Testing of the accuracy dependency
of prismless distance measurement

on the beam incidence angle
Pavel Třasák, Martin Štroner, Václav Smítka, Rudolf Urban

Department of Special Geodesy
Faculty of Civil Engineering

Czech Technical University in Prague
pavel.trasak@fsv.cvut.cz

Keywords: prismless distance measurement, accuracy, testing, incident angle

Abstract

The article assesses the precision development of distance measurement using prismless dis-
tance meters, both in relation to the changing length of the measured distance and the changing
incidence angle of the distance meter’s beam. The article presents the design and performance
of an original experiment, the characteristics of instruments used, statistical evaluation of ex-
perimental data and formulation of conclusions on the precision rate of distance measurement
using prismless instruments.

Introduction

The problems falling under research plan VZ 1 “Reliability, optimization and durability of
building materials and constructions”, partial task “Geodetic monitoring ensuring the relia-
bility of structures”, also involve testing surveying measuring instruments, which is a key part
of metrological safeguarding of instruments and aids used in on-site surveying measurements.

Measurements using prismless distance meters are becoming increasingly more common in
surveying practice allowing the measurement of points directly on structures eliminating the
need for reflective beacons (reflective foils, corner cube prisms). Their principal advantages
include time economies and frequently also considerable cost economies in the case of poor
accessibility of measured points. The measurement of points situated on rock walls, in mines
or on façades of buildings may serve as an example.

The precision rate of measurements using prismless distance meters tends to be lower than
in measurements applying reflective prisms or foils, which, however, does not pose a problem
in many jobs. To utilize this technology with adequate effectiveness, it is advisable to know
the characteristics of the measurement. It is a generally known and recognized fact that
the precision of measurements made with this type of distance meters falls with the growing
deflection from the normal incidence onto the measured surface. The article describes a
measuring experiment whose objective is to confirm or disprove the above-mentioned fact
about a systematically falling precision of measured distances.

Due to the fact that different manufacturers of measuring instruments may use different
electro-optical systems of determining measured distances, three different instruments com-
monly applied in surveying practice were used for the experiment – total stations equipped
with prismless distance meters and also a terrestrial laser scanner.

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Figure 1: Used instruments

Instruments and aids used

The testing was performed with instruments and measurement aids currently available at the
Department of Special Geodesy at Faculty of Civil Engineering, CTU in Prague.

Tested measuring instruments

As mentioned above, the total of 4 measuring instruments were used during the measuring
experiment (3 total stations, 1 terrestrial laser scanner). For the reason of preserving the
maximum objectivity of the experiment, the measuring instruments were selected to cover
the most varied characteristics possible. The choice of instruments was conditioned on their
diversity in terms of the instrument design (different manufacturers), technological differences
(varied age of instruments) and in terms of varied precision rates of implemented prismless
distance meters. References to literature containing detailed information on the instruments
are displayed in Fig. 1, while precision rate characteristics are presented in Tab. 1.

Trimble S6 Topcon GPT-7501 Topcon GPT-2006 Leica HDS 3000
σφ 0.3 mgon 0.3 mgon 2.0 mgon 3.8 mgon
σz 0.3 mgon 0.3 mgon 2.0 mgon 3.8 mgon
σDH 1 mm + 1 ppm 2 mm + 2 ppm 3 mm + 2 ppm

σDB 3 mm + 2 ppm 5 mm
10 mm (< 25 m)

4 mm (< 50 m)
3 mm + 2 ppm (> 25 m)

Table 1: Characteristics of selected measuring instruments, where
σφ is standard deviation of measured horizontal directions, σz of measured zenithal

distances, σDH of distances measured by a prism distance and σDB of distances measured
by a prismless distance meter

A device simulating a reflective surface

The target surface allowing the reflection of a distance meter’s beam of electromagnetic rays
used was a wooden board with dimensions of 420 mm (height) × 320 mm (width). The

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Figure 2: A target wooden board fixed onto the photogrammetric camera carrier and placed
on a surveyor’s tripod

board was fixed onto the carrier of a terrestrial photogrammetric camera (Fig. 2), which, in
combination with a surveyor’s tripod, allows precise positioning of the vertical axis of rotation
of the target board above the target point (baseline point, see below) and precise turning of
the reflective surface.

