  The aim is to describe new geometric approaches to define the statistics of
spatio-temporal and polarimetric measurements of the states of an
electromagnetic wave, using the works of Maurice Fr{\'e}chet, Jean-Louis Koszul
and Jean-Marie Souriau, with in particular the notion of 'average' state of
this digital measurement as a Fr{\'e}chet barycentre in a metric space and a
model derived from statistical mechanics to define and calculate a maximum
density of entropy (extension of the notion of Gaussian) to describe the
fluctuations of the electromagnetic wave. The article will illustrate these new
tools with examples of radar application for Doppler, spatio-temporal and
polarimetric measurement of the electromagnetic wave by introducing a distance
on the covariance matrices of the electromagnetic digital signal, based on
Fisher's metric from Information Geometry.
