622 
two models defined in eq. 2 and eq. 3 
according to the underlying surface. 
First, we remind that both models account 
for single specular reflection only. Thus, their 
estimates are always positive and they vanish 
in the antispecular direction. The models fail 
to reproduce the negative polarisation often 
observed close to backscattering. The negative 
branch of polarisation does not exceed -0.005 
over bare soil and -0.002 over the vegetation. 
Measurements plotted in Fig. la have been 
acquired over bare soil with a large solar 
zenith angle of 65°. The polarised reflectance is 
negative close to Ore antispecular direction and 
increases up to 0.14 for a viewing angle of 70° 
to the sun (the angle of reflection is then 68°). 
The model accurately reproduces the 
measurements away from the backscattering 
direction assuming a refractive index of 1.50. 
It slightly underestimates the observations for 
viewing angles between 30° and 50° and 
overestimates the measurements for viewing 
angles greater than 50°. 
Fig.lb is for a low and dense vegetation site. 
The measurements are here compared with the 
model designed for the vegetation, the 
refractive index of epicutilar wax, m=1.50, was 
assumed (Vanderbilt and Grant, 1985). This 
model predicts polarised reflectances much 
smaller, around 0.02, than for the bare soil and 
it is confirmed by the measurements. The 
angular signature is clearly reproduced, 
although the measurements are noisier. 
Fig. 2 shows the same as Fig. 1, but for the 
perpendicular plane. The variations in 
polarised reflectance are smaller than in the 
principal plane because the measurements 
scan a more limited range of incidence angle. 
4.b Polarised reflectance at aircraft level 
We now present airborne POLDER 
measurements and a comparison with simple 
models. Fig. 3 shows the polarised reflectance 
measured over the CCD matrix at 450 nm. The 
polarisation is determined for each pixel and is 
here expressed as isolines (thick lines). In the 
principal plane, the neutral point (no 
polarisation) is found for a viewing angle of 
40°, in the backscattering hemisphere. The 
Figure 3 : Polarised reflectance measured by the airborne POLDER instrument. The 
doted lines indicate the viewing angles: the centre of the figure corresponds to 
nadir viewing. The circles are for zenith viewing angles of 10°, 20°, 30°, 40° and 
50°. The concentric lines give the azimuth 0°-180°, 30°-240°, 60°-270°... The solar 
zenith angle is 54° and backscattering is on the right side of the figure, slightly off 
tire location of minimal polarisation. The polarised reflectance is here expressed 
in % and the wavelength is 450 nm.