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The process can be thought of as combining the series of spatially distributed observations as if all had been made simultaneously with an antenna as long as the beamwidth and focused on that particular point. The "synthetic aperture" simulated at maximum system range by this process not only is longer than the real antenna, but, in practical applications, it is much longer than the radar aircraft, and tremendously longer than the radar spacecraft.
Image resolution of SAR in its range coordinate expressed in image pixels per distance unit is mainly proportional to the radio bandwidth of whatever type of pulse is used. In the cross-range coordinate, the similar resolution is mainly proportional to the bandwidth of the Doppler shift of the signal returns within the beamwidth. Since Doppler frequency depends on the angle of the scattering point's direction from the broadside direction, the Doppler bandwidth available within the beamwidth is the same at all ranges.
Hence the theoretical spatial resolution limits in both image dimensions remain constant with variation of range. However, in practice, both the errors that accumulate with data-collection time and the particular techniques used in post-processing further limit cross-range resolution at long ranges. The conversion of return delay time to geometric range can be very accurate because of the natural constancy of the speed and direction of propagation of electromagnetic waves.
However, for an aircraft flying through the never-uniform and never-quiescent atmosphere, the relating of pulse transmission and reception times to successive geometric positions of the antenna must be accompanied by constant adjusting of the return phases to account for sensed irregularities in the flight path. SAR's in spacecraft avoid that atmosphere problem, but still must make corrections for known antenna movements due to rotations of the spacecraft, even those that are reactions to movements of onboard machinery.
Locating a SAR in a manned space vehicle may require that the humans carefully remain motionless relative to the vehicle during data collection periods. Although some references to SARs have characterized them as "radar telescopes", their actual optical analogy is the microscope, the detail in their images being smaller than the length of the synthetic aperture. In radar-engineering terms, while the target area is in the " far field " of the illuminating antenna, it is in the "near field" of the simulated one.
Returns from scatterers within the range extent of any image are spread over a matching time interval. The inter-pulse period must be long enough to allow farthest-range returns from any pulse to finish arriving before the nearest-range ones from the next pulse begin to appear, so that those do not overlap each other in time. On the other hand, the interpulse rate must be fast enough to provide sufficient samples for the desired across-range or across-beam resolution. When the radar is to be carried by a high-speed vehicle and is to image a large area at fine resolution, those conditions may clash, leading to what has been called SAR's ambiguity problem.
The same considerations apply to "conventional" radars also, but this problem occurs significantly only when resolution is so fine as to be available only through SAR processes. Since the basis of the problem is the information-carrying capacity of the single signal-input channel provided by one antenna, the only solution is to use additional channels fed by additional antennas. The system then becomes a hybrid of a SAR and a phased array, sometimes being called a Vernier array. Combining the series of observations requires significant computational resources, usually using Fourier transform techniques.
The high digital computing speed now available allows such processing to be done in near-real time on board a SAR aircraft. There is necessarily a minimum time delay until all parts of the signal have been received. The result is a map of radar reflectivity, including both amplitude and phase. The amplitude information, when shown in a map-like display, gives information about ground cover in much the same way that a black-and-white photo does.
Variations in processing may also be done in either vehicle-borne stations or ground stations for various purposes, so as to accentuate certain image features for detailed target-area analysis. Although the phase information in an image is generally not made available to a human observer of an image display device, it can be preserved numerically, and sometimes allows certain additional features of targets to be recognized.
Unfortunately, the phase differences between adjacent image picture elements "pixels" also produce random interference effects called "coherence speckle ", which is a sort of graininess with dimensions on the order of the resolution, causing the concept of resolution to take on a subtly different meaning. This effect is the same as is apparent both visually and photographically in laser-illuminated optical scenes.
The scale of that random speckle structure is governed by the size of the synthetic aperture in wavelengths, and cannot be finer than the system's resolution. Speckle structure can be subdued at the expense of resolution. Before rapid digital computers were available, the data processing was done using an optical holography technique. The analog radar data were recorded as a holographic interference pattern on photographic film at a scale permitting the film to preserve the signal bandwidths for example, ,, for a radar using a 0.
Then light using, for example, 0. This worked because both SAR and phased arrays are fundamentally similar to optical holography, but using microwaves instead of light waves. The "optical data-processors" developed for this radar purpose    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.
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. 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. These curvatures are not evident unless large extents of near-range terrain, including steep slant ranges, are being viewed.
When viewed as specified above, fine-resolution radar images of small areas can appear most nearly like familiar optical ones, for two reasons.
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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.
Note that 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. 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.
An important fact that applies to SARs but not to real-aperture radars is that 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 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. Carl A. Independently of Wiley's work, experimental trials in early by Sherwin and others at the University of Illinois ' Control Systems Laboratory showed results that they pointed out "could provide the basis for radar systems with greatly improved angular resolution" and might even lead to systems capable of focusing at all ranges simultaneously.
