623 
NDVI 
polarised reflectance increases in the forward 
direction up to 0.019 for a zenith viewing angle 
of 51°. Larger polarised reflectances are 
observed at the corners of the matrix (in the 
forward hemisphere) which correspond to 
larger viewing angles. We note that the 
polarised reflectance is symmetric with respect 
to the principal plane, as expected. 
Similar figures are obtained for wavelength 
865 nm. From measurements such as those 
shown in Fig. 3, one can extract the polarised 
reflectance angular signature. These are 
discussed below. 
In the single scattering approximation, the 
polarised reflectance generated in the 
atmosphere writes: 
D = T M°0 ( 4 ) 
P 4 cos^ ) cos(0 v ) 
where x is the atmospheric optical thickness, a 
is the scattering angle, and Pp is the polarised 
phase function. We note that the polarisation 
model for the bare soil has a similar form. 
Thus, p P cos(0 s ) cos(0 v ) depends mostly 
on the scattering angle. Moreover, we have 
seen in the previous section that the surface 
polarised reflectance is larger for a bare soil 
than for a vegetated area. We verify this 
theory on the airborne measurements at 865 
nm. A normalised polarised reflectance is 
defined as the product of p P and 
cos 0 S cos 0 V . This is done for each pixel of 
the CCD matrix. For each bin of phase angle 
and NDVI (calculated from the measurements 
at 670 and 865 nm), we then averaged the 
normalised polarised reflectance. In Fig. 4, we 
plot the results expressed as isolines. 
Fig. 4 confirms that the phase angle (or 
scattering angle, or incidence angle) is the 
main driver of the polarised reflectance. It is 
close to 0 for backscattering (0° phase angle) 
and increases up to about 0.5 for the largest 
phase angle (around 80°). For phase angles 
lower than 30° (incidence angle lower than 
15°), both surface models indicate a small 
polarisation (eq. 2 and 3) and no signal from 
the surface is evidenced in Fig. 4. As the phase 
angle increases, so does the difference between 
the polarisation of vegetation and bare soil. 
For large phase angles, the measurement 
decreases as the NDVI increases. Thus, we 
verify on airborne measurements that bare 
soils (low NDVI) generate more polarised 
radiance than vegetation (large NDVI) do. The 
difference in normalised polarised reflectance 
is on the order of 0.15 between low NDVI and 
high NDVI targets in the field of. view. 
0 0.25 0.5 
Fi gure 4 : Normalised polarised reflectance (see 
text for explanation) at 865 nm as a function 
of NDVI and phase angle. The reflectance 
is in %. 
Fig. 5 shows the polarised reflectance, in the 
principal plane, for 450 and 865 nm (symbols) 
measured by airborne POLDER. We selected 
this plane since it shows the largest dynamic. 
Fig. 5 measurements have been acquired 
during a clear day (aerosol optical thickness of 
0.26 at 550 nm). Similarly, Fig. 6 shows the 
measurements acquired during a hazy day 
(T55o=0.76). Note that, although the two 
figures are not registered (they were not 
acquired over exactly the same surface), they 
are representative of the measurements, 
because those show little variability within a 
given flight. 
As expected, the polarised reflectance is 
larger at 450 nm than at 865. This results from 
the large increase in polarised reflectance 
generated by Rayleigh scattering for shorter 
wavelengths. At 450 nm, the measurements 
are comparable to what is expected for a clear 
atmosphere. On the other hand, at 865 nm, the 
measurements (open diamonds) are much 
larger than for molecular scattering (lower 
thick line). Thus, at this wavelength, we must 
consider the polarised reflectance generated by 
the surface, and that resulting from aerosol 
scattering. 
Polarised reflectance generated by the 
surface lies between the two dashed lines 
(models of eq. 2 and 3) depending on the