcano. The city of Santa Cruz de Tenerife is visible as the purple and white area on the lower right edge of the island. Lava flows at the summit crater appear in shades of green and brown, while vegetation zones appear as areas of purple, green and yellow on the volcano's flanks.]]

Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes. SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture (the size of the antenna). Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical (a large antenna) or synthetic (a moving antenna) – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer – therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.

To create a SAR image, successive pulses of radio waves are transmitted to "illuminate" a target scene, and the echo of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single beam-forming antenna, with wavelengths of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. Signal processing of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the synthetic antenna aperture and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna.

Motivation and applications

thumb|right|The surface of [[Venus, as imaged by the Magellan probe using SAR, colorized with false color.]]

SAR is capable of high-resolution remote sensing, independent of flight altitude, and independent of weather, as SAR can select frequencies to avoid weather-caused signal attenuation. SAR has day and night imaging capability as illumination is provided by the SAR.

SAR images have wide applications in remote sensing and mapping of surfaces of the Earth and other planets. Applications of SAR are numerous. Examples include topography, oceanography, glaciology, geology (for example, terrain discrimination and subsurface imaging). SAR can also be used in forestry to determine forest height, biomass, and deforestation. Volcano and earthquake monitoring use differential interferometry. SAR can also be applied for monitoring civil infrastructure stability such as bridges. SAR is useful in environment monitoring such as oil spills, flooding, urban growth, military surveillance: including strategic policy and tactical assessment. SAR is a Doppler technique. It is based on the fact that "radar reflections from discrete objects in a passing radar beam field each [have] a minute Doppler, or speed, shift relative to the antenna".<blockquote>Carl Wiley, working at Goodyear, Arizona, (which later became Goodyear Aerospace, and eventually Lockheed Martin Corporation) in 1951, suggested the principle that — because each object in the radar beam has a slightly different speed relative to the antenna — each object will have its own doppler shift. A precise frequency analysis of the radar reflections will thus allow the construction of a detailed image.</blockquote>

In order to realise this concept, electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different small positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width. That is the source of the term "synthetic aperture," giving it the property of an imaging radar. for the second step, additional pre-processing such as image co-registration and phase calibration is used.

In addition, multiple baselines can be used to extend 3D imaging to the time dimension. 4D and multi-D SAR imaging allows imaging of complex scenarios, such as urban areas, and has improved performance with respect to classical interferometric techniques such as persistent scatterer interferometry (PSI).

Algorithm

SAR algorithms model the scene as a set of point targets that do not interact with each other (the Born approximation).

While the details of various SAR algorithms differ, SAR processing in each case is the application of a matched filter to the raw data, for each pixel in the output image, where the matched filter coefficients are the response from a single isolated point target. In the early days of SAR processing, the raw data was recorded on film and the postprocessing by matched filter was implemented optically using lenses of conical, cylindrical and spherical shape. The Range-Doppler algorithm is an example of a more recent approach.

Existing spectral estimation approaches

Synthetic-aperture radar determines the 3D reflectivity from measured SAR data. It is basically a spectrum estimation, because for a specific cell of an image, the complex-value SAR measurements of the SAR image stack are a sampled version of the Fourier transform of reflectivity in elevation direction, but the Fourier transform is irregular. Thus the spectral estimation techniques are used to improve the resolution and reduce speckle compared to the results of conventional Fourier transform SAR imaging techniques. is a popular algorithm used as new variant of FFT algorithms for the processing in multidimensional synthetic-aperture radar (SAR) systems. This algorithm uses a study of theoretical properties of input/output data indexing sets and groups of permutations.

A branch of finite multi-dimensional linear algebra is used to identify similarities and differences among various FFT algorithm variants and to create new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set of factors, called functional primitives, which are individually identified with an underlying software/hardware computational design.

