Visualisation of directional reflectance factors
The previous sections have shown how it is possible to measure the variation in reflectance factor with view angle, which is important because it can be used to estimate the BRDF of the surface. However, for many purposes it is sufficient to be able to visualise the way in which the HCRF varies with view angle. This can provide an insight into the inherent reflectance properties of the surface, and in particular whether the BRDF along the solar principal plane is 'bowl-shaped' or 'bell-shaped'. Knowing this allows us to categorise the surface and make inferences about how it may best be sensed from aircraft and satellite platforms.
The co-ordinate system that is conventionally used for this purpose is shown below. It comprises a polar plot in which azimuth view angles are measured relative to a reference direction, which may be fixed (e.g. magnetic north) or may vary over time (e.g. the solar azimuth at the time the measurements are made). Aligning the reference direction on the Sun is recommended as this then defines the solar principal plane as the 0-180 degree axis. Azimuth angles are most commonly measured clockwise from the 0 degree index, although some researchers chose anti-clockwise. It would seem logical to align the 0 degree index with the Sun, but many researchers prefer to align the 180 degree index with the Sun, as this means that the plot can have zero degrees at the top and have the Sun at a southerly azmiuth, which is more intuitive to those from the northern hemisphere.
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The zenith angles of both the Sun and the sensor are measured radially from the centre of the plot. Visualisations of BRDF at one point in time can therefore include a symbol on the plot to show the position of the Sun (azimuth and zenith) at the time the measurements were made. It will be evident from this brief discussion that visualisations of BRDF must always be accompanied by a clear explanation of the coordinate system used. |
| Polar plot The most commonly used representation of the directional reflectance of a surface. |
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| 3D Polar plot It is possible to make the polar plot more informative by representing it as a 3D surface in which the z-axis represents the HCRF. |
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| Solar Principal Plane plot The BRDF of a non-patterned surface generally shows most variability in the solar principal plane and so one way to capture this is to plot the directional reflectance in this plane as a function of view angle. |
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| Anisotropy plot This type of plot exploits further the redundancy found in polar plots and the solar principal plane plot. It is based on the observation that most of the interesting information is captured by measurements in the principal plane, and represents the most significant features of the BRDF by measurements made at just three geometric configurations: nadir view, the hot-spot and the specular point. |
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