ACTA IMEKