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www.geospatialworld.net | May-June 2020 49 As outlined above, a SAR image has two dimensions, range and azimuth. e resolution in these dimensions is achieved using different aspects of the signal recorded by the radar, and as a result, the resolution in the range direction can (and most oen is) different to that in the azimuth direction. 2 e spatial resolution of SAR data is defined by the impulse response (IPR). e IPR of a SAR system is the response of the sen- sor and processing to a theorectical spatial impulse target, i.e., a target that is infinitesimally small in all dimensions. 3 IPR is a two-dimen- sional entity that is characterized by the range-dimension width (the width of the IPR in the ranging dimension) and the cross-range (or azimuth) dimension width. e generally-accepted definition of radar resolution is the width of the IPR at points at 3 dB below the peak of the IPR . In the range dimension, a larger transmied bandwidth cor- responds to improved range resolution. In the cross-range dimension, a larger Doppler bandwidth corresponds to beer azimuth resolution. IPR is also affected by the processing used to form the image, e.g., windowing, and distortions in the signals due to hardware limitations or uncompensated platform motion. Unless specified, IPR , and thus inherent SAR sensor resolution, is defined in the slant-range plane. When the SAR image is translated to the ground plane, the mapping from slant range to ground range causes the IPR to broaden (Figure 1b). erefore, the IPR-defined range resolution in the ground plane is always worse than that in the slant plane. Resolution in the cross-range direction does not change in the slant plane to ground plane mapping. 4 e ground-range resolution (resolution in the ranging direction in the ground plane) depends on the bandwidth of the transmied signal and the angle from which the ground is imaged (look angle 5 ). Larger bandwidth enables a beer range resolution. For instance, the theoretical resolution with a 300 MHz bandwidth is 0.5 m in the slant plane and 0.91 m in the ground plane at a look angle of 30 degrees. With a bandwidth of 500 MHz, the slant range resolution is 0.3 m and the ground-range resolution is 0.55 m for the same look angle. As mentioned, the azimuth resolution depends on the Doppler bandwidth. A larger Doppler bandwidth can be obtained by pointing the antenna beam at a target for a longer time. Many existing SAR satel- lites use phased array antennas to steer the beam to dwell on objects. As these phased array antennas are designed to scan over a few degrees, the azimuth resolution achieved is on the order of tens of centimeters. Capella SAR satellites have a transmier bandwidth of 500 MHz, so can achieve 0.3 m resolution in the slant plane. e satellites have 2 For more details of SAR processing , please see A. Moreira, P. Prats-Iraola, M. Younis, G. Krieger, I. Hajnsek and K. P. Papathanassiou, "A tutorial on synthetic aperture radar," in IEEE Geoscience and Remote Sensing Magazine, vol. 1, no. 1, pp. 6-43, March 2013. 3 "Anatomy of a SAR Impulse Response" om Sandia National Laboratories. 4 Note that for squinted SAR , things are a lile different, because the ranging and cross-ranging directions are not orthogonal to one another. 5 For spaceborne systems, the difference between look angle and incidence angle maers because of the curvature of the earth. also been designed to point to a spot on the ground for tens of seconds, thereby achieving centimeter-scale azimuth resolution. is fine resolution is used to reduce speckle in the images (see section below) and provide high-quality multi-looked SAR imagery. An example of high-resolution multi-looked Capella imagery is shown in Figure 2. Noise level and image quality In addition to spatial resolution, other metrics are important in overall interpretability of a SAR image. e radar measures the intensity of the reflected signal at each resolution cell in the image. e intensity depends on the transmied power, antenna gain, distance between the scaerer and the radar, and geometry, roughness, and material properties of the object being imaged. For interpreting intensity in a radar image, two features are important: the ability to make out objects against the inherent noise generated by the sensor, and the ability to discriminate two objects that have similar intensities. e first is captured by the noise equivalent sigma zero (NESZ) of a SAR image. e second is captured by the concept of radiometric resolution. 6 A target is detectable in a SAR image when, for a certain pixel reso- lution, the received power and therefore the intensity at the pixel level overcomes the thermal noise that the system electronics generate. In SAR, NESZ is the most commonly used metric that captures the effect of system noise on image quality. It can be analytically predicted during the design of the radar and can be empirically measured over "dark" targets in the SAR image. For instance, calm lakes are highly reflective targets in the side-look- ing geometry and allow the characterization of the noise level of the sensor. e effect of NESZ on image interpretability is demonstrated with the images in Figure 3. e SAR data were processed to 0.5 m ground range resolution and 0.5 m azimuth resolution. In both cases, bright scaerers, e.g., buildings, are clearly detectable. e difference between the two is the NESZ (–10 dB versus –20 dB). e aircra and the roads are far more discernible in the image that has an NESZ of –20 dB. In particular, the aircra shadows are much clearer in the –20 dB NESZ image. is shows that lower NESZ values are preferable when targets with low-backscaering intensity need to be detected. NESZ varies also with transmied bandwidth (range resolution). A SAR image generated with a 300 MHz transmied bandwidth (0.5 m 6 hps://www.sciencedirect.com/topics/earth-and-planetary-sciences/radiomet- ric-resolution. Figure 2: Optical (le), Sentinel-1 (middle), and Capella (right) images of a farm in California. e Sentinel-1 image has a resolution of 20 m. e Capella aerial image has been processed to 0.5 m ground-range resolution and 0.5 m azimuth resolution.

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