#REDIRECT Synthetic aperture radar
[[Image:Venus globe.jpg|thumb|right|300px|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. It can only be used by moving instruments over relatively immobile targets, but it has seen wide applications in remote sensing and mapping. ==Basic operation== [[Image:AirSAR-instrument-on-aircraft.jpg|thumb|left|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 is done using Fast Fourier Transform techniques; it requires significant computational resources, and is normally done at a ground station after the observation is complete. The result is a map of radar reflectivity (including both amplitude and phase) on the ground. 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. ==More complex operation== [[Image:Death-valley-sar.jpg|thumb|left|SAR image of Death Valley colored using polarimetry]] 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. ===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 images are used as the three color channels in a synthesized image. This is what has been done in the picture above. Interpretation of the resulting colors requires significant testing of known materials. ===Interferometry=== Rather than discarding the phase information, information can be extracted from it. If two observations of the same terrain from very similar positions are available, a great deal of interesting information can be extracted. This technique is called interferometry 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 with a single airplane pass. One aircraft application at the Canada Center for Remote Sensing produced digital elevation maps with a resolution of 5 m and altitude errors also on the order of 5 m. 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 obervations, 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. ===Ultra-wideband SAR=== Normal radar emits pulses with a very narrow range of frequencies. This places a lower limit on the pulse length (and therefore the resolution in the distance direction) but greatly simplifes the electronics. Interpretation of the results is also eased by the fact that the material response must be known only in a narrow range of frequencies. Ultra-wideband radar emits very short pulses consisting of a very wide range of frequencies, from zero up to the radar's normal operating frequency. Such pulses allow high distance resolution but much of the information is concentrated in relatively low frequencies (with long wavelengths). Thus such systems require very large receiving apertures to obtain correspondingly high resolution along the track. This can be achieved with synthetic aperture techniques. The fact that the information is captured in low frequencies means that the most relevant material properties are those at lower frequencies than for most radar systems. In particular, such radar can penetrate some distance into foliage and soil. ==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 ortho-normal (right angle) 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 up-shifted signal (slightly higher in frequency) and targets behind the platform return a Doppler down-shifted 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. ==Chirped (Pulse Compressed) Radars== A common techniqe for many RADAR systems (sometimes found in SAR systems) is to "chirp" the signal. In a "chirped" radar, the pulse is allowed to be much longer (which usually hinders range resolution - but increases the probability of detection because more energy is returned), but this longer pulse is also allowed to have a frequency shift during the pulse (hence the chirp or frequency shift). When the "chirped" signal is returned, it is passed to a dispersive delay line (often a SAW device (Surface Acoustic Wave) that has the property of varying velocity of propogation 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). == 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 CV-990. However, in 1986, this plane crashed 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 was flown by the Canada Center for Remote Sensing until about 1996 when it was decommissioned for cost reasons. Most land-surveying applications are now carried out by satellite observation. Satellites such as ERS-1, JERS-1, 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. SIR-A flew on the first dedicated science mission of the space shuttle in 1982. SIR-b flew in 1984 on the space shuttle. SIR-c flew on the space shuttle endeavour twice in 1994. The Magellan_probe 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-Huygens mission to Saturn (planet) is currently using SAR to map the surface of the planet's major moon Titan (moon), whose surface is partially hidden from direct optical inspection by atmospheric haze. The Mineseeker Project ([http://www.mineseeker.com/]) 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. == See also == * radar * remote sensing * Earth observation satellite * Magellan_probe space probe * inverse_Synthetic_aperture_radar == External links == * [http://southport.jpl.nasa.gov The Imaging Radar Home Page] (NASA SAR missions) * [http://airsar.jpl.nasa.gov Airborne Synthetic Aperture Radar (AIRSAR)] ) (NASA Airborne SAR) * [http://www.ccrs.nrcan.gc.ca/ccrs/data/satsens/airborne/sarbro/sbmain_e.html The CCRS airborne SAR page] (Canadian airborne missions) * [http://www.rsi.ca/ RADARSAT international] (Canadian radar satellites) * [http://earth.esa.int/ers/ The ERS missions] (European radar satellites) * [http://www.eorc.nasda.go.jp/JERS-1/ The JERS satellites] (Japanese radar satellites) * [http://www.jpl.nasa.gov/radar/sircxsar/ Images from the Space Shuttle SAR instrument] * [http://www.mineseeker.com/ The Mineseeker Project] has technical information about ultra-wideband SAR * [http://www.asf.alaska.edu/ The Alaska Satellite Facility] has numerous tehnical documents, including [http://www.asf.alaska.edu/SciSARuserGuide.pdf an introductory text] on SAR theory and scientific applications Radar
==Doppler Beam Sharpening== Is this really compatible with SAR? The Doppler shift from targets ahead/behind seems like it is actually the same effect as the phase shift that is used to assemble multiple samples. For a sidelooking radar that is not a SAR, it's clear this could help. --User:Aarchiba 18:54, Dec 14, 2004 (UTC) == Doppler Beam Sharpening == Hmmm... I'm not sure if I understand your question, but let me say (from many years of experience) that most SAR radars use doppler beam sharpening. Let me first say that it is EXTREMELY DIFFICULT to separate frequency shift from phase shift... that the time the shift is occurring. After the fact it's not a problem, but with a dynamic signal, it's nigh impossible to separate the two... This "reality" is often used with FM radios - in that the same receive chain detects either PM (phase modulation) or FM with little difference... Now as to the whole issue of dopper shifts... maybe it helps to separate the different contributing components (simplified). First, there are the two large scale doppler components: motion of the imaging platform and motion of "point" targets in the area being imaged. Normally (when MTI is not the intended capability) you'd like the point target to have no motion. Then there are the two "microdoppler" components: vibrations that cause spreading of the doppler signature - either by the imaging platform or by any point target vibrations. Unless you are taking advantage of microdoppler signature analysis then you'd just as soon these components were zero. Finally there are the periodic rotational/translational components - think of these as periodic movements on the target or imaging platform... actually used with benefit in ISAR imaging of ships (waves and swells cause regular rotational and translational displacements). Now, if the goal is GROUND/SURFACE imaging... then typically... all the doppler components except the imaging platform - are assummed to be zero (as I said, simplified... we ignored yaw, roll, and pitch changes by the imaging platform - which all make life more difficult)... This has proven to be a resonable assumption in real world SAR systems. Never-the-less, imaging platforms do record/transfer the three space coordinates, three space accellerations, three space pitch/roll/yaw rates, and three space pitch/roll/yaw accelerations. GA maps also play a roll (GA = gravitational anomaly) to ensure the Z accelerations are normalized... A complicated but interesting subject in itself. Anyway, many SAR systems treat the phase change as a frequency change by using DFT/FFT processing to determine the doppler shift amounts. This means that given a single range gate time period, the number of actual bins relates to the processing power available and the phase/frequency resolution (A/D speed, bits of resolution, linearity)... Obviously there are diminishing returns while working with all this that are fed by real energy beam width... i.e.... if the transmitted signal is way down when 15 degrees off orthonormal... then why bother to process data that would have doppler shifts that correlate to that far off axis... think in terms of basic trig... if the range gate being processed is 100 km away (60+ miles), the system has a ten meter "resolution" - - and the real beamwidth is 20 degrees... (+/- 10 degrees)... then the total number of bins that needs to be processed (tan "theta" = Opposite/Adjacent... since we know theta = 20 degrees and the adjacent side is 100,000 meters (100 km)... then the Opposite side is approximately 35,000 meters long... (simple triangle)... with 10 meter bins... then we're looking at 3,500 angular bins... just along that one range resolution cell... that must map into 3,500 discrete phase/frequency shifts... or 1750 discrete upshifted bins and 1750 discrete downshifted bins... Anyway... as I digressed WAY TOO MUCH... Doppler beam sharpening... is exactly how many SAR systems actually do their imaging... (mapping mode - - - spot modes are another story)....