Advantages
  • Additive group-theoretic properties of multidimensional input/output indexing sets are used for the mathematical formulations, therefore, it is easier to identify mapping between computing structures and mathematical expressions, thus, better than conventional methods.
Disadvantages
  • FFT cannot separate sinusoids close in frequency. If the periodicity of the data does not match FFT, edge effects are seen. It is a nonparametric covariance-based method, which uses an adaptive matched-filterbank approach and follows two main steps:
  1. Passing the data through a 2D bandpass filter with varying center frequencies (<math>\omega_1, \omega_2</math>).
  2. Estimating the power at (<math>\omega_1, \omega_2</math>) for all <math>\omega_1 \in [0, 2\pi), \omega_2 \in [0, 2\pi)</math> of interest from the filtered data.

The adaptive Capon bandpass filter is designed to minimize the power of the filter output, as well as pass the frequencies (<math>\omega_1, \omega_2</math>) without any attenuation, i.e., to satisfy, for each (<math>\omega_1, \omega_2</math>),

: <math>\min_h h^*_{\omega_1,\omega_2} Rh_{\omega_1,\omega_2}</math> subject to <math>h^*_{\omega_1,\omega_2} a_{\omega_1,\omega_2} = 1,</math>

where R is the covariance matrix, <math>h^*_{\omega_1,\omega_2}</math> is the complex conjugate transpose of the impulse response of the FIR filter, <math>a_{\omega_1,\omega_2}</math> is the 2D Fourier vector, defined as <math>a_{\omega_1,\omega_2} \triangleq a_{\omega_1} \otimes a_{\omega_2}</math>, <math>\otimes</math> denotes Kronecker product.

  • Capon method can provide much better resolution.
Disadvantages
  • Implementation requires computation of two intensive tasks: inversion of the covariance matrix R and multiplication by the <math>a_{\omega_1,\omega_2}</math> matrix, which has to be done for each point <math>\left(\omega_1, \omega_2\right)</math>.

Empirically, the APES method results in wider spectral peaks than the Capon method, but more accurate spectral estimates for amplitude in SAR. In the Capon method, although the spectral peaks are narrower than the APES, the sidelobes are higher than that for the APES. As a result, the estimate for the amplitude is expected to be less accurate for the Capon method than for the APES method. The APES method requires about 1.5 times more computation than the Capon method.

Advantages
  • Filtering reduces the number of available samples, but when it is designed tactically, the increase in signal-to-noise ratio (SNR) in the filtered data will compensate this reduction, and the amplitude of a sinusoidal component with frequency <math>\omega</math> can be estimated more accurately from the filtered data than from the original signal.
Disadvantages
  • The autocovariance matrix is much larger in 2D than in 1D, therefore it is limited by memory available.
Disadvantages
  • Resolution loss due to the averaging operation.

Advantages

  • It is invariant to the imaging mode: which means, that it uses the same algorithm irrespective of the imaging mode present, whereas, frequency domain methods require changes depending on the mode and geometry.

The procedure of this concept is elaborated as follows.

The backprojection algorithm is computationally expensive. It is specifically attractive for sensors that are wideband, wide-angle, and/or have long coherent apertures with substantial off-track motion.

Multistatic operation

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

Multiple 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 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 principal advantages of multiple static antennas are that a moving target can be characterized (assuming the capture electronics are 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 with SAR aboard an 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

:<math>\frac{N^2 + N}{2}</math>

where N is the number of unique antenna positions.

Scanning modes

Stripmap mode airborne SAR

thumb|Illustration of the SAR stripmap operation mode.

The antenna stays in a fixed position. It may be orthogonal to the flight path, or it may be squinted slightly forward or backward.

Spotlight mode SAR

thumb|Depiction of the Spotlight Image Mode

The spotlight synthetic aperture is given by

: <math>Lsa = r_0 \Delta\theta_a</math>

where <math>\Delta\theta_a</math> is the angle formed between the beginning and end of the imaging, as shown in the diagram of spotlight imaging and <math>r_0</math> is the range distance.