Description of the experiment

The measuring experiment was planned to test measurements made by prismless distance
meters of selected instruments under various incidence angles of the distance meter’s laser
beam to the surface of the measured object (wooden reflective board). Due to the fact that
different behaviour of measuring instruments during the measurement of different distances
may be expected, the measurement precision was tested not only in relation to the incidence
angle of the distance meter’s beam to the reflective surface, but also in relation to the length
of the measured distance.

The site selected for the performance of the measuring experiment were the premises of the
ground-floor technological storey of the building of the Faculty of Civil Engineering, CTU in
Prague where all-day unchangeable conditions may be expected affecting the use of a prismless
electronic (laser) distance meter (or affecting the transmission of the distance meter’s beam
of electromagnetic rays respectively), i.e. all-day constant temperature, atmospheric pressure
and air humidity, and, further, a uniform unchangeable light exposure of the whole measured
space.

In the first phase of the experiment, the baseline was set out with a precision of 1 centime-
tre, and the points for the positioning of the measured surface were located at distances

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of 5 m, 10 m, 20 m, 40 m from the measuring station S (the measuring instrument’s cen-
tre). As experimental data processing does not consider working with actual deflections of
measured distances, but only with sample standard deviations determined from repetitive
measurements, 1-cm precision in setting out the baseline is quite sufficient.

Both the measuring instrument (this generally applies to all selected instruments) and the
reflective board (together with the photogrammetric camera carrier) were fixed onto surveyor’s
tripods and located above the baseline points at an approximate height of ca 1.2 m. The
turning of the target board for the experiment was selected in an interval of 0 to 90 gon.
While gradually turning the surface in 15-gon steps, the total of 7 board turning positions
were obtained (0 gon, 15 gon, 30 gon, 45 gon, 60 gon, 75 gon, 90 gon).

Figure 3: Baseline diagram

During the whole time of the experiment, the tested instrument was placed at the initial
point of the baseline, and the tripod with the reflective target board was gradually centred
and levelled over individual baseline points. For each configuration set-up, i.e. for each
distance (4 distances in all) and for each turning of the reflective board (7 turnings in all),
repetitive measurements of the horizontal distance were performed using a prismless electronic
distance meter.

Specification of the number of repetitive distance measurements

The number n of repetitive measurements of the distance was specified based on the consid-
eration of the magnitude of the standard deviation of the sample standard deviation of the
measured distance σs [5], which is defined by the relation

σs =
σ√

2(n− 1)
, (1)

where σ is the standard deviation of the distance. Based on the previously formulated con-
dition that the standard deviation σs may maximally equal 10% of the magnitude of the
standard deviation σ the range of random sampling equals

σ
1√

2(n− 1)
= 0.1σ ⇒ n = 51. (2)

For the total number of 7 different positions of partial turning of the target board (0 gon, 15
gon, 30 gon, 45 gon, 60 gon, 75 gon, 90 gon) and 51 repetitive measurements, the total of 357
distances were to be measured at each target point of the baseline. For the whole baseline

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(4 different target points), the total number of distances measured by one measuring instru-
ment equals 1428 (28 random samples). In the whole experiment considering 4 instruments,
the total of 5712 distances are measured.

Assessment and results of the experiment

Processing procedure

As mentioned above, the objective of the experiment was to assess the precision develop-
ment of distance measurements made by a prismless distance meter, both in relation to the
growing length of the measured distance and the growing turning of the reflective surface.
The principal characteristic describing the distance meter’s accuracy considered in this case
is the sample standard deviation determined from repetitive measurements of a distance in a
certain configuration (at a certain distance and partial turning of the reflective surface), i.e.
the sample standard deviation of a random sample with a size of 51 values. This deviation is
governed by the relation

s =

√√√√ 1
n− 1

n∑
i=1

(xi −x)2, (3)

where n is the sample size, xi is the i-th measured distance and is the sample mean of
measured distances.