In both of those programs, processing of the radar returns was done by electrical-circuit filtering methods. In essence, signal strength in isolated discrete bands of Doppler frequency defined image intensities that were displayed at matching angular positions within proper range locations. When only the central zero-Doppler band portion of the return signals was used, the effect was as if only that central part of the beam existed. That led to the term Doppler Beam Sharpening. Displaying returns from several adjacent non-zero Doppler frequency bands accomplished further "beam-subdividing" sometimes called "unfocused radar", though it could have been considered "semi-focused".
Wiley's patent, applied for in , still proposed similar processing. The bulkiness of the circuitry then available limited the extent to which those schemes might further improve resolution. The principle was included in a memorandum  authored by Walter Hausz of General Electric that was part of the then-secret report of a Dept. A follow-on summer program in at the University of Michigan , called Project Wolverine, identified several of the TEOTA subjects, including Doppler-assisted sub-beamwidth resolution, as research efforts to be sponsored by the Department of Defense DoD at various academic and industrial research laboratories.
In that same year, the Illinois group produced a "strip-map" image exhibiting a considerable amount of sub-beamwidth resolution. Initially called the side-looking radar project, it was carried out by a group first known as the Radar Laboratory and later as the Radar and Optics Laboratory. It proposed to take into account, not just the short-term existence of several particular Doppler shifts, but the entire history of the steadily varying shifts from each target as the latter crossed the beam. An early analysis by Dr.
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Leith of that group showed that such a fully focused system should yield, at all ranges, a resolution equal to the width or, by some criteria, the half-width of the real antenna carried on the radar aircraft and continually pointed broadside to the aircraft's path. The required data processing amounted to calculating cross-correlations of the received signals with samples of the forms of signals to be expected from unit-amplitude sources at the various ranges. At that time, even large digital computers had capabilities somewhat near the levels of today's four-function handheld calculators, hence were nowhere near able to do such a huge amount of computation.
Instead, the device for doing the correlation computations was to be an optical correlator. It was proposed that signals received by the traveling antenna and coherently detected be displayed as a single range-trace line across the diameter of the face of a cathode-ray tube , the line's successive forms being recorded as images projected onto a film traveling perpendicular to the length of that line. The information on the developed film was to be subsequently processed in the laboratory on equipment still to be devised as a principal task of the project.
In the initial processor proposal, an arrangement of lenses was expected to multiply the recorded signals point-by-point with the known signal forms by passing light successively through both the signal film and another film containing the known signal pattern. The subsequent summation, or integration, step of the correlation was to be done by converging appropriate sets of multiplication products by the focusing action of one or more spherical and cylindrical lenses.
The processor was to be, in effect, an optical analog computer performing large-scale scalar arithmetic calculations in many channels with many light "rays" at once. Ultimately, two such devices would be needed, their outputs to be combined as quadrature components of the complete solution. Fortunately as it turned out , a desire to keep the equipment small had led to recording the reference pattern on 35 mm film. Trials promptly showed that the patterns on the film were so fine as to show pronounced diffraction effects that prevented sharp final focusing.
That led Leith, a physicist who was devising the correlator, to recognize that those effects in themselves could, by natural processes, perform a significant part of the needed processing, since along-track strips of the recording operated like diametrical slices of a series of circular optical zone plates. Any such plate performs somewhat like a lens, each plate having a specific focal length for any given wavelength.
The recording that had been considered as scalar became recognized as pairs of opposite-sign vector ones of many spatial frequencies plus a zero-frequency "bias" quantity. The needed correlation summation changed from a pair of scalar ones to a single vector one. Each zone plate strip has two equal but oppositely signed focal lengths, one real, where a beam through it converges to a focus, and one virtual, where another beam appears to have diverged from, beyond the other face of the zone plate.
The zero-frequency DC bias component has no focal point, but overlays both the converging and diverging beams. The key to obtaining, from the converging wave component, focused images that are not overlaid with unwanted haze from the other two is to block the latter, allowing only the wanted beam to pass through a properly positioned frequency-band selecting aperture. Each radar range yields a zone plate strip with a focal length proportional to that range.
This fact became a principal complication in the design of optical processors. Consequently, technical journals of the time contain a large volume of material devoted to ways for coping with the variation of focus with range. For that major change in approach, the light used had to be both monochromatic and coherent, properties that were already a requirement on the radar radiation. Lasers also then being in the future, the best then-available approximation to a coherent light source was the output of a mercury vapor lamp , passed through a color filter that was matched to the lamp spectrum's green band, and then concentrated as well as possible onto a very small beam-limiting aperture.
While the resulting amount of light was so weak that very long exposure times had to be used, a workable optical correlator was assembled in time to be used when appropriate data became available. Although creating that radar was a more straightforward task based on already-known techniques, that work did demand the achievement of signal linearity and frequency stability that were at the extreme state of the art.