The spotlight mode gives better resolution albeit for a smaller ground patch. In this mode, the illuminating radar beam is steered continually as the aircraft moves, so that it illuminates the same patch over a longer period of time. This mode is not a traditional continuous-strip imaging mode; however, it has high azimuth resolution.

Scan mode SAR

thumb|Depiction of ScanSAR Imaging Mode

While operating as a scan mode SAR, the antenna beam sweeps periodically and thus cover much larger area than the spotlight and stripmap modes. However, the azimuth resolution become much lower than the stripmap mode due to the decreased azimuth bandwidth. Clearly there is a balance achieved between the azimuth resolution and the scan area of SAR. Here, the synthetic aperture is shared between the sub swaths, and it is not in direct contact within one subswath. Mosaic operation is required in azimuth and range directions to join the azimuth bursts and the range sub-swaths.

Three-component scattering power model

The three-component scattering power model by Freeman and Durden

Four-component scattering power model

For PolSAR image analysis, there can be cases where reflection symmetry condition does not hold. In those cases a four-component scattering model can be used to decompose polarimetric synthetic-aperture radar (SAR) images. This approach deals with the non-reflection symmetric scattering case. It includes and extends the three-component decomposition method introduced by Freeman and Durden to a fourth component by adding the helix scattering power. This helix power term generally appears in complex urban area but disappears for a natural distributed scatterer.

There is also an improved method using the four-component decomposition algorithm, which was introduced for the general polSAR data image analyses. The SAR data is first filtered which is known as speckle reduction, then each pixel is decomposed by four-component model to determine the surface scattering power (<math>P_{s}</math>), double-bounce scattering power (<math>P_{d}</math>), volume scattering power (<math>P_{v}</math>), and helix scattering power (<math>P_{c}</math>).

Although this method is aimed for non-reflection case, it automatically includes the reflection symmetry condition, therefore in can be used as a general case. It also preserves the scattering characteristics by taking the mixed scattering category into account therefore proving to be a better algorithm.

Interferometry

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&nbsp;m and altitude errors also about 5&nbsp;m. Interferometry was used to map many regions of the Earth's surface with unprecedented accuracy using data from the Shuttle Radar Topography Mission.

If the two samples are separated in time, perhaps from two 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 to separate the two kinds of phase difference; a third pass may be necessary 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.

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&nbsp;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 the target and back again, the measured displacement is twice the unit of wavelength. This means in differential interferometry one fringe cycle − to + or one wavelength corresponds to a displacement relative to SAR antenna of only half wavelength (2.8&nbsp;cm). There are various publications on measuring subsidence movement, slope stability analysis, landslide, 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.

Tomo-SAR

SAR Tomography is a subfield of a concept named as multi-baseline interferometry. It has been developed to give a 3D exposure to the imaging, which uses the beam formation concept. It can be used when the use demands a focused phase concern between the magnitude and the phase components of the SAR data, during information retrieval. One of the major advantages of Tomo-SAR is that it can separate out the parameters which get scattered, irrespective of how different their motions are.

On using Tomo-SAR with differential interferometry, a new combination named "differential tomography" (Diff-Tomo) is developed. were the first effective analog optical computer systems, and were, in fact, devised before the holographic technique was fully adapted to optical imaging. Because of the different sources of range and across-range signal structures in the radar signals, optical data-processors for SAR included not only both spherical and cylindrical lenses, but sometimes conical ones.

Image appearance

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.

thumb|25cm resolution SAR image of downtown Cleveland, Ohio by [[Umbra Space|Umbra]]

Range, cross-range, and angles

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.

Visibility

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.

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.

Mirroring artefacts and shadows

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.

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

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.

Commercial industry

In recent years, the commercialization of synthetic aperture radar (SAR) technology has expanded, with private companies launching SAR satellites to provide high-resolution imaging capabilities for various applications. These include environmental monitoring, disaster response, defense and intelligence, infrastructure monitoring, and maritime surveillance.