The final result of data processing within the experiment is the assessment of input random
samples (4 × 28 in total), determination of sample standard deviations and assessment of
whether their development within a changing configuration is random or whether it is influ-
enced by significant effects participating in the reduced accuracy of distances measured by
prismless distance meters. Experimental data is processed using the following procedure:

1. Testing of outliers in random samples and their potential elimination.

2. Verification of normality of random samples.

3. Homogeneity assessment of random samples.

4. Setting of the confidence interval for the standard deviation of a measured distance.

5. Regression analysis, setting of a linear change in the standard deviation of a measured
distance.

6. Graphic interpretation of accuracy evolution of a measured distance.

Elimination of outliers

In repetitive measurements of distances using an electronic distance meter, potential effects
of sporadic gross measurement errors are presumed (caused e.g. by a potential sudden fluc-
tuation of natural conditions in the vicinity of the measured distance). This leads to the
occurrence of outlying measurement values in random samples of measured distances. It is
advisable to eliminate outliers from the random samples during their processing thus enhanc-
ing the objectivity of the results of evaluated data.

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Based on an assumption that random samples belong to the population with a normal prob-
ability distribution and sample sizes are relatively large, the outliers to be eliminated were
detected on the basis of Grubbs’ test [6].

Testing on the 5% significance level detected individual outliers of measured distances (in the
most unfavourable case, 3 outliers were eliminated from a random sample).

Verification of normality of random samples

Random samples of repetitive distance measurements are presumed to belong to the popula-
tion with a normal probability distribution. To confirm this assumption, experimental data
are subjected to testing using D’Agostino’s K2 test [7].

The result of testing on the 5% significance level confirmed the normality of all tested random
samples.

Homogenity assessment of random samples

The verification of homogeneity of random samples of measured distances is one of the pos-
sibilities allowing the assessment of the effect of the configuration (the effect of the length
of the measured distance and the turning of the reflective surface) on the accuracy rate of a
distance measured by a prismless distance meter. The principle of this method consists in
the application of statistical homogeneity tests. These tests work with groups k of random
samples and verify the null hypothesis that the variances of the populations σ2i , to which
random samples belong, are equal to each other

H0 : σ21 = σ22 = . . . = σ2g
H1 : σ21 6= σ22 6= . . . 6= σ2g

. (4)

Hence, created groups of random samples of measured distances allow testing whether the
sample standard deviations of measured distances si (or sample variances s2i respectively) are
in correspondence with the joint standard deviation of the distance σ (or the variances of the
population σ2 respectively). Thus, provided all samples corresponding to the same distance
(4 groups with 7 samples each) are sorted out, and provided the null hypothesis is not rejected
during the testing of these groups, it may be verified that the accuracy rate of the measured
distance does not rely on the turning of the reflective surface (i.e. on the incidence angle of
the distance meter’s beam).

Based on the assumptions about the normality of random samples, Bartlett’s test was selected
for the testing of homogeneity. The testing criterion of Bartlett’s test testing the group k of
random samples is the variable B, which is defined by the expression

B =

[
(N − 1) ln s2c −

∑k
i=1(ni − 1) ln s2i

]
C

, (5)

where the constant C equals

C =
1 +

(∑k
i=1

1
ni−1

− 1
N−k

)
3(k − 1)

(6)

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s2i is the sample variance of the i-th sample of measured distances with a range ni

s2i =
1

ni − 1

n∑
j=1

(ixj −i x)2, i = 1, 2, . . . ,k, (7)

and s2c is the pooled estimation of the variance expressed in the form

s2c =
1

N − 1

k∑
i=1

ni∑
j=1

(ixj −i x)2, N =
k∑
i=1

ni. (8)

Assuming the validity of the null hypothesis and the condition of the minimum number of
tested samples ni ≥ 6, the variable B roughly has the distribution χ2.

The acceptance or rejection of the null hypothesis about the equality of variances of popula-
tions is assessed on the level of significance

P(B > χ2α,(k−1)) = α = 0.05, (9)

where χ22α,(k−1) is the critical value of the distribution χ
2 with (k − 1) degrees of freedom.

Provided the value of the testing criterion B exceeds the critical value χ22α,(k−1), the null
hypothesis on the level of significance α is rejected and homogeneity of samples is not proved.

Besides the decision on the rejection or confirmation of the null hypothesis on the selected
level of significance α, the testing also results in the determination of the p–value, i.e. the
probability at which the testing criterion equals the critical value

P(B = χ2p,(k−1)) = p. (10)

The determined p–value describes the limit level of significance, i.e. the maximum probability
of the rejection of the null hypothesis, despite its validity.

