ENVIRONMENTAL ENGINEERING

ENVIRONMENTAL
ENGINEERING
May 22-23, 2008
The 7 th International Conference
Faculty of Environmental Engineering
Vilnius Gediminas Technical University
Saulėtekio ave 11, LT-10223 Vilnius, Lithuania
Phone: +370 5 2745090; Fax.: +370 5 2744731; e-mail: ap2008@ap.vgtu.lt
CALIBRATION OF CODED LEVELLING STAFFS
Vytautas Giniotis, Donatas Rekus, Ceslovas Aksamitauskas
Department of Geodesy and Cadastre, Vilnius Gediminas technical university,
Saulėtekio al. 11, LT-10223 Vilnius, Lithuania,
e-mail: gkk@ap.vgtu.lt
Abstract. Digital levels are a precise instruments used for precise leveling. Operation of digital levels is based on the
digital processing of video indications of a coded staff. Changes in leveling methodology and sources of specific
errors occur using digital levels for precise levelling. The marks on the leveling meters also are modified and consist
from the coded strokes put on the meter’s surface in specific order. The accuracy of performance of all the measuring
equipment mostly depends on accuracy of position of those strokes. This paper deals with an analysis of an accuracy
calibration of leveling meters
Keywords: coded staff, digital levelel, leveling error, accuracy, calibration.
1. Introduction
Changes in leveling methodology and sources of
specific errors occurs using digital levels for precise
levelling. Precision investigations of a particular model of
levels and coded staffs and digital levelling are necessary.
Operation of levelling instruments is based on the digital
processing of image of the coded meter. Every company
producing the leveling instruments has developed its own
codes and methods of their processing: correlation
(LeicaWild NA2000/2002/3000/3003 systems),
geometric method (Zeiss DiNi 10/20 systems), phase
method (Topcon DL – 101/102 systems) [1-6].
At the beginning of measurement a visual pointing
of the instrument into the surface of leveling meter is
performed. After that the instrument automatically points
the focus of its optical system on the surface of the meter
and then a rough correlation calculation is performed
followed by the precise correlation. According to data
received in the processor of the instrument an exact
distance from the axes of the instrument to the surface of
the level mete is calculated. According to the information
received by decoding it from the photoelectric matrix the
height of the level placing is calculated in the processor.
During this operation the coded view of the meter is
compared with that saved in the memory of the
instrument. A true meter’s height position is determined
according to the shift of the image in the photoelectric
sensor (pixels) matrix.
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Processing of information is quite complicated in
various leveling systems. For example, in Leica systems
the code bars (strokes) are put on the all length – 4050
mm of the meter. The bar code has 2000 elements, each
of them having 2,025 mm in width. It is evident, that the
production of such meter is quite complicate; its accuracy
mostly depends on the errors of placement of the coded
bars. The matrix of the photodiodes (pixels) has 256
elements placed with the pitch of 25 µm from each other.
Accuracy of placement of these cells also has an
influence on the overall accuracy of the instrument’s
performance.
An accuracy of the calibration of placement of the
coded bars on the surface of the meters is analyzed in this
paper.
2. Calibration of the coded staffs
The system calibration can be used to determine the
correction values of rod readings and hence the scale of the
digital leveling system, secondly to examine its behavior
and thirdly, to estimate the accuracy.
During the last decades the geodetic instruments
have become more automatic and electronic, fine
constructed and externally well operating systems. The
software has replaced more and more observer’s task.
Also the levelling experienced the similar development:
The discovery of the digital levelling in the beginning of
the 90’s really conduced the levelling into the new era. [12,
13]

In old times the levelling instruments were simply
constructed, but they were also manufactured in great care
applying precision mechanics. So, we users knew more
and understand better the function of the leveling
instruments and in most cases, we were able to quickly
locate the functional faults and to correct small
imperfections. When we operate with a digital levelling
system, a CCD camera takes picture from the rod, which
covers a certain sector of the bar code scale above and
below the horizontal level. The picture is then compared to
the picture of the whole scale stored in the memory of the
instrument. Each manufacturer has its own method to
process the rod reading [1, 2]. In a digital level the rod
readings are automatically processed applying electrooptical
technique, while in conventional levelling the
observer manually gets a rod reading using the optical
tools of the instrument, e.g., line of sight, hair cross,
ocular, micrometer, line of level etc. A CCD camera
replaces the human eye. In processing a rod reading the
digital levelling employs more than just one code line.
