## 2 Fundamentals of SAR for Antenna Sizing and Transmitting Power Consideration
### Pulse Width  
The pulse width is the duration of each radar pulse. The pulse width depends on several factors, including the desired resolution, range coverage, and the trade-offs between them. Longer pulse widths provide better range resolution, while shorter pulses are better for azimuth resolution. The selection of pulse width depends on the specific application. For instance, for high-resolution imaging, a short pulse width is preferred, while for wide area coverage, a longer pulse width may be more suitable. Short pulses are typically used in high-resolution imaging modes, such as Spotlight or Stripmap modes. Short pulses provide excellent range resolution. They are ideal for distinguishing between closely spaced targets. They are suitable for capturing fine surface details and small objects. Short pulses are also effective in reducing the effect of range ambiguities. Short pulse widths are often in the range of a few nanoseconds to a few microseconds. Values might be in the range of 1 to 50 microseconds. Medium pulse widths are often used in standard-resolution modes, like ScanSAR. These pulse widths strike a balance between range and azimuth resolution, making them suitable for medium-level imaging requirements. They can capture a wider swath while maintaining a reasonably good resolution. Long pulses are used in wide area coverage modes, such as wide swath ScanSAR or wave mode. Medium pulse widths often fall in the range of tens of microseconds to a few hundred microseconds. Medium pulses strike a balance between range and azimuth resolution. Values might be in the range of 50 to 200 microseconds. Long pulses are employed when a wide coverage area is more important than a high resolution. They allow the satellite to cover a larger geographical area in a single pass, making them suitable for applications like maritime surveillance, disaster monitoring, and environmental observation. Long pulse widths can range from hundreds of microseconds to milliseconds. Long pulses are used for wide area coverage modes, where a high azimuth resolution is not critical. Values might be in the range of 200 microseconds to a few milliseconds. Some modern SAR systems have adaptive pulse width capabilities. An adaptive pulse width allows flexibility in choosing the most suitable pulse width for a given scenario. For example, it may use shorter pulses for high-resolution imaging and switch to longer pulses for wide area coverage. This adaptability optimizes the SAR system's performance for different mission objectives. The system might automatically select pulse widths based on the scenario. It is important that the specific pulse width values chosen for a SAR mission are based on a balance between the need for high resolution and the desire to cover a larger area. The choice also depends on the available technology and the trade-offs between resolution and swath width. Different imaging modes within a SAR mission may offer a range of pulse width options to address various user requirements [37; 38; 48]. The pulse width of approximately 2.9 \(\upmu\)s Stripmap mode in Sentinel-1 (C-band) is optimized for medium resolution and wide area coverage [14; 15; 16; 17]. For TerraSAR-X (X-band), Spotlight mode is 0.12 \(\upmu\)s. Therefore, Fine Quad-Pol mode provides high resolution and quad-polarization imaging capabilities [6; 7]. COSMO-SkyMed (X-band) uses 36 \(\upmu\)s. The ScanSAR mode in COSMO-SkyMed is well-suited for wide area coverageand environmental monitoring [9]. ALOS-2 (L-band) is 20 \(\upmu\)s. Stripmap mode in ALOS-2 balances resolution and coverage for various applications, including disaster monitoring [18; 19]. For Radarsat, it is 1 \(\upmu\)s which combines high resolution and quad-polarization capabilities. Variable pulse widths allow ENVISAT to adapt to different imaging needs, including ocean observations and land applications; and it is variable, up to 50 \(\upmu\)s [3].