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Radar sensors, mounted on satellite platforms, airplanes, or even a tripod on the ground, make it possible to measure ground displacement with millimeter accuracy, thanks to a particular technique known as SAR (Synthetic Aperture Radar) interferometry (InSAR) (see Ferretti, 2014, for a comprehensive review). The satellites both send and receive signals, recording the complex returns and using them for both imaging and range (distance) estimation (Fig. 2.1). Unlike optical systems, the sensors operate in the microwave domain, with wavelengths of a few centimeters, 100,000 times longer than those of the visible spectrum. Being an active system, a radar sensor can function 24 hours a day and year‐round, as it can see through clouds, fog, and rain, independent of the Earth's illumination.

An important feature of a SAR system is its ability to record both amplitude and phase information. While the amplitude depends on the amount of energy backscattered toward the sensor, the phase is related to the distance between the phase center of the radar antenna and the target on ground. More precisely, the phase value ϕ of a pixel P of a radar image can be modeled as a mixture of four distinct contributions (Ferretti et al., 2007a):

(2.1)

where ϑ is the phase shift related to the location and to the reflectivity of all elementary scatterers within the resolution cell associated with pixel P. The coefficient is the most significant contribution in any geodetic application, as it is associated with the sensor‐to‐target distance r. The term a is a delay introduced by the medium (the Earth's atmosphere) that the electromagnetic wave propagates through. This quantity, known as the atmospheric phase screen (APS), is often the main source of noise and can compromise the quality of any distance estimate. The last term, n, is a phase contribution related to system noise (thermal noise, quantization, etc.).

Figure 2.1 A schematic showing the relationship between ground displacement and signal phase shift. The numeric value of the wavelength, λ, is that used by the ERS satellites operated by the European Space Agency (ESA).

The phase values contained in a single SAR image are of little practical use, as it is impossible to separate the different contributions in equation (2.1), at least without prior information. The basic idea of SAR interferometry is to measure the phase change, or interference, over time, between two radar images, generating an interferogram I:

(2.2)

If we consider an idealized situation where the noise is negligible, the surface character (reflectivity) and atmospheric conditions are constant between the two SAR acquisitions, then equation 2.2 reduces to

(2.3)

Therefore, if a point on the ground moves during the time interval between the acquisition of the two radar images with similar geometry, the distance between the sensor and the target changes, creating a phase shift proportional to the displacement (Fig. 2.1). Equation (2.3) explains why interferometric SAR techniques can measure range variations with high sensitivity: the unit of length of the measurement is the wavelength (a few centimeters long) rather than the range resolution of the radar sensor (typically a few meters). A displacement of the radar target by a distance of λ/2 will create a phase shift of 2π radians. Therefore, a range variation of just 1 mm creates a phase shift of more than 20 degrees between two SAR images acquired in the X‐band (λ = 3 cm), which can be easily detected.

A direct approach, involving the computation of phase variations on a pixel‐by‐pixel basis between two radar images, can be used successfully only if the reflective character of the radar target does not change over time, the signal‐to‐noise‐ratio (SNR) is high enough, and the atmospheric phase components are negligible. When this is not the case, the analysis of a single interferogram is not sufficient to produce useful estimates and a multi‐interferogram approach is required. In fact, the analysis of long temporal series of SAR images, as described in the next subsection, is perhaps the best way to disentangle the different phase contributions and retrieve high‐quality displacement data.