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Synthetic_aperture_radar
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Synthetic Aperture Radar
#REDIRECT Synthetic aperture radar
Synthetic aperture radar
[[Image:Venus globe.jpg|thumb|right|300px|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. It can only be used by moving instruments over relatively immobile targets, but it has seen wide applications in remote sensing and mapping. ==Basic operation== [[Image:AirSAR-instrument-on-aircraft.jpg|thumb|left|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 is done using Fast Fourier Transform techniques; it requires significant computational resources, and is normally done at a ground station after the observation is complete. The result is a map of radar reflectivity (including both amplitude and phase) on the ground. 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. ==More complex operation== [[Image:Death-valley-sar.jpg|thumb|left|SAR image of Death Valley colored using polarimetry]] 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. ===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 images are used as the three color channels in a synthesized image. This is what has been done in the picture above. Interpretation of the resulting colors requires significant testing of known materials. ===Interferometry=== Rather than discarding the phase information, information can be extracted from it. If two observations of the same terrain from very similar positions are available, a great deal of interesting information can be extracted. This technique is called interferometry 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 with a single airplane pass. One aircraft application at the Canada Center for Remote Sensing produced digital elevation maps with a resolution of 5 m and altitude errors also on the order of 5 m. 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 obervations, 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. ===Ultra-wideband SAR=== Normal radar emits pulses with a very narrow range of frequencies. This places a lower limit on the pulse length (and therefore the resolution in the distance direction) but greatly simplifes the electronics. Interpretation of the results is also eased by the fact that the material response must be known only in a narrow range of frequencies. Ultra-wideband radar emits very short pulses consisting of a very wide range of frequencies, from zero up to the radar's normal operating frequency. Such pulses allow high distance resolution but much of the information is concentrated in relatively low frequencies (with long wavelengths). Thus such systems require very large receiving apertures to obtain correspondingly high resolution along the track. This can be achieved with synthetic aperture techniques. The fact that the information is captured in low frequencies means that the most relevant material properties are those at lower frequencies than for most radar systems. In particular, such radar can penetrate some distance into foliage and soil. ==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 ortho-normal (right angle) 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 up-shifted signal (slightly higher in frequency) and targets behind the platform return a Doppler down-shifted 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. ==Chirped (Pulse Compressed) Radars== A common techniqe for many RADAR systems (sometimes found in SAR systems) is to "chirp" the signal. In a "chirped" radar, the pulse is allowed to be much longer (which usually hinders range resolution - but increases the probability of detection because more energy is returned), but this longer pulse is also allowed to have a frequency shift during the pulse (hence the chirp or frequency shift). When the "chirped" signal is returned, it is passed to a dispersive delay line (often a SAW device (Surface Acoustic Wave) that has the property of varying velocity of propogation 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). == 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 CV-990. However, in 1986, this plane crashed 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 was flown by the Canada Center for Remote Sensing until about 1996 when it was decommissioned for cost reasons. Most land-surveying applications are now carried out by satellite observation. Satellites such as ERS-1, JERS-1, 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. SIR-A flew on the first dedicated science mission of the space shuttle in 1982. SIR-b flew in 1984 on the space shuttle. SIR-c flew on the space shuttle endeavour twice in 1994. The Magellan_probe 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-Huygens mission to Saturn (planet) is currently using SAR to map the surface of the planet's major moon Titan (moon), whose surface is partially hidden from direct optical inspection by atmospheric haze. The Mineseeker Project ([http://www.mineseeker.com/]) 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. == See also == * radar * remote sensing * Earth observation satellite * Magellan_probe