To correctly calibrate the VIL data, the system limited data points had to be removed from the data set. At far ranges the backscattered radiation can not be separated from the system noise because the VIL signal decreases due to the range squared dependence and attenuation. When the VIL raw data is corrected for the range squared dependence, the places where the VIL signal increases monotonically as a function of the range is where the signal could not be separated from the noise as seen in Figure 15. This limit of detectability occurs where the VIL signal starts to increase with range around bin 250. The large increase in the signal around the range bin 500 was the result of radiation backscattered from a cirrus cloud.
To remove the noise dominated points, the points where the raw signal was within the noise regime had to be determined. At far ranges, the raw backscattered signal becomes linear with range when the backscattered power is plotted on a natural log scale. This was a result of both the attenuation of the transmitted pulse in the atmosphere and the range squared decrease of the signal. Shot noise occurs along with the raw signal. If the shot noise was random, as expected, then the noise should occur as a Gaussian distribution about the raw data. This would not affect the slope of the VIL data with range in Figure 15. So, if the VIL raw data was sorted according to their magnitudes and replotted on a log-linear plot, then the signal which was small and could not be separated from the noise would appear as a straight line at the lower signal magnitudes (Figure 16).
This process was applied to each VIL raw profile where the VIL backscatter signal was sorted according to their magnitudes. The sorted values were approximated using a straight line median fit. The straight line median fit was first applied to the whole sorted profile. The points occurring above the fit had large signal backscatter and were remove from the sorted set. The remaining sorted points were then refitted using a straight line median fit. After a number of successive fits, where a chosen threshold was met, the remaining points consisted only of the small signal values which could not be separated from the noise (they appear as a straight line in Figure 16). These noise points were discarded from the original data set. For the shot used in Figure 15 and Figure 16, over one half of the data points had to be discarded. The remaining data points are the signal backscattered by aerosols and molecules in the atmosphere.
Figure 15: Removal of the noise points from the VIL raw data. The x-axis is
the range bin number and the y-axis is 128 
ln (P / E) for the raw
data and 128 
ln (P * R * R / E) for the range squared corrected
raw data. The solid line is the range squared corrected VIL profile. The
long dashed line is the VIL raw data profile.
Figure 16: Removal of the noise points from the VIL raw data. The x-axis
is the sorted bin number. The y-axis is 128 
ln (P / E). The
solid line is sorted VIL raw data (sorted according to magnitudes).
The dashed line is the straight line median best fit
to the sorted noise points.