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International Archives of the Photogrammetry, Remote Sensin g 
ranging problem (Poor, 1994). For high SNR, the uncertainty in 
range estimation is given by 
Ó = (4) 
l 
TRIS SNR RI 
via 
where BW = root-mean-square signal bandwidth. 
To lower the range uncertainty, one has to increase the SNR 
and/or the effective signal bandwidth. This increase in 
bandwidth agrees with intuition since a large bandwidth 
corresponds to a signal pulse with sharp edges and hence betters 
discrimination against background noise. This result for the 
radar ranging problem can also be applied to peak detector 
algorithms used in Section 2.1.1. A better estimate of the range 
uncertainty, ó.,, can be obtained by including walk error caused 
by variations in pulse amplitude and shape (Amann et al., 
2001). Finally, TOF systems have an ambiguity interval that is 
related to the time spacing between consecutive pulses, which 
can be several kilometres. 
Other systems based on continuous wave (CW) modulation get 
around the measurement of short pulses by modulating the 
power or the wavelength of the laser beam. For AM, the 
modulated signal is projected onto a surface, the scattered light 
is collected on a single photodiode and a circuit measures the 
phase difference between the two waveforms which in fact is a 
time delay. The range uncertainty is approximately given by 
Ó = al ai. (5) 
r- AM dz JSNR. 
An = wavelength of the amplitude modulation (c/,) 
44/7 uncertainty in range estimation AM system. 
where 
Again, intuition tells us that a low frequency, fn (long 
wavelength) makes the phase detection less reliable (see Eqn. 
4). Because the returned wave cannot be associated with a 
specific part of the original signal, it is not possible to derive 
the absolute distance information from a simple AM method. 
This is known as the ambiguity interval and can be in the order 
of several meters. The range ambiguity is given by 4,/2. To get 
around the inconvenience of a range ambiguity interval, one can 
use multiple frequency waveforms. For instance, assuming a 
two-tone AM system (low frequency of 10 MHz and high 
frequency of 150 MHz) and a SNR=1 000, the range uncertainty 
is about 0.5 cm (using the high frequency) and the ambiguity, 
IS m (using the low frequency). Different papers compare the 
last two systems (TOF and AM) (Koskinen et al, 1991; 
Baltsavias, E.P. 1999b.; Wehr et al., 1999). 
The last CW system covered in this section is based on 
frequency modulated (FM) laser radar with coherent detection. 
Here, the frequency of the laser beam is linearly modulated 
either directly at the laser diode or with an acousto-optic 
modulator. The linear modulation is usually shaped by a 
triangular or saw-tooth wave, which gives rise to what is known 
a a chirp. The important aspects of this technology are 
determined by the coherent detection taking place on the optical 
detector and the fact that the beat frequency resulting from this 
optical mixing encodes the round trip time delay using a much 
smaller bandwidth compared to TOF systems (Amann et al., 
2001; Schneider et al., 2001). It can also determine absolute 
distances, These systems can achieve for a tuning range of 250 
and 
975 
Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
GHz, a measurement uncertainty of about 10 um (Schneider et 
al., 2001). For instance, some commercial systems can provide, 
over a range of 2 m to 10 m, a measurement uncertainty of 
about 40 um at a data rate of 10 points/sec and 150 um at about 
1000 points/sec. Furthermore, the dynamic range is about 10°. 
Interesting enough, for ranges between 2 m and 10 m, there is a 
limited number of laser scanners available commercially. In 
fact, this range of distances represents a transition between 
triangulation and time delay-based systems. Triangulation- 
based systems require a large baseline to operate in that range. 
On the other hand, time-delay systems can achieve relatively 
low measurement uncertainty in that distance range but have to 
face other concerns like higher costs and in some cases limited 
operating depth of field (Blais, 2004). Furthermore, because of 
the increased distance attainable with time delay-based systems, 
the scanning mechanism can produce non-negligible errors. For 
example, a galvanometer-based scanner with an angular 
uncertainty of 50 uRad produces at a distance of 200 m a lateral 
spatial uncertainty of about | cm (in a direction perpendicular 
to the laser beam, see Figure 2). This fact cannot be neglected at 
long distances especially when the scanner manufacturer uses a 
laser with low divergence. 
2.2 Close-range digital photogrammetry 
In this section, we won't go in the details of photogrammetry. It 
is a topic that is well covered by the ISPRS society's 
conferences. The variety of techniques available and level of 
expertise is such that 3D reconstructions and feature 
measurements are done on heterogeneous sources of images. 
For instance, Gruen et al. 2003 report the results of their 
photogrammetric work on the Great Buddha of Bamiyan. The 
authors performed a computer reconstruction of the statue, 
which served as basis for a physical miniature replica. The 
three-dimensional model was reconstructed from low-resolution 
images found on the Internet, a set of high-resolution metric 
photographs taken in 1970, and, a data set consisting of some 
tourist quality images acquired between 1965 and 1969. 
We now look at some issues and best practices that are 
important when integrating this technology with 3D laser 
scanners. The latest shift in photogrammetry has been the 
passage to fully digital technologies. In particular, low cost 
digital cameras with high pixel counts (> 6 mega-pixels image 
sensors), powerful personal computers and photogrammetric 
software are driving. a lot of new applications for this 
technology. The fundamental principle used by 
photogrammetry is in fact triangulation, which is illustrated on 
Figure ] for laser scanners. By replacing the projector by 
another camera, one gets a two-camera arrangement (also called 
stereoscopy). In its simplest form, a feature is observed from 
two distinct views and the two corresponding lines of sight are 
intersected in space to find a three-dimensional coordinate 
(forward intersection). In actual situations where the measuring 
chain is not perfect (poor image contrast, noise, etc.), a multi- 
station convergent geometry must be used in a bundle 
adjustment in order to minimize the three-dimensional 
coordinates uncertainties. 
The range equations are expressed in terms of camera baseline, 
distance (camera-object) and the so-called stereo disparity. 
Usually the baseline to depth ratio (D/Z) is used to characterise 
a given set-up. Errors in detecting the centroid of a particular 
target on the image sensor of the stereoscopic system produce 
errors in determining the location of the target in object space.