In conventional levelling the scale is based on the
scale of a rod, while in digital levelling we can speak
about two scales: Scale of an instrument and scale of a rod.
The digital level gives the former, but in fact the scale of
level is expected to be equal with the scale of rod.
However, with time, the scale of level can be changed e.g.
by aging of the CCD sensor. Also the scale of level is
sensitive for scratches of code elements or shadows on
invar band etc.
All coded meters can be calibrated by use of the
interferometric comparators. Usually it is enough to
measure every stroke (or bar) of 2.025 mm width at the
pitch determined. The gaps between the bars are at the
distances in times of 2.025 mm. Vertical comparators are
mostly used for this purpose. By horizontal comparators
the thermal expansion coefficients and thermal resistance
of the meter are investigated. The meters are calibrated at
0, 10, 20, 30 and 40 0 C of temperature.
The comparators partly repeat the operations of
leveling. (Fig.1)
Fig. 1. The FGI system calibration in the FGI laboratory
Some of the height leveling can be used for
measurement or calibration of precision leveling meters.
Usually the vertical position of the calibration is used
having the purpose to keep the same position as it is
during the working operations. Nevertheless, there are
variants of calibration in the horizontal position as it
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saves the height of the calibration laboratory and makes
an operation easier. The vertical comparators are arranged
in Graz University of Technology (Austria), at Institute of
Geodesy (Finland), Munich Bundeswer University,
Germany. Horizontal structure of the comparator is
applied in ETH University, Zurich.
In the system calibration the rod is set on the vertical
conveyor controlled by laser interferometer and the digital
level at a certain distance from the rod as illustrated in Fig.
2. The rod is moved step by step in vertical direction and
the rod readings are observed with the instrument during
the stop between the steps. The readings are taken from
different sectors of the bar code rod and then compared
with true values obtained by the laser interferometer. [9]
Fig.2 Especially designed for the Zeiss DiNi12 digital
levelling system with two observation pillars.
3. Photogrametric calibration
Principles of photogrammetry can be used for the
comparing the views of the etalon and meter to be
calibrated. The correlation factor determination can be
used successfully as well as in the case of Digital leveling
operation. The etalon view is save din the PC memory,
and the view of tested meter must be extracted from the
CCD camera. All the measurements are performed in the
PC screen using analyzing gap covering the both images
(Fig. 3 and 4).
At first, adjustments of the meters views in the
direction of x and y axes must be taken. As it is seen in
Fig. 1, badi mage projection causes the faults in the
images, not horizontal alignment result in the cosine error
to be present at the misalignment angle ϑ. It is evident
that the true length h of the image will differ from the
misaligned length l as ∆ l = l(1 − lcos ϑ)
.
The meters have an opportunity to be shifted along
each other on the computer screen. CCD camera is
supplied by the analyzing window for the selection the
part of the meters that are selected for the comparison
between themselves [7-11]. The analyzing window is
shifted along the length of the meters or replaced by steps
at least three times – at the beginning, in the middle and
at the end of the meters. In this case it is easier to apply
zooming process for the part taken in step measurement.

It would be impossible in such view as it is shown in Fig.
1.
The readings are taken by using the standard
software AutoCad. The readings are shown only as an
example without any statistical processing. According to
the rexample it can be stated that the accuracy of
measurement by this method can reach tens of microns in
average.
2
1
- 0,2 0 0,2 0,4 0,6 3
ϑ
y
x
Fig. 3. General view of photogrametric calibration of leveling
meters: 1 etalon meter, 2 meter to be calibrated, 3
linear and vernier scale for readings, 4 moving reticle
An accurate comparing of the meters can be
accomplished by the correlation method. A better case to
apply this is comparison of the same type of the meters,
for example, both coded meters by the same producer.
The signals from the photoelectric sensors (pixels) is
output to the PC making an array of numerical values
from the both meters at the same position. It coincides
with the known area-based method described in [11]. The
difference is only in the aim of its applying. In our case it
is the comparison of the position of edges of the bars on
the tested meter. The processing of the images goes in the
same way as according to the method above. Smaller
subarrays from the both arrays are taken and the
correlation factor is calculated using the formula [11]:
r
m
n
∑∑
4
[( A − A)( B −B)]
ij
ij
i= 1 j=
1
=
1/ 2
⎧ m n m n
⎪ ⎡
2 ⎤⎡
2 ⎤⎫
⎪
⎨⎢∑∑( Aij
− A) ⎥⎢∑∑( Bij
−B)
⎥⎬
i= 1 j= 1 i= 1 j=
1
⎪⎩⎣ ⎦⎣ ⎦⎪⎭
r – correlation coefficient; m and n – numbers of rows and
columns; A ij – digital number from subarray A in the row
i and in the column j; A - average of all digital numbers
in subarray A, and B - average of all digital numbers in
subarray B. i = 0, 1, 2, 3,…, m; j = 0, 1, 2, 3,…, n.
