Surface Displacement Measurement from Remote Sensing Images. Olivier Cavalie

recommendations for remote sensing (ITU-R 2009), and particularly for active microwave sensors with regard to Radiocommunication Requirements (RR) Art. 5 (Table 1.3).

Table 1.3. Allocated frequencies and bandwidths for active SAR civil sensors in space as mentioned by the ITU-R (2009)

Allocated frequencies by RR Art. 5(MHz)	Conventional letter	ITU required bandwidth (MHz)
432–438	P	6
1,215–1,300	L	20–85
3,100–3,300	S	20–200
5,250–5,570	C	20–320
8,550–8,650	X	20–100
9,300–9,900	X	20–600

      There are concerns, however, about other ITU attributions that affect these frequencies, in particular in the C-band (wireless LAN, mobile phones) and L-band (radio location and radio navigation), according to the ITU-R (2010). Sometimes military radars are also active in such frequencies. Both can cause real interferences in image data and make them partly useless. Each frequency has its own properties, and all categories have either flown (L, S, C, X) or are being scheduled (P-band with Biomass).

We can note from Table 1.3 that the highest bandwidth is available in the X-band: as a result of this point combined with the more compact antennas needed for such missions and the inferred cost reduction, many new satellites are aiming at the X-band. In the ITU WRC 2015 meeting, an extension to a 1,200-MHz bandwidth (9,200–10,400 MHz) was approved, but some countries have expressed reservations and stick to 9,300–9,900 MHz (ITU-R 2020). In addition, this table is not applicable everywhere: for instance, the P-band is not accepted over the United States for SAR civil sensors. SAR missions of the interest detailed in this chapter and associated frequency bands are listed in Figure 1.1.

Figure 1.1. Relevant SAR missions and associated frequency bands (future missions in gray italics). For a color version of this figure, see www.iste.co.uk/cavalie/images.zip

      Radar swath and pulse repetition frequency (PRF): Stripmap is the simplest working mode of a SAR system. More advanced modes can be explained relative to this mode. In stripmap, the resolution after synthesis in the azimuth direction (along-track) is given by half the antenna length La/2. The Doppler bandwidth in the azimuth is given by BDop = vs/c/(La/2), where vs/c is the satellite velocity. The PRF fP needs to be higher than BDop to avoid spectral layover in the azimuth. In contrast, in the range direction (across-track), the PRF must be limited to avoid range ambiguities or, to put it another way, the swath will be maximized if the PRF is minimized: swath < c/2fP . This explains why stripmap swath is lower in X-band compared to C-band missions (a shorter antenna means higher PRFs and narrower swaths).

      If higher resolution is needed, it is possible to expand BDop by electronic steering in the azimuth (the same resolution is kept in range) and thus to increase the length of observation along the orbit: this is called the spotlight mode. The counterpart is that it is no longer possible to obtain a continuous along-track imaging as in stripmap, but only sparse scenes. If a larger swath is needed, then the approach is to use ScanSAR modes: the Doppler bandwidth is shared between different subswaths. By adding an azimuth steering mode like a “reverse” spotlight, it is possible to obtain a Sentinel-1-like mode called the terrain observation by progressive scan (TOPS) mode (Zan and Guarnieri 2006). The range resolution can stay the same as the stripmap mode. In some missions with multi-incidence angles (Envisat or Radarsat-1, for instance), loss of range resolution has been mitigated for some modes by increasing the transmitted bandwidth to assure a better ground-range resolution for the lowest incidence angles.

      Yaw steering: Most SAR missions use yaw steering on board, so that the spacecraft compensates for Earth rotation and the point perpendicular to the orbit is effectively at zero Doppler. Radarsat-1 was not yaw steered, which resulted in a Doppler shift of several PRFs.

      Incidence angle: In contrast to optical sensors, SAR imaging sensors cannot look to the nadir, as this would create simultaneous echoes in the same pixel from both sides. In addition, the best resolution is obtained at the largest incidence angle, at the expense of lower power received due to the increased distance from the ground. The choice of the incidence angle is critical in mountainous areas due to layover on one side and shadows on the other side of mountains.

      Orbit precision: This is an important parameter used to combine SAR images for interferometry. An orbit that is not precisely known will lead to an important phase gradient in the interferogram. There are three kinds of orbit that can be successively delivered:

       – the first is a predicted orbit that usually comes along with the product when produced in real time;

       – then, a few hours or days after the data acquisition, a restituted orbit is available with more precision;

       – finally, after three or four weeks, the most precise orbit can be delivered to users, thanks to dedicated payloads and specific computing.

      Nowadays, with precise orbit determination payloads onboard, orbit precision can be known at the order of a few centimeters.

Orbital tube: Recent SAR missions have integrated the use of differential interferometry in their specifications (Sentinel-1, ALOS-2, the Radarsat Constellation mission) and have put constraints on orbit housekeeping. Thus, the orbit must stay in a tube called the “orbital tube”, with a radius as small as one hundred or a few hundreds of meters to keep the perpendicular baseline small (see Chapter 4, section 4.2).

      Duty cycle, down-link rate and onboard storage: The duty cycle is equivalent to the percentage of time that the radar will be able to work along the orbit. SAR systems need a lot of energy, making it impossible for them to work permanently. Depending on the design of the satellite power unit, a system can deliver between a few seconds of imaging and about 1/4 of the orbit time. There is a huge difference between very small satellites of a few hundreds of kilograms and big platforms of two or three tons. The down-link rate and onboard storage capacity are often two key elements that usually come together. A data relay satellite is sometimes helpful to cope with all the constraints or avoid multiple ground antennas for down-linking, but this usually needs a laser link and data relay commercial contract, which can also be quite expensive.

      Instrument noise equivalent σ₀: This parameter is very important when looking at amplitude images. It gives the minimum value that can be reached by