The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008
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pack properties from the intensity values. Similarly, over wet
sand in comparison to dry sand, backscatter strength is smaller.
For the relative orientation of TLS data acquired from different
stand points Wendt and Heipke (2006) have proposed using the
intensities. They suggested a 1/r 2 correction factor before using
the intensity images in matching procedures. While this factor
can be justified theoretically, our work shows that it may not be
optimal. In any case, quality figures estimated in the matching
process will measure more of the actual texture similarity and
less of the device influences, if calibration methods are applied
to the data in advance. Also the visual appearance of laser
scanning intensity images can possibly be improved by
applying calibration procedures.
The ranging precision depends on the amount of backscattered
energy, as higher energy levels lead to a higher signal-to-noise
ratio, because the background noise can be considered as
constant. The question arises, how much of the ranging
precision depends on distance and on object brightness.
Finally, studying the intensity values is a means of
investigating the laser scanners as such and improves the
understanding of the measurement process. In the airborne case,
but also for terrestrial laser ranging, pulsed systems use the
intensity values for correcting the raw travel-time observation.
This correction may become as big as a decimeter (personal
communication), and it is the original motivation for recording
the intensity. This, but also noise behavior, may become
relevant in geometric calibration procedures.
Not all of these hypotheses will be investigated within this
paper, but they show that there is a potential for using the
intensity values. Especially the possibility to infer reflectivity
of targets which are i) planar and have ii) known reflectivity
behavior will be investigated. This builds the base for the other
items of the above list.
3. THEORY
3.1 Model driven approach
The basic equation for describing the strength of the backscatter
from an object surface is the Lidar (light detection and ranging)
equation (Jelalian, 1992). It relates the emitted optical power P E
to the received optical power P R .
Pr = Pe Dr / (4n p E 2 r 4 ) CT TlAtmTlSys (1)
The term a is the backscattering cross section and is a product
of the directional reflection strength (p D ) and the area of the
object. p E is the beam divergence, r the range, Dr the receiving
aperture diameter, and the q-terms describe atmospheric and
system transmission. If the reflecting surface is larger than the
laser footprint, then the object is called an extended target. This
removes the beam divergence from the equation and introduces
a 1/r 2 dependency of the emitted power as opposed to 1/r 4 .
Pr - Pe Dr / ( (4r) 2 ) p D qAtmHsys (2)
This equation can be simplified further under the assumption,
that the target is a perfect Lambertian reflector. In that case the
backscatter strength depends on the (Lambertian) target
reflectivity p and the angle of incidence a.
P R = n Pe p cos(a) / (4r 2 ) q Atm q Sy s (3)
Knowing the emitted and the received power, and having
measured the range and intensity value, allows determining the
product p-cos(a). For smooth surfaces the angle of incidence
may be estimated from a local surface model, which can be
obtained by surface fitting to the neighbouring points. In ALS
this has already proven successful (Hôfle and Pfeifer, 2007).
The above equations furthermore idealize the emitter-receiver
configuration and therefore are not valid in close proximity of
the sensor itself. The beam profile is more complex, too. It is
minimal at the beam waist and a linear increase of the footprint
is only given at larger distances (Young, 2000).
In addition, emitter and receiver are assumed to be coaxial as in
a strictly monostatic system. To avoid optical cross talk, emitter
and detector are often separated (Ingensand, 2006). Thus,
different fields of view (FoV) of detector and emitter have to be
considered. Their opening angle and their direction can be
different, and (see above) there is a small “base” between them.
Depending on the i) geometrical configuration and the ii) range,
the visibility of the beam footprint for the detector may run
through the following stages: not visible - partly visible - fully
visible - partly visible - not visible. This effect is overlaid to the
1/r 2 decrease of received energy. A simplified simulation is
shown in Figure 1. As it is demonstrated the received energy
starts increasing with increasing range, because more and more
of the footprint gets into sight. For larger ranges it starts
decreasing again, because most of the footprint is visible
already, and the decay of received power with 1/r 2 is stronger.
An in-depth discussion of this “form factor” can be found in
Riegl and Bernhard (1974) and Stelmaszczyk et al. (2005).
Figure 1. Simplified simulation of the effect of partly
overlapping footprints. Beam diameter at exit: 3mm,
beam divergence: 0.35mrad. The beam energy is
distributed according to a Gaussian bell curve, and no
energy is assumed to be outside of the circle where the
energy drops to 1/e 2 . Base between emitter and receiver
centre: 3cm, parallel axes, detector diameter: 3cm,
opening angle: lmrad. The dashed curve shows the
portion of the visible footprint in the detector FoV. The
solid light gray line shows the portion of footprint
energy visible in the detector FoV. The footprint starts
getting into sight at a range of 20m and is fully visible
from 50m onwards. The thin, dash-dotted black curve
shows the theoretical 1/r 2 decay of received power
according to Eq. (1), and the dark gray curve the
combined effect.
The effects of beam waist, detector aperture, and base, can be
considered, provided these parameters are known. Servicing of
the device may lead to new values, and long term stability may
not necessarily be given. Additionally, these parameters may