The results of testing the homogeneity of groups of random samples of measured distances
are displayed in Tab. 2.

The results of testing the groups of random samples in which the null hypothesis was not
rejected on the 5% level of significance during the testing of homogeneity, i.e. in which
the effect of the distance meter’s beam incidence angle on the accuracy rate of the distance
measured by a prismless distance meter was not proved on the selected level of significance,
are written in bold in the table above.

Confidence interval for the standard deviation of a measured distance

Another method used for the investigation of the effect of turning the reflective surface on the
precision of a measured distance is the method based on the interval estimation of the standard
deviation of a measured distance. The method consists in the creation of a two-sided 95%
confidence interval for the standard deviation of the measured distance σ. Assuming that the
random sample of measured distances (serving for the construction of the confidence interval)
is taken from the population with a normal probability distribution, the 95% confidence
interval is set as

P



√√√√ (n− 1)s2
χ21−α/2,n−1

≤ σ ≤

√√√√(n− 1)s2
χ2
α/2,n−1

≤


 = 1 −α = 0.95, (11)

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Trimble S6 Topcon GPT-7501
Distance

C χ20.05,6
p-value

[m] [%]
5 45.452

12.592

0.0
10 22.737 0.1
20 15.019 2.0
40 94.285 0.0

Distance
C χ20.05,6

p-value
[m] [%]
5 9.305

12.592

15.7
10 7.599 26.9
20 11.881 6.5
40 69.255 0.0

Topcon GPT-2006 Leica HDS 3000
Distance

C χ20.05,6
p-value

[m] [%]
5 45.452

12.592

0.7
10 22.737 80.6
20 15.019 3.6
40 94.285 23.1

Distance
C χ20.05,6

p-value
[m] [%]
5 14.442

12.592

2.5
10 1.792 93.8
20 8.384 21.1
40 15.096 2.0

Table 2: Results of Bartlett’s test of homogeneity of samples

where 1−α is the confidence coefficient, n is the sample size, s is the sample standard deviation
of a measured distance and χ21−α/2,(n−1) (resp. χ

2
α/2,(n−1) ) is the value of the distribution χ

2

with (n− 1) degrees of freedom.

The principle of assessing the configuration effect on the precision rate of distance measure-
ment consists in the sorting out of random samples into individual groups according to the
length of measured distances (see sorting into groups in par. "Homogenity assessment of ran-
dom samples"), determination of confidence intervals for the standard deviation of a distance
and assessment whether the confidence intervals in individual groups overlap and, therefore,
there exists a common interval in which a standard deviation of a distance common for the
whole group is found. In the case that such an interval is found, we may claim that random
samples are in correspondence with the same standard deviation of a distance and that the
precision rate of distance measurement is not affected by a change in turning the reflective
surface at a certain measured distance.

The occurrence of intervals of a potential common standard deviation was studied only graph-
ically, and the results are displayed in Fig. 4.

The results in the figure above correspond to a greater part to the results obtained during the
testing of homogeneity of samples (see par. "Homogenity assessment of random samples").

Setting a linear change in the standard deviation of a measured distance

With respect to the linearly growing incidence angle of the distance meter’s beam to the
reflective target surface, according to a speculated, generally recognized opinion (see par.
"Introduction"), a linear or another monotonous growth pattern of the standard deviation of
a measured distance σ may be assumed. Based on this assumption, the dependence between
the incidence angle of the distance meter’s beam and the accuracy rate of a distance measured
by a prismless distance meter may be investigated using the regression analysis method. The

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Figure 4: 95% confidence interval for the standard deviation of a distance

principle of this method consists in the plotting of a regression line

s = aω + b (12)

through a set of sample standard deviations of the distance s and assessment of the significance
of the slope a of this line representing a linear change in the sample standard deviation s in
relation to the changing angle of the turning of the reflective surface ω. Using the least squares
method the estimation of the slope of the regression line in the form

â =
∑n
i=1(ωi −ω)si∑n
i=1(ωi −ω)2

, (13)

where si is the sample standard deviation and ωi is the incidence angle of the distance meter’s
beam for the i-th turning of the reflective surface, n is the number of turnings of the reflective
surface (n = 7) and ω is the sample mean incidence angle of the distance meter’s beam.

