Charles Toth 
  
From a strictly theoretical point of view, the problem of how well a discrete representation describes the continuous 
case is well understood from Shannon's information theory. Probably the most relevant and well-known expression is 
related to sampling frequency. Rephrasing it for our case in one-dimension, it is stated simply that if a surface has a 
given maximum detail level (the surface changes are less than a predefined value), then there is an optimal sampling 
distance, and thus, any discrete representation which has this optimal sampling distance (or shorter) can reconstruct (1) 
from (2) without any degradation. 
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min 2 fs 
In other words, if fnax is the highest spectral frequency for a given surface, then d,,;, sampling distance is sufficient for 
the complete representation of this surface. In fact, the continuous surface can be restored without any error from the 
discrete representation in this ideal case. Obviously, for two-dimensional representations the directional spatial 
frequencies can be considered. 
d”min € sn. and d’ min € i (4) 
2 f "max 2 fm 
One major problem with real surfaces is that vertical surfaces, in theory, would require an infinitely short sampling 
distance (the spatial frequency is unbounded). Another important aspect of the sampling process is the quantitaziation 
of the elevation data (basically the smallest elevation difference that can be distinguished). This is normally an 
overlooked aspect since on modern digital systems the number representation provides such a wide range that the error 
introduced by converting the continuous signal into a discrete one is really negligible. 
3 MAIN CHARACTERISTICS OF STATE-OF-THE-ART SYSTEMS 
3.1 LIDAR System 
EarthData Technologies’ AeroScan LIDAR, Fig. | is a custom-made high-performance system and represents the most 
recent technology available in airborne laser scanning. The data acquisition parameters can be adjusted in a wide range, 
providing considerable flexibility to accommodate the needs of various applications. Most remarkably, the flying height 
can be as high as 20,000 ft. The maximum scan FOV is 75 degrees. The maximum scan rate is about 7.5 Hz at 75 
degree FOV or can go up to 20 Hz for smaller FOV's. The maximum pulse rate is 15 kHz. The laser sensor operates at 
the wavelength of 1064 nm, with pulse length of 11.7 ns and beam divergence of 0.33 mrad. The sensor system can 
record up to five returns. Operating with 40 degrees FOV at 65 m/s airspeed and at 2500 m AGL flying altitude, the 
along track spacing is about 3 m, while the cross track spacing is roughly 4 m. The illuminated footprint is 0.8 m and 
the typical accuracies on the ground are 0.25 m in cross track, 0.25 m in along track (somewhat smaller than the cross 
track value) and 0.15 m in height error. 
  
Figure 1. EarthData Technologies AeroScan LIDAR system. 
  
900 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.