Gr
(b)
Figure 9: Shown in (a) is a systematic angular error, for
example the mounting bias, causing a reconstruction er-
ror a whose magnitude depends on the range. As a con-
sequence, points that were measured along a straight
flight path are unequally displaced, causing an angular
distortion in the reconstruction as shown in (b).
er —-—- A
Figure 10: An effective angular error ó' causes an ele-
vation error that decreases as the profiling laser system
moves in uphill direction. This causes a slope error Ay
of the reconstructed surface.
; tan y cos à"
m d 1
any 1 +tanysinö da
tan y — tan y'
cos ó'
tan y| 1 —- ——— ————
»( ] 4 tan y sin ó'
tan? y - ó'
1 + tany - ô'
Ay
Il
(13)
(14)
Eq. 14 is obtained by approximating cosé’ = 1 and
sind’ = ó'. Considering fairly small angular errors, the
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
approximation does not introduce noticeable errors.
Figure 11: A systematic angular error of ó' introduces a
slope error. The reconstructed surface is tilted by Ay,
compared to the true, horizontal surface.
Scanning System and Horizontal Surfaces Let us fi-
nally examine the impact of angular errors of a laser
scanning system. The first example, shown in Fig. 11,
is related to a horizontal surface, flown with a scanning
system that has an angular error ó. This error is mea-
sured in the plane defined by the range vector and the
displacement vector, called error plane here. Fig. 12 de-
picts the effective angular error ó'. It is obtained by pro-
jecting the error plane into the scan plane. Thus, we
obtain
5’ = §cos(e — 1) (15)
ofen
= bu
«x
£1010
.-—
Figure 12: A systematic angular error can be character-
ized by the angle ö, the angular offset, and the azimuth
€ of the trace of the error plane. The scan direction is
defined by azimuth r. The effective angular error is the
projection of the error plane into the scan plane.
Fig. 11 illustrates the effective angular error ó' causes a
displacement vector a'. Its magnitude depends on the
range. The shorter the range, the smaller the error. The
direction is approximately perpendicular to the range
vector. We find for the slope error the following simple
relationship
Ay. = sind’ (16)
Scanning Sy
ample of a
laser scannin
Fig. 13(a) der
of one scann
example, the
set.
Figure 13: A
surface. Fiv
are shown. ^
tive angular
reconstructe
to the range
surface, the
a consequen
slope (a). If
angular relat
pressed by d
The error a’
angular erroi
This error ok
would mean
plane. On th
offset is per
The magnitu
range. Footp
a smaller err:
scan sweep,