The significance of a change in the sample standard deviation s in relation to a change in the
turning of the reflective surface ω may be assessed on the basis of the statistical hypothesis
test where the null hypothesis of the null slope of a regression line is investigated

H0 : a = 0,
H1 : a 6= 0.

(14)

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The testing criterion is defined by the relation

t =
|â|
sâ
, (15)

where sâ is the estimation of the standard deviation of the regression line slope estimation

Sâ =
Sr√∑n

i=1(ωi −ω)2
(16)

where sr is the residual standard deviation expressed in the form

Sr =

√∑n
i=1(Si − (âωi + b̂))2

n− 2
. (17)

The acceptance or rejection of the null hypothesis of the null slope of the regression line is
assessed on the level of significance

P(t > tα/2,n−2) = α = 0.05, (18)

where tα/2,n−2 is the critical value of Student’s distribution t with n− 2 degrees of freedom.

If the value of the testing criterion t exceeds the critical value tα/2,n−2, the null hypothesis
on the level of significance α is rejected and the null value of the slope of the regression line
is not proved.

P – the value for the test of the slope of the regression line equals the probability

P(t > tp/2,n−2) = p. (19)

The resulting values of changes in sample standard deviations, together with the results of
the testing, are shown in Tab. 3.

The results of testing where the null hypothesis was not rejected on the 5% level of significance
during the testing, i.e. in which a null linear change in the sample standard deviation was
proved on the selected level of significance, are written in bold in the table above. As the
results imply, the non-effect of the unfavourable trend in the accuracy evolution of prismless
distance measurement was proved in the absolute majority of cases.

Graphic interpretation of precision development of a measured distance

To simplify the interpretation of the precision development of prismless measurement of dis-
tances in relation to a selected measurement configuration (see above), the resulting sample
standard deviations of the distance s determined from repetitive measurements were dis-
played in three-dimensional graphs, both in relation to the growing measured distance and
the growing incidence angle of the distance meter’s beam (i.e. turning of the reflective sur-
face). To get a more illustrative picture of the precision development of measured distances,
the set of sorted out standard deviations was approximated on a plain surface (Fig. 5). The
approximation was performed using the bicubic interpolation method.

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Trimble S6
Distance â Sâ

t t0.025,5
p-value

[m] [µm/gon] [µm/gon] [%]
5 2.9 0.4 8.119

2.571

0.0
10 1.0 0.7 1.423 21.4
20 0.7 0.5 1.396 22.2
40 3.3 1.4 2.384 6.3

Topcon GPT-7501
Distance â Sâ

t t0.025,5
p-value

[m] [µm/gon] [µm/gon] [%]
5 0.6 1.1 0.572

2.571

59.2
10 0.5 1.0 0.485 64.8
20 0.5 1.2 0.404 70.3
40 4.8 3.5 1.394 22.2

Topcon GPT-2006
Distance â Sâ

t t0.025,5
p-value

[m] [µm/gon] [µm/gon] [%]
5 0.8 1.7 0.501

2.571

63.8
10 1.4 0.5 2.966 3.1
20 1.4 1.5 0.927 39.6
40 -1.1 1.2 0.982 37.1

Leica HDS 3000
Distance â Sâ

t t0.025,5
p-value

[m] [µm/gon] [µm/gon] [%]
5 6.9 1.4 4.983

2.571

0.4
10 2.9 1.3 2.214 7.8
20 3.1 2.3 1.348 23.6
40 0.4 4.6 0.088 93.4

Table 3: Assessment of linear changes in sample standard deviations

Conclusion

In the branch of engineering geodesy and laser scanning, it is currently generally recognized
that the precision rate of distance measurement obtained by a prismless distance meter falls
with the growing incidence angle of the distance meter’s beam to the reflective surface of the
target object. Therefore, a measuring experiment was performed to confirm or disprove the
validity of this opinion.

