Theory of GNSS Reflectometry - GNSS Remote Sensing: Theory, Methods and Applications - page 180

Fig. 8.6 Number of simultaneously reflected GNSS satellites as a function of the latitude-
coordinate of their specular point on the Earth surface, and accumulated in 1 day of observations.
The scenario is the same as in Fig. 8.4 - top , using a 10-s time sampling. Black is for all visible
GNSS transmitters (elevation cut-off = 0 ı ); red / green / blue for elevation cut-off of 30 ı /45 ı /60 ı
respectively

where the two (incident and reflected) 1-dimension rays intersect the surface. The
image generated in such reflection events is called specular image, and it appears
with the same size than the source and at the same distance below the surface as the
source is in the front (specular point being the reference).
A wave-optics picture of the specular reflection is also possible. Then, following
Huygens-Fresnel principles, every point on the wave front, and in particular on the
sea-surface, acts as a point-source of a secondary spherical wave. The scattered or
reflected signal at any subsequent point between the surface and the observer is the
sum of all these secondary spherical waves. If the incident signal is a planar wave
of given incidence angle and azimuth, the reflected signal results in another planar
wave, equal incidence and opposite azimuth; and most of the energy contribution
comes from the point-sources of spherical waves located at a limited area on the
surface (panel b in Fig. 8.7 ). This limited area surrounds the specular point. We
could call it 2-dimensional specular zone, or Fresnel zone.
A particularity of the specular reflections is that the resulting scattered field has
a well defined phase:

k r g

exp f ! 0 t (8.1)

where ! 0 is the angular speed of the carrier, k is the carrier's electromagnetic
wavenumber, and r position vector along the ray trajectory.