An adequate instrument was designed and built by the Radar Laboratory and was installed in a C Curtiss Commando aircraft. Army and was flown and maintained by WRRC's own pilots and ground personnel, it was available for many flights at times matching the Radar Laboratory's needs, a feature important for allowing frequent re-testing and "debugging" of the continually developing complex equipment. By contrast, the Illinois group had used a C belonging to the Air Force and flown by AF pilots only by pre-arrangement, resulting, in the eyes of those researchers, in limitation to a less-than-desirable frequency of flight tests of their equipment, hence a low bandwidth of feedback from tests.
Later work with newer Convair aircraft continued the Michigan group's local control of flight schedules. Michigan's chosen 5-foot 1. It was understood that finer resolution would require the added development of means for sensing departures of the aircraft from an ideal heading and flight path, and for using that information for making needed corrections to the antenna pointing and to the received signals before processing. Although the program had been considered for termination by DoD due to what had seemed to be a lack of results, that first success ensured further funding to continue development leading to solutions to those recognized needs.
At the time, the nature of the data processor was not revealed. Although it did not refer to the use of those techniques for radar, readers of both journals could quite easily understand the existence of a connection between articles sharing some authors. The lessons it provided were well learned by subsequent researchers, operational system designers, image-interpreter trainers, and the DoD sponsors of further development and acquisition.
In subsequent work the technique's latent capability was eventually achieved. That work, depending on advanced radar circuit designs and precision sensing of departures from ideal straight flight, along with more sophisticated optical processors using laser light sources and specially designed very large lenses made from remarkably clear glass, allowed the Michigan group to advance system resolution, at about 5-year intervals, first to 15 feet 4.
The latter levels and the associated very wide dynamic range proved suitable for identifying many objects of military concern as well as soil, water, vegetation, and ice features being studied by a variety of environmental researchers having security clearances allowing them access to what was then classified imagery. Similarly improved operational systems soon followed each of those finer-resolution steps.
Space Based Radar Theory Applications
Even the 5-foot 1. However, at about the same time, digital computers finally became capable of doing the processing without similar limitation, and the consequent presentation of the images on cathode ray tube monitors instead of film allowed for better control over tonal reproduction and for more convenient image mensuration. Achievement of the finest resolutions at long ranges was aided by adding the capability to swing a larger airborne antenna so as to more strongly illuminate a limited target area continually while collecting data over several degrees of aspect, removing the previous limitation of resolution to the antenna width.
This was referred to as the spotlight mode, which no longer produced continuous-swath images but, instead, images of isolated patches of terrain.
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It was understood very early in SAR development that the extremely smooth orbital path of an out-of-the-atmosphere platform made it ideally suited to SAR operation. Early experience with artificial earth satellites had also demonstrated that the Doppler frequency shifts of signals traveling through the ionosphere and atmosphere were stable enough to permit very fine resolution to be achievable even at ranges of hundreds of kilometers.
That seemingly slow rate of advances was often paced by the progress of other inventions, such as the laser, the digital computer , circuit miniaturization, and compact data storage. Once the laser appeared, optical data processing became a fast process because it provided many parallel analog channels, but devising optical chains suited to matching signal focal lengths to ranges proceeded by many stages and turned out to call for some novel optical components.
Since the process depended on diffraction of light waves, it required anti-vibration mountings , clean rooms , and highly trained operators. Even at its best, its use of CRTs and film for data storage placed limits on the range depth of images. At several stages, attaining the frequently over-optimistic expectations for digital computation equipment proved to take far longer than anticipated. For example, the SEASAT system was ready to orbit before its digital processor became available, so a quickly assembled optical recording and processing scheme had to be used to obtain timely confirmation of system operation.
Modern methods now provide both high speed and high quality. Although the above specifies the system development contributions of only a few organizations, many other groups had also become players as the value of SAR became more and more apparent. Especially crucial to the organization and funding of the initial long development process was the technical expertise and foresight of a number of both civilian and uniformed project managers in equipment procurement agencies in the federal government, particularly, of course, ones in the armed forces and in the intelligence agencies, and also in some civilian space agencies.
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Since a number of publications and Internet sites refer to a young MIT physics graduate named Robert Rines as having invented fine-resolution radar in the s, persons who have been exposed to those may wonder why that has not been mentioned here. Actually, none of his several radar-image-related patents  actually had that goal.
Instead, they presumed that fine-resolution images of radar object fields could be accomplished by already-known "dielectric lenses", the inventive parts of those patents being ways to convert those microwave-formed images to visible ones. However, that presumption incorrectly implied that such lenses and their images could be of sizes comparable to their optical-wave counterparts, whereas the tremendously larger wavelengths of microwaves would actually require the lenses to have apertures thousands of feet or meters wide, like the ones simulated by SARs, and the images would be comparably large.
Apparently not only did that inventor fail to recognize that fact, but so also did the patent examiners who approved his several applications, and so also have those who have propagated the erroneous tale so widely. Persons seeking to understand SAR should not be misled by references to those patents. 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.
Space-surface bistatic synthetic aperture radar with navigation satellite transmissions: a review
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. It is significant, though, to realize that, 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.
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