Spaceborne Imaging Radar
3.1 SAR Systems as Tools for Sea Ice Monitoring
3.1.1 Imaging Geometry and Spatial Resolution
The geometry of a side-looking imaging radar system is sketched in Figure 3.1. As the sensor platform moves in the azimuth (along-track) direction, the side-looking antenna sends an
3 . 1 s a r s y s t e m s a s to o l s f o r s e a i c e m o n i to r i n g 29
empulse in the slant-range (across-track) direction. The antenna dimensions determine the size of the illuminated area on the ground. The swath width is the coverage of the image in range direction [124]. While slant range is measured along the radar’s line of sight, the measurements can be re-sampled to ground range, which is measured along the Earth surface as distance from nadir (the point directly below the sensor platform). Ground range detected images are still in the radar geometry. For visualization on a map or combination with other data sources, they can be geo-located to a map projection [121].
Dr Da
Swath w idth L
Flight direction
h Azimuth
Range
Groun d ran
ge Slan
t ran ge
IA
Figure 3.1:Simplifiedsarimaging geometry (modified from [125]). (𝐷𝑟×𝐷𝑎): antenna dimen-sions,ℎ: platform flight altitude,𝐿: Synthetic aperture length.
The illumination geometry is often given in terms of theia, which is the angle between the radar beam and the normal to the surface. Theia increases across the swath from near range (close to the satellite track, lowia) to far range (far from the satellite track, highia). The geometry can also be described in terms of the elevation angle, which is the angle between the radar beam and the vertical direction at the Earth surface.
30 c h a p t e r 3 s pac e b o r n e i m ag i n g r a da r The image that is acquired by a radar system as sketched in Figure 3.1 consists of pixels that are associated with a given area on the Earth surface. The spatial resolution of that image is defined as the minimum distance between the two closest points on the ground that can still be distinguished [126]. For a real aperture radar (rar), the resolution in both range and azimuth direction depends on the physical size of the antenna (𝐷𝑟x𝐷𝑎), the pulse duration𝜏, the signal wavelength𝜆, and the flight altitudeℎof the sensor platform:
𝑟𝑔𝑟 = 𝑐𝜏 Here,𝑟𝑔𝑟 is the ground range resolution,𝑟𝑎𝑧 is the azimuth resolution,𝑐 is the speed of light,𝜃 is theia, and𝑅0is the slant distance from the platform to the point at the ground where the azimuth resolution is considered.
Assuming typical values for the radar system parameters (𝜏=10𝜇s,𝜃=30◦[65]) yields a ground range resolution of 3000 m. This is insufficient for operational sea ice observations and ice charting, as well as many othersarapplications (Table 1.1, Section 1.3). Given Equation 3.1, the obvious way to improve range resolution would be to narrow the transmitted pulse. However, a shorter pulse carries less energy and thus limits the sensitivity of the radar. This problem is solved by transmitting a frequency modulated pulse, called a chirp, in which the frequency is linearly changed during the duration of the signal. On reception of the returned signal, the chirp is correlated with a replica of itself, resulting in a very short, compressed pulse. This technique, called pulse compression, is applied in bothrarandsar [123]. The resulting resolution in range direction depends on the bandwidth𝐵𝑐of the transmitted chirp and is given by:
𝑟𝑔𝑟 = 𝑐 2𝐵𝑐sin𝜃
(3.2) Typical ground range resolution for imaging radars using pulse compression is on the order of tens of meters (Section 3.1.2, Table 3.2).
The azimuth resolution depends on the antenna size and the distance to the surface.
Assuming typical values for an airborne system (𝜆=0.03 m,𝐷𝑎=3 m,𝑅0=2000 m) yields an along-track resolution of 20 m [65]. However, placing the same system in space, at an altitude of around 1000 km, results in much coarser azimuth resolution (no better than 10 km). According to Equation 3.1, the easiest way to improve azimuth resolution would be to physically increase the antenna size, which is not feasible for spaceborne instruments.
The actual solution uses sophisticated data processing that makes use of the forward motion of the sensor platform and the phase and Doppler shift of the signal, that is caused by the movement of the sensor platform. Thissarprocessing synthesizes an apparently long antenna, which is several orders of magnitude larger than the physical antenna on board the satellite. The length of the synthetic aperture is determined by the time that a particular target on the ground is illuminated by the radar (Figure 3.2). The mathematical
3 . 1 s a r s y s t e m s a s to o l s f o r s e a i c e m o n i to r i n g 31 basis forsarprocessing can be found in several of the textbooks mentioned above. It leads to the remarkably simple result, that the along-track resolution is given by:
𝑟𝑎𝑧 = 𝐷𝑎
2 (3.3)
sarazimuth resolution does not depend on the flight altitude of the sensor platform. The imaging system can therefore be transferred to spaceborne satellites without loss of detail in the images. Furthermore, Equation 3.3 shows that a shorter antenna will actually result in improved resolution, albeit at the expense of sensitivity. In practice azimuth resolution is limited by the desired area coverage and observation geometry (Section 3.1.2), as well as technological factors, such as the data collection rate and volume, the pulse power, phase control, and calibration [126].
Target
Length of synthesized antenna
Target enters
antenna beam Target exits
antenna beam
Flight direction
Figure 3.2:Forward movement of thesarplatform over a target on the surface. The length of the synthesized antenna is determined by the time that the target is illuminated by the radar.