Capella Space, an American Earth observation company, operates a constellation of SAR satellites designed to provide all-weather, high-resolution imagery. Capella was the first U.S. company to deploy a commercial SAR satellite and continues to expand its fleet with advanced SAR capabilities, including higher resolution, faster revisit times, and automated tasking. SAR data is often used by government agencies, defense organizations, and commercial customers to monitor changes on Earth in near real-time.

Other commercial SAR providers include ICEYE, a Finnish company specializing in small SAR satellites, and Airbus, which operates the TerraSAR-X and PAZ missions. The commercial SAR industry has grown significantly as advancements in satellite miniaturization, cloud-based data processing, and artificial intelligence enhance accessibility and utility for a broad range of users.

History

Relationship to phased arrays

<!--for clarification: remove "across the range dimension" to avoid confusing radar range with array geometry.!-->

A technique closely related to SAR uses an array (referred to as a "phased array") of real antenna elements spatially distributed over either one or two dimensions perpendicular to the radar-range dimension. These physical arrays are truly synthetic ones, indeed being created by synthesis of a collection of subsidiary physical antennas. Their operation need not involve motion relative to targets. All elements of these arrays receive simultaneously in real time, and the signals passing through them can be individually subjected to controlled shifts of the phases of those signals. One result can be to respond most strongly to radiation received from a specific small scene area, focusing on that area to determine its contribution to the total signal received. The coherently detected set of signals received over the entire array aperture can be replicated in several data-processing channels and processed differently in each. The set of responses thus traced to different small scene areas can be displayed together as an image of the scene.

In comparison, a SAR's (commonly) single physical antenna element gathers signals at different positions at different times. When the radar is carried by an aircraft or an orbiting vehicle, those positions are functions of a single variable, distance along the vehicle's path, which is a single mathematical dimension (not necessarily the same as a linear geometric dimension). The signals are stored, thus becoming functions, no longer of time, but of recording locations along that dimension. When the stored signals are read out later and combined with specific phase shifts, the result is the same as if the recorded data had been gathered by an equally long and shaped phased array. What is thus synthesized is a set of signals equivalent to what could have been received simultaneously by such an actual large-aperture (in one dimension) phased array. The SAR simulates (rather than synthesizes) that long one-dimensional phased array. Although the term in the title of this article has thus been incorrectly derived, it is now firmly established by half a century of usage.

While operation of a phased array is readily understood as a completely geometric technique, the fact that a synthetic aperture system gathers its data as it (or its target) moves at some speed means that phases which varied with the distance traveled originally varied with time, hence constituted temporal frequencies. Temporal frequencies being the variables commonly used by radar engineers, their analyses of SAR systems are usually (and very productively) couched in such terms. In particular, the variation of phase during flight over the length of the synthetic aperture is seen as a sequence of Doppler shifts of the received frequency from that of the transmitted frequency. Once the received data have been recorded and thus have become timeless, the SAR data-processing situation is also understandable as a special type of phased array, treatable as a completely geometric process.

The core of both the SAR and the phased array techniques is that the distances that radar waves travel to and back from each scene element consist of some integer number of wavelengths plus some fraction of a "final" wavelength. Those fractions cause differences between the phases of the re-radiation received at various SAR or array positions. Coherent detection is needed to capture the signal phase information in addition to the signal amplitude information. That type of detection requires finding the differences between the phases of the received signals and the simultaneous phase of a well-preserved sample of the transmitted illumination.

See also

References

Bibliography

  • InSAR measurements from the Space Shuttle
  • The Alaska Satellite Facility has numerous technical documents, including an introductory text on SAR theory and scientific applications
  • SAR Journal SAR Journal tracks the Synthetic Aperture Radar (SAR) industry
  • – Jet Propulsion Laboratory