Some issues regarding the calibration of the terrestrial laser scanner Leica Scanstation C10.
Antanaviciute, Urte ; Obuchovski, Romuald ; Parseliunas, Eimuntas Kazimieras 等
Introduction
Terrestrial 3D laser scanners (TLS)--a new class of survey
instruments--have become popular and are increasingly used in providing
as-built and modelling data in various applications, including land
surveying, archaeological studies, architecture, bridge structures, and
highway surveys. These scanners could measure thousands of data points
(distance, angle, and reflected return signal power) per second and
generate a very detailed "point cloud" data set. In addition,
these measurements are performed much faster than traditional geodetic
surveys in most cases; therefore, terrestrial laser scanning has become
an additional surveying technique in the geodesy over the last several
years. However, in contrast to traditional geodetic instruments (e.g.
total stations, levels, Global Navigation Satellite Systems), accuracies
and the systematic errors of most of the available laser scanners are
not well-known. An investigation and analysis are essential to use
terrestrial laser scanners for high precision applications (e.g.
engineering surveying). In order to minimise the systematic influence of
the instrumental errors, scanners have to be calibrated and observations
have to be corrected on the basis of the calibration parameters
(Ingensand 2006). The standardised calibration routines exist for the
traditional geodetic and photogrammetric instruments. In the context of
TLS, the reliable accuracy assessment is rather complicated due to the
fact that laser scanners are constructed in a way completely different
from the traditional survey equipment. (Pfeifer, Briese 2007). The
accuracy specifications given by laser scanner producers in their
publications and pamphlets are not comparable. Experience shows that the
given accuracy parameters should not be trusted in some instances;
besides, accuracy of these instruments --which are built in small
series--varies from instrument to instrument and depends on individual
calibration. Much work has been done on point-based TLS calibration by
exploiting their similarities with theodolites or a total station
(Parian, Grun 2005; Lichti, Franke 2005; Lichti, Licht 2006; Lichti
2007; Reshetyuk 2006). Self-calibration approaches have recently been
investigated by a number of researchers and can be categorised according
to the type of targeting. Two types are reported: signalised point
targets and planar features. The common thread between both approaches
is the collection of a highly redundant set of spherical observations
(range, horizontal direction and elevation angle) from different
locations in a strong geometric configuration. (Bae, Lichti 2007;
Dorninger et al. 2008; Schneider 2009). The application of mentioned
procedures requires a laboratory or a calibration room with known
geometrical parameters of targets or planar features. The mentioned
calibration procedures use the 3D coordinates of the measured points;
however, the laser scanners actually measure the ranges, vertical and
horizontal angles (Pfennigbauer, Ullrich 2010). Therefore, it is
important to evaluate each measured parameter separately (Chow et al.
2010).
Some work has been done in distance measurement accuracy evaluation
(Salo et al. 2008; Cheok et al. 2007) with the following indication that
the accuracy depends on many factors such as scanner model, range
measuring method, target properties and etc. Angle measurement accuracy
tests indicate that the angle measurement accuracy (especially vertical
one) depends on the design of a laser beam deflecting unit (Schneider,
Schwalbe 2008; Reshetyuk 2009, 2010).
It is important to point out that no standard measure of the
scanner performance and method for its evaluation exists (Lichti 2010).
The method proposed by the authors of this paper allows evaluating the
distance and angle measurement accuracies under real environmental
conditions. Additionally, the proposed method does not require a special
calibration laboratory; consequently, a standard geodetic baseline could
be used.
1. Calibration of the distance measuring device of the terrestrial
laser scanner at the cyclic error determination baseline
The calibration of the distance measuring device of the terrestrial
laser scanner Leica Scanstation C10 was performed using the cyclic error
determination baseline at the Calibration Laboratory of the Research
Institute of Geodesy of Vilnius Gediminas Technical University (Jokela
et al. 2002; Buga et al. 2008, 2011). The cyclic error determination
baseline consists of 16 points, distances between which are approx. 1
metre. During the calibration procedure, the terrestrial laser scanner
was force-centred at the first mount and distance measurements were
performed to the force-centred targets (6 inches in diameter) positioned
on the other mount (Fig. 1).
[FIGURE 1 OMITTED]
The point cloud of the each scanned target consists of approx.
39000 points. From these point clouds, the coordinates of the centres of
targets were determined using Cyclone software by Leica Ltd. As usual,
distances between the scanner and targets were calculated using the
formula:
S = [square root of ([([X.sub.t] - [X.sub.s]).sup.2] + [([Y.sub.t]
- [Y.sub.s]).sup.2])], (1)
where [X.sub.t] and [Y.sub.t]--coordinates of the target centre,
[X.sub.s] and [Y.sub.s]--coordinates of the scanner.
Calibration parameters of the distance measuring device of the
laser scanner were evaluated by comparing the calculated distances with
known standard distances. Further data handling and calculations were
performed using the standard methodology of the numerical data
processing of the calibration results (Putrimas 2010). The final results
are presented in Table 1.