It is evident that a total array of numbers
representing position of the bars on the surface of the
levels will be received from the array of sensors of the
CCD camera converting voltage output into the digital
form. General diagram of photosensors (pixels) with the
view of the coded bar of shown in
1 2 3
ooooooooooooooooooooooo
oooo
ooooooooooooooooooooooo
oooo
ooooooooooooooooooooooo
oooo
ooooooooooooooooooooooo
oooo
ooooooooooooooooooooooo
Fig. 4. Array of photosensors and the bars of the meter on it: 1 –
coded bars of the meter, 2 array of CCD sensors, 3
analyzing window
⎡a11 a12 a13 a14
...
⎢
⎢
a21 a22 a23 a24
...
⎢a31 a32 a33 a34
...
A = ⎢
⎢a41 a42 a43 a41
...
⎢
a51 a52 a53 a54
...
⎢
⎢⎣
... ... ... ... ...
⎡b11 b12 b13 b14
... ⎤
⎢
⎥
⎢
b21 b22 b23 b24
...
⎥
⎢b31 b32 b33 b34
... ⎥
B = ⎢
⎥
⎢b41 b42 b43 b41
... ⎥
⎢
b51 b52 b53 b54
...
⎥
⎢
⎥
⎢⎣
... ... ... ... ... ⎥⎦
Fig. 5. Digital output from the search array of photosensors and
the analyzing window for subarrays selection
A digital output from the photosensors presented in
the form of matrixes A and B, from the view of etalon
meter and calibrated meter respectively, are shown in Fig.
3.
The correlation coefficient is calculated from the
subarrays selected by analyzing window. The error of the
displacement (difference between the position of bars on
the meters) is determined by the local correlation
coefficient. Such operations are performed for this
process:
• preliminary correlation coefficient calculation at
the beginning, middle and the end part of the
meters using the formula (1);
• shift of the subarray B at the predetermined pitch
∆ t and repeating an operation as described
above;
• repeating the first two operations in the
investigation region ± k∆ t , where k = 1, 2, 3, ...
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
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covering the zone of expected error of the
meter‘s bars placement;
• statistical processing of the results of correlation
coefficient calculations determining the position
in the discrete numbers of pitches ∆ t in the
length x of the meter.
More exact evaluation of edges of the bars can be
performed by using the feature-based digital image
assessment technique. In case of a blur image of the
meters additional statistical means must be taken for
determination the position of bars. The values of the
photogrammetric points of the image are assessed by
evaluates of standard deviations Sx;
S
y and
S
xy
( ∑ xi)( ∑ yi)
= x y −
∑ ( , )
. (2)
n
Both coordinates x and y are needed for better
determination of position of the bar’s points as it can be
seen in Fig. 3. Linear regression equation y = α + β x
dx
can be used for this as well, where β =
dy
is the slope
of the line, parameter α is a constant at value x=0. The
same can be determined
Sxy ∑
as ;
yi ∑ xi
β = α = −β
2
Sx
n n .
Accordingly the sample correlation coefficient can
be calculated as
r =
S
xy
2 2
x y
SS
. (3)
Such calculations as it is presented in [11] would be
easier for the determination of the points on the meter‘s
bar edges, and their systematic error will be determined
by changing the pitch ∆ t of subarray sample selection.
Using the analyzing window on the search array of
digital numbers, its position must be changed by steps at
the chosen pitch ∆ t . So a maximal value of correlation
coefficients will be determined at some values i∆ t of the
meter’s length, different from those on the etalon meter.
This difference will be equal to the systematic error of the
bars position at all its length.
3. Conclusions
Preliminary experiments show a possibility to
perform the calibration of leveling meters using the
photogrammetric methods of its comparison. Digital
output array processing using an analyzing window is to
be used. Area based comparison method used in general
purpose photogrammetry can be applied for this purpose
calculating the correlation coefficients at the shift of the
images to each other by the discrete pitch that show the
difference between the position of meter’s bar edges
where maximal values of the correlation coefficient exist.
The systematic error of the meter under the calibration is
determined by the values of position where these
maximal values are found along the total length of the
meter.
References
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