Radar imaging

In depth

The radar looks to one side of the flight path and measures the delay $t$ between sending a pulse and receiving its echo. The slant range to the target follows from the speed of light.

where $R$ is the slant range, the distance along the line of sight from the antenna to the target, in $\mathrm{m}$; $c$ is the speed of light, $2.998\times 10^{8}\ \mathrm{m\,s^{-1}}$; and $t$ is the round-trip delay of the echo, in $\mathrm{s}$, halved because the pulse travels out and back.

Figure 1 shows the geometry, with the incidence angle $\theta$ at the ground. Two targets can be told apart in range if their echoes do not overlap in time. A pulse with bandwidth $B$ resolves a slant range of $c/2B$, and projecting that onto the ground gives the ground-range resolution [1].

where $\delta_r$ is the ground-range resolution, in $\mathrm{m}$; $c$ is the speed of light; $B$ is the bandwidth of the transmitted pulse, in $\mathrm{Hz}$; and $\theta$ is the incidence angle, between the radar beam and the vertical at the ground.

Along the flight direction a real antenna of length $L_a$ has a beam of angular width $\lambda/L_a$, which at the range of a satellite would cover many kilometres. Synthetic aperture processing combines the echoes recorded as the satellite moves, so that the data behave as if they came from an antenna as long as the distance flown while the target stays in the beam. The resulting azimuth resolution depends on neither range nor wavelength, and a shorter antenna gives a finer result [1].

where $\delta_{az}$ is the azimuth resolution, along the flight direction, in $\mathrm{m}$; and $L_a$ is the length of the real antenna in that direction, in $\mathrm{m}$.

The brightness of a pixel is the backscatter coefficient $\sigma^0$, usually quoted in decibels. It depends on the roughness of the surface compared with the wavelength, on its dielectric constant (which rises sharply with moisture), and on the geometry. The wavelength matters because radar sees structure at about its own scale. The Sentinel-1 satellites use C band at 5.405 GHz, a wavelength of 5.55 cm [2]. Shorter X band waves, near 3 cm, are scattered mainly by the top of a canopy, while longer L band waves, about 24 cm, reach further down to the branches and ground. Transmitting and receiving in horizontal (H) and vertical (V) polarisation gives channels such as HH, VV and VH that respond differently to surface structure [3, 4].

Two characteristics of radar images surprise newcomers. Because the signal is coherent, neighbouring pixels of a uniform surface fluctuate randomly, an effect known as speckle that is modelled as multiplicative noise [5]. It is reduced by averaging several looks at the cost of resolution. And the side-looking geometry distorts steep terrain, as panel (b) of Figure 1 shows. Slopes facing the sensor are compressed (foreshortening) and can fold over the ground in front (layover), and slopes facing away can be left without any signal (shadow) [1].

Optical and radar together

Optical and radar data record different things. Optical bands give spectral information about pigments, minerals and water, and are blocked by cloud. Radar gives structure and moisture and keeps working under cloud. Combining them, at the level of pixels, extracted features or final decisions, often improves land cover mapping over either alone, and the literature reviews the methods and their pitfalls [6, 7].