Table 1 indicates that systematic errors are relatively small (less
than 1.3 mm) in short distance measurements. These errors are slightly
greater for short distance (up to 3 metres) measurements.
Systematic distance measurement errors are shown in Figure 2.
The constant R of the terrestrial laser scanner was calculated
using all systematic errors of the measured distances and is equal to
-0.4 mm. Figure 2 shows that systematic error changes from -1.3 mm to
+0.4 mm.
[FIGURE 2 OMITTED]
2. Calibration of the distance measuring device of the terrestrial
laser scanner at Kyviskes Calibration Baseline
Calibration of the distance measuring device of the terrestrial
laser scanner Leica Scanstation C10 was also performed at Kyviskes
Calibration Baseline. This base consists of 6 pillars erected in a
straight line with the distance between the first and the last pillar
amounting to 1320 m. Distances between the inner pillars are as follow:
1-2 - 100 m, 2-3 - 260 m, 3-4 - 760 m, 4-5 - 180 m, 5-6 - 20 m (Joke la
et al. 2002; Buga et al. 2008, 2011). During the calibration procedure,
measurements of five different sectors of the calibration base were
performed. The longest chosen distance amounted to 260 metres, i.e. did
not exceed the maximal possible range of the terrestrial laser scanner.
The measurements were performed between pillars 1-2; 2-3; 4-5; 4-6 and
5-6. Laser scanner and targets were force-centred on the pillars (Fig.
3).
[FIGURE 3 OMITTED]
The calibration results are presented in Table 2.
As Table 2 provides, systematic errors change from -16.9 mm to 3.7
mm and the constant R of the terrestrial laser scanner is equal to -8.5
mm. The standard deviation of systematic errors change from 0.00 mm to
0.5 mm and the standard uncertainty of the mean systematic error value
has a range from 0.0 mm to 0.1 mm. A noticeable increase of the
systematic error values could be observed in distances above 100 m.
Systematic error values are shown in Figure 4.
As the analysis of calculated distance measurement accuracies
suggests, the systematic error tends to linearly increase with growing
distance. For distances up to 100 metres, this error does not exceed 3.7
mm and, therefore, conforms to the technical specification of the
investigated laser scanner, i.e. 4 mm/50 m.
[FIGURE 4 OMITTED]
3. Calibration of the horizontal angle measuring device of the
terrestrial laser scanner
Calibration of the horizontal angle measuring device of the
terrestrial laser scanner Leica Scanstation C10 was also performed at
Kyviskes Calibration Baseline. The experiment was carried out by placing
targets on pillars 5 and 6. The accuracy of horizontal angle measurement
was estimated from three different scanner positions with different
angles with respect to the mentioned targets. Measured distances were
corrected for systematic errors as described in the previous chapter.
Based on trigonometric formulas, the comparison of measured and known
(reference) horizontal angles was performed.
The measured angle between TLS and targets can be estimated by
applying the coordinates of the targets and scanner:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
here [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-
coordinates of the scanner position, [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]- coordinates of the targets. The elements of the
formulae (2) are shown in Figure 5.
[FIGURE 5 OMITTED]
The well-known cosine formulae were used to calculate value of the
angle [beta]:
[S.sub.3.sup.2] = [S.sub.1.sup.2] + [S.sub.2.sup.2] -
2[S.sub.1][S.sub.2] cos([beta]) (3)
and
[[beta].sub.t] arccos [S.sub.1.sup.2] + [S.sub.2.sup.2] -
[S.sub.3.sup.2] / 2[S.sub.1][S.sub.2]. (4)
The above formulae (4) should be used two times in carrying out the
calibration process. The first time they should be used when the
measured angle [[beta].sub.i] is calculated from laser scanner data
(coordinates). And the next time the formulae (4) should be used for
reference or real angle determination from the known reference distance
[S.sub.3] and measured corrected distances [S.sub.1] and [S.sub.2].
Calibration results of the horizontal angle measuring device are
presented in Table 3.
As Table 3 provides, systematic errors vary from -3.5" to
0.6" depending on the angle sharpness. The angular constant of the
terrestrial laser scanner is equal to A = -1.3". The standard
deviation of systematic errors varies from 2.1" to 5.1" and
the standard uncertainty of the mean systematic error value has a range
from 0.9" to 2.1".
Conclusions
The calibration method of the horizontal angle measuring device is
proposed. It is based on placing the scanner in front of the calibration
base reference line and measuring the angle in front of this line. The
reference value of this angle is obtained from the lines of a triangle
applying cosine formulae.
It is estimated that the accuracy of the investigated scanner
distance measuring device is noticeably (from ~4 mm to ~14 mm) decreases
for the distances more than 100 metres. It is necessary to perform more
tests with several scanners in order to determine whether it is a
constructive defect or a random scanner deficiency.
The accuracy parameters of the investigated laser scanner Leica
Scanstation C10 correspond with the accuracy criteria specified in the
scanner technical specification.
Caption: Fig. 1. The cyclic error determination baseline mounts
with targets
Caption: Fig. 2. Graphical representation of systematic errors of
the terrestrial laser scanner distance measuring device based on the
calibration at the cyclic error determination baseline.
