Polar Plot
The figure below shows a polar plot representation of the directional reflectance factors of a hardwood forest canopy. In this example, the BRDF is assumed to be symmetric about the solar principal plane, so only half of the hemisphere is shown. The position of the Sun is shown by the symbol at approximately 65 degrees zenith, 180 degrees azimuth. Separate polar plots are shown for the visible wavelengths (left-hand plot) and near infra-red wavelengths (right-hand plot).
Directional Reflectance of a hardwood forest canopy measured from a helicopter using a multiband radiometer. Left hand plot depicts visible wavelengths, right hand plot depicts near infra-red. (from Kimes et. al.,1986, IEEE Transactions on Geoscience and Remote Sensing, GE-24, 281-293).
Isolines have been drawn joining points of equal HCRF, and in this way the shape of the reflectance factor surface becomes visible. For this forest canopy, the surface in the visible wavelengths defines a shallow bowl centred on nadir. In the near infra-red, the bowl-shape is more pronounced and is offset so that the minimum is slightly displaced from nadir view. This means that the lowest HCRF would be measured by a sensor viewing at a zenith angle of around 20 degrees from the zero azimuth direction. This configuration is shown in the AnisView plot below. The polar plot of infra-red wavelengths also shows a slight 'hot-spot', that is, the region of enhanced reflectance where the sensor is viewing directly 'down-Sun', where no shadows are visible.
Representation of the view/illumination geometry corresponding to the near infra-red reflectance factor minimum measured by Kimes et al. (1986) from a hardwood forest canopy. The Sun is at a zenith angle of 65 degrees (yellow) and the sensor at an zenith angle of 20 degrees, viewing the surface from the other side of nadir (blue). (Produced using the AnisView program created by Vogt and Verstraete, 2002).
