International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
scattering cross section do with a standard deviation of 0.05 m,
shown in Figure 2 at a distance of 9 m. The emitted pulse is in
our example a long-tailed *10ns" Q-switched pulse, which bears
only a faint resemblance to an idealised rectangular pulse. The
backscattered waveform, which is obtained as convolution of
the emitted signal with the assumed terrain cross section, is —
due to the narrow shape of the cross section in this example —
basically a time-delayed and slightly widened version of the
emitted pulse.
distance (m)
+ zero crossing
+ maximum
x centar of gradty
O threshold
t5F X const. frac. HH
cross section — |
j| | \
X !
| ii L
\ «- emitted pulse
ost |
= '
|
|
|
Ai! eu. fe ™
« reflected pulse
\
signal amplitude
A i
or
estimated travel time
0 20 40 © 80 700 120
time (ns)
Figure 2. Emitted pulse and single-mode return signal for a
Gaussian cross section. Also shown are the time differences
between corresponding trigger-pulses derived from the emitted
and reflected signal. The dashed horizontal line at y = 0.2
indicates the threshold level used by the threshold and centre of
gravity methods.
In order to determine the precise distance of an object, the
detected pulse in the reflected signal must be related to the
emitted pulse; here, we assume this is done by applying the
same pulse detector to both signals, although other approaches
are possible. The measured time differences (and thus distances)
between corresponding trigger-pulses indicated in Figure 2 —
the estimated travel time - should be 60 ns (9 m) for all five
detectors; however; even in this quite benign case, only the
three “difference”-based detectors give correct results (see
Table 1); for example, the estimated travel time for the
threshold method is 59.7 ns, resulting in a range error of (60 —
59.7)x0.3/2 — 0.045 m.
4.0 Experiments
In this subsection, we will highlight the properties of the
different pulse detectors by applying them to several simulated
waveforms; quantitative results for all experiments are given in
Table 1. The first experiment, shown in Figure 3, assumes
wheat crops on rough ground. The differential scattering cross
section of wheat is assumed to consist of two peaks, the first
relating to the wheat and the second to the underlying ground.
Since the scattering centres of wheat and the ground are
relatively close (only 0.6 m apart), their vertical profiles are
merged into a unimodal waveform by the convolution (Figure 3,
bottom). As can be seen from Table 1, the best results are
obtained by the zero crossing method; it is also the only
detector that generates two trigger-pulses and correctly resolves
(discriminates) the waveform into ground and vegetation
components. However, as noted before, zero crossing is
sensitive to noise.
0 1 1 L L
17.5 9 10.5 12 13.5
distance (m)
I
zero crossing
maximum
15F x center of gravity H
threshold
+
const. frac.
430
signal amplitude
i 1 i 1
50 60 70 80 90 100 110 120
time (ns)
Figure 3. Return pulse of a wheat field. Top: Assumed effective
scattering cross section of a wheat field (crops on rough
ground). Bottom: Reflected signal and derived trigger-pulses.
zc
0. 0.
0.01 0.1
0. ; - 0.2
0.01 -0.161| -0.101
-1.2 - -
0. -0.049| 0.
0.11 - -0.371| O.
0. : -0.21 - 0.1
5 .0 0.075| -0.1 0.2 -0.1 0.01
Table 1. True object distances and range errors (in m) for the
different detectors. The positional errors are obtained by
multiplying the difference between true and estimated travel
time by 0.3/2, e.g., 1 ns corresponds to 0.15 m. Detection
methods: zc = zero crossing, max = maximum, thr = threshold,
cog 7 centre of gravity, cf — constant fraction.
In the second experiment, shown in Figure 4, we assume a
somewhat more complex scenario: the laser beam passes
through a treetop with two prominent branches, then through
low vegetation (bushes) and finally reaches the ground. Again,
zero crossing detects all five objects (see Table 1); however, the
error for the treetop volume is rather high due its wide spread
and the interference of the branches.
Note that the trigger-pulses derived by center of gravity tend to
lie between those derived by zero crossing and maximum
(nearer to zero crossing for slow edges and nearer to maximum
for fast, steep edges). It is also interesting to note that in this
example both constant fraction and zero crossing are able to
distinguish between low vegetation and ground, although their
respective cross sections are still rather close (1 m).
Internati
0.4 [-
signal amplitude
e
S
or
Figure 4
scattering
vegetatio
trigger-pi
In the th
performa
laser bea
pulse dia
scattering
of the tilt
cross sec
measured
the best
demonstr
excels at
Cross sec
like max
prematurt
simple c
detectors
gravity),
I m.
signal amplitude
Figure 5.
scattering
and deriv