==
Caption: Fig. 3. Target scanned at Kyviskes calibration baseline
Caption: Fig. 4. Graphical representation of systematic errors of
the terrestrial laser scanner distance measuring device based on the
calibration at Kyviskes Calibration Baseline
Caption: Fig. 5. Scheme for determination of the horizontal angle
measured by TLS
doi: 10.3846/20296991.2013.840356
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Urte ANTANAVICIUTE. Senior Data Operator. SE
"GIS-CENTRAS". Seliu g. 66, LT-08109 Vilnius, Lithuania. Ph
+37062065308, e-mail:
[email protected]
MSc at VGTU (2013).
Research interests: calibration of geodetic instruments, geodesy,
terrestrial laser scanning, cartography.
Romuald OBUCHOVSKI. Doctor of Technological Sciences. Vilnius
Gediminas Technical University. Dept of Geodesy and Cadastre, Sauletekio
al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274
4705, e-mail:
[email protected]
MSc at VGTU (2002).
Research interests: geomagnetic field, gravity field, terrestrial
laser scanning.
Eimuntas Kazimieras PARSELIUNAS. Professor, Doctor. Department of
Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio
al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274
4705, e-mail:
[email protected].
Doctor (1992). Habilitation procedure in 2008. Author of two
teaching books and more than 50 scientific papers. Participated in many
international conferences.
Research interests: graphs theory in geodesy, adjustment of
geodetic networks, geoinformation systems.
M. G. Darius POPOVAS. Assistant Professor. Department of Geodesy
and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11,
LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705,
e-mail:
[email protected].
Doctor of Technological Sciences (VGTU), 2011.
Research interests: terrestrial laser scanning, GNSS.
Dominykas SLIKAS. Doctoral student. Department of Geodesy and
Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11,
LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705,
e-mail:
[email protected].
MSc at VGTU (2007).
Research interests: calibration of geodetic instruments,
engineering geodesy, airborne and terrestrial laser scanning.
Urte Antanaviciute (1), Romuald Obuchovski (2), Eimuntas Kazimieras
Parseliunas (3), M. G. Darius Popovas (4), Dominykas Slikas (5)
Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223
Vilnius, Lithuania E-mails:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected] (corresponding author)
Received 28 August 2013; accepted 18 September 2013
Table 1. Final results pertaining to calibration parameters of the
distance measuring device of the laser scanner based on calibration
at the cyclic error determination baseline
Segment Standard Mean measured Systematic error
number distance, m distance, m of distances, mm
1 0.9993 1.0005 -1.2
2 2.0000 2.0011 -1.1
3 3.0006 3.0019 -1.3
4 4.0007 4.0014 -0.7
5 4.9990 4.9986 +0.4
6 5.9981 5.9987 -0.6
7 6.9995 7.0004 -0.9
8 7.9967 7.9970 -0.3
9 8.9990 8.9993 -0.3
10 9.9999 10.0002 -0.3
11 10.9976 10.9981 -0.5
12 11.9995 11.9999 -0.4
13 12.9980 12.9980 0.0
14 13.9992 13.9989 +0.3
15 15.0038 15.0040 -0.2
R = -0.4
Segment Standard deviation of Standard uncertainty
number systematic error, mm of mean systematic
error value, mm
1 0.4 0.1
2 0.4 0.1
3 0.1 0.0
4 0.3 0.1
5 0.5 0.2
6 0.3 0.1
7 0.3 0.1
8 0.4 0.1
9 0.2 0.1
10 0.5 0.2
11 0.2 0.1
12 0.2 0.1
13 0.2 0.1
14 0.1 0.0
15 0.9 0.3
Table 2. Final results of calibration parameters pertaining to
the distance measuring device of the laser scanner based on the
calibration at Kyviskes Calibration Baseline
Segment Reference Mean measured Systematic error
number distance, m distance, m of distances, mm
1 20.0102 20.0095 0.7
2 100.1632 100.1595 3.7
3 180.0930 180.1070 -14.0
4 200.1032 200.1191 -15.9
5 260.0118 260.0287 -16.9
R = -8.5
Segment Standard deviation of Standard uncertainty
number systematic error, mm of mean systematic
error value, mm
1 0.0 0.0
2 0.2 0.1
3 0.4 0.1
4 0.4 0.1
5 0.5 0.1
Table 3. Final results pertaining to calibration parameters of the
horizontal measuring device of the laser scanner based on the
calibration at Kyviskes calibration baseline
Measured Mean values of Reference angle Angle
angle the measured angle [degrees] '" systematic error
[degrees]'" "
1 17 40 3.4 17 40 4.0 0.6
2 26 8 32.4 26 8 31.4 -1.0
3 49 19 30.2 49 19 26.7 -3.5
A = -1.3
Measured Standard deviation Standard uncertainty of
angle of systematic error mean systematic error value
" "
1 2.6 1.0
2 5.1 2.1
3 2.1 0.9