space probe * inverse_Synthetic_aperture_radar == External links == * [http://southport.jpl.nasa.gov The Imaging Radar Home Page] (NASA SAR missions) * [http://airsar.jpl.nasa.gov Airborne Synthetic Aperture Radar (AIRSAR)] ) (NASA Airborne SAR) * [http://www.ccrs.nrcan.gc.ca/ccrs/data/satsens/airborne/sarbro/sbmain_e.html The CCRS airborne SAR page] (Canadian airborne missions) * [http://www.rsi.ca/ RADARSAT international] (Canadian radar satellites) * [http://earth.esa.int/ers/ The ERS missions] (European radar satellites) * [http://www.eorc.nasda.go.jp/JERS-1/ The JERS satellites] (Japanese radar satellites) * [http://www.jpl.nasa.gov/radar/sircxsar/ Images from the Space Shuttle SAR instrument] * [http://www.mineseeker.com/ The Mineseeker Project] has technical information about ultra-wideband SAR * [http://www.asf.alaska.edu/ The Alaska Satellite Facility] has numerous tehnical documents, including [http://www.asf.alaska.edu/SciSARuserGuide.pdf an introductory text] on SAR theory and scientific applications Radar
Synthetic aperture radar
==Doppler Beam Sharpening== Is this really compatible with SAR? The Doppler shift from targets ahead/behind seems like it is actually the same effect as the phase shift that is used to assemble multiple samples. For a sidelooking radar that is not a SAR, it's clear this could help. --User:Aarchiba 18:54, Dec 14, 2004 (UTC) == Doppler Beam Sharpening == Hmmm... I'm not sure if I understand your question, but let me say (from many years of experience) that most SAR radars use doppler beam sharpening. Let me first say that it is EXTREMELY DIFFICULT to separate frequency shift from phase shift... that the time the shift is occurring. After the fact it's not a problem, but with a dynamic signal, it's nigh impossible to separate the two... This "reality" is often used with FM radios - in that the same receive chain detects either PM (phase modulation) or FM with little difference... Now as to the whole issue of dopper shifts... maybe it helps to separate the different contributing components (simplified). First, there are the two large scale doppler components: motion of the imaging platform and motion of "point" targets in the area being imaged. Normally (when MTI is not the intended capability) you'd like the point target to have no motion. Then there are the two "microdoppler" components: vibrations that cause spreading of the doppler signature - either by the imaging platform or by any point target vibrations. Unless you are taking advantage of microdoppler signature analysis then you'd just as soon these components were zero. Finally there are the periodic rotational/translational components - think of these as periodic movements on the target or imaging platform... actually used with benefit in ISAR imaging of ships (waves and swells cause regular rotational and translational displacements). Now, if the goal is GROUND/SURFACE imaging... then typically... all the doppler components except the imaging platform - are assummed to be zero (as I said, simplified... we ignored yaw, roll, and pitch changes by the imaging platform - which all make life more difficult)... This has proven to be a resonable assumption in real world SAR systems. Never-the-less, imaging platforms do record/transfer the three space coordinates, three space accellerations, three space pitch/roll/yaw rates, and three space pitch/roll/yaw accelerations. GA maps also play a roll (GA = gravitational anomaly) to ensure the Z accelerations are normalized... A complicated but interesting subject in itself. Anyway, many SAR systems treat the phase change as a frequency change by using DFT/FFT processing to determine the doppler shift amounts. This means that given a single range gate time period, the number of actual bins relates to the processing power available and the phase/frequency resolution (A/D speed, bits of resolution, linearity)... Obviously there are diminishing returns while working with all this that are fed by real energy beam width... i.e.... if the transmitted signal is way down when 15 degrees off orthonormal... then why bother to process data that would have doppler shifts that correlate to that far off axis... think in terms of basic trig... if the range gate being processed is 100 km away (60+ miles), the system has a ten meter "resolution" - - and the real beamwidth is 20 degrees... (+/- 10 degrees)... then the total number of bins that needs to be processed (tan "theta" = Opposite/Adjacent... since we know theta = 20 degrees and the adjacent side is 100,000 meters (100 km)... then the Opposite side is approximately 35,000 meters long... (simple triangle)... with 10 meter bins... then we're looking at 3,500 angular bins... just along that one range resolution cell... that must map into 3,500 discrete phase/frequency shifts... or 1750 discrete upshifted bins and 1750 discrete downshifted bins... Anyway... as I digressed WAY TOO MUCH... Doppler beam sharpening... is exactly how many SAR systems actually do their imaging... (mapping mode - - - spot modes are another story)....
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