The results reached during the experiment (displayed in Tab. 2, Tab. 3 and in Fig. 4, Fig. 5)
lead to a conclusion that the incidence angle of the distance meter’s beam to the reflective
surface has no effect on the standard deviation of a distance measured by a prismless distance

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measurements on the beam incidence angle

Figure 5: Graphic display of precision development of distance measurement by a prismless
distance meter

meter. The values of sample standard deviations of measured distances (determined from
repetitive measurements) show random fluctuations and do not imply any systematic drop
in the accuracy rate of prismless measurement of distances. An exception is the case of
a rapid growth in the sample standard deviation of a distance at a measured distance of
40 m and turning of the reflective surface by 90 gon using Trimble S6 and Topcon GPT-7501
measuring instruments. This growth, however, cannot be included in the final conclusions
of the experiment as it represents an extremely unfavourable case of distance measurement.
Assuming a cone-shaped divergence of the distance meter’s laser beam, the magnitude of the
laser track at a distance of 40 m is so large and the width of the tested reflective surface in the
direction of a falling beam at a turning by 90 gon is so small that it cannot be guaranteed that
the whole distance meter’s beam will be reflected from this board. The results of measurement
in this case are highly untrustworthy.

No significant systematic (linear) deterioration in the accuracy rate of prismless distance
measurement in relation to the growing incidence angle of the distance meter’s beam to the
reflective target surface was proved on the basis of regression analysis of measured data.

Besides the principal objective of the experiment, another new finding was made while compar-
ing the values of sample standard deviations of measured distances with corresponding stan-
dard deviations of measurement stated by the instrument manufacturers (σDB, see Tab. 1).
These sample standard deviations describe the random component of the total standard de-
viation σDB and are significantly lower in value than the standard deviations. We may,
therefore, assume that the manufacturers consider a relatively high systematic component of
the standard deviation of a distance, which, of course, is not manifested in repetitive distance
measurements.

To conclude, we may state that the generally recognized opinion of the effect of the distance
meter’s beam incidence angle (turning of the target reflective surface) on the accuracy rate

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of distances measured by a prismless distance meter is not correct for distances measured in
an interval of 0 m – 40 m. This effect was not manifested during the performance of the
measuring experiment.

The article was written with support from research plan MSM 6840770001 “Reliability, opti-
mization and durability of building materials and constructions”, partial task “Geodetic mon-
itoring ensuring the reliability of structures”.

References

1. Corporate literature for instrument Trimble S6 (in Czech)1 2010-05-15.

2. Corporate literature for instrument Topcon GPT – 7501 (in Czech). http://obchod.
geodis.cz/geo/gpt-7500. 2010-05-15.

3. Štroner, M. - Suchá, J. - Pospíšil, J.: Verification of Characteristics of Total Stations
TOPCON GPT-2006 – Part 1 (in Czech). Stavební obzor. 2007, Vol. 16, No. 2, pp.
45-48. ISSN 1210-4027.

4. Corporate literature for instrument Leica HDS 3000. http://hds.leica-geosystems.
com/en/5574.htm. 2010-05-15.

5. Böhm, J. – Radouch, V. – Hampacher, M.: Theory of Errors and Adjustment Calculus
(in Czech), 2nd edition, Praha, Geodetický a kartografický podnik 1990. /ISBN 80-
7011-056-2/.

6. Eckschlager, K. – Horsák, I. – Kodejš, Z.: Assessment of Analytical Results and Methods
(in Czech), 1st edition, Praha, SNTL – Nakladatelství technické literatury 1980.

7. D’Agostino, R. B. – Belanger, A. – D’Agostino, Jr., R. B.: A Suggestion for Using
Powerful and Informative Tests of Normality. The American Statistician, Vol. 44,
No. 4, pp. 316–321, 1990.

1http://www.geotronics.cz/index.php?page=shop.product_details&flypage=flypage.tpl&product_
id=4&category_id=15&option=com_virtuemart&Itemid=7

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http://obchod.geodis.cz/geo/gpt-7500
http://obchod.geodis.cz/geo/gpt-7500
http://hds.leica-geosystems.com/en/5574.htm
http://hds.leica-geosystems.com/en/5574.htm
http://www.geotronics.cz/index.php?page=shop.product_details&flypage=flypage.tpl&product_id=4&category_id=15&option=com_virtuemart&Itemid=7
http://www.geotronics.cz/index.php?page=shop.product_details&flypage=flypage.tpl&product_id=4&category_id=15&option=com_virtuemart&Itemid=7


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