Fourier-Correlation Imaging
Résumé
We investigated whether correlations between the Fourier components at slightly shifted frequencies of the fluctuations of the electric field measured with a one-dimensional antenna array on board a satellite flying over a plane allow one to measure the two-dimensional brightness temperature as a function of position in the plane. We found that the achievable spatial resolution that resulted from just two antennas is on the order of h$_χ$, with χ = ${c}$/( Δ${r}$ω$_0$), both in the direction of the flight of the satellite and in the direction perpendicular to it, where Δ${r}$ is the distance between the antennas, ω$_0$ is the central frequency, h is the height of the satellite over the plane, and ${c}$is the speed of light. Two antennas separated by a distance of about 100 m on a satellite flying with a speed of a few km/s at a height of the order of 1000 km and a central frequency of order GHz allow, therefore, the imaging of the brightness temperature on the surface of Earth with a resolution of the order of 1 km. For a single point source, the relative radiometric resolution is on the order of √χ, but, for a uniform temperature field in a half plane left or right of the satellite track, it is only on the order of 1/χ$^{3/2}$, which indicates that two antennas do not suffice for a precise reconstruction of the temperature field. Several ideas are discussed regarding how the radiometric resolution could be enhanced. In particular, having ${N}$ antennas all separated by at least a distance on the order of the wave-length allows one to increase the signal-to-noise ratio by a factor of order ${N}$ but requires averaging over ${N}^2$ temperature profiles obtained from as many pairs of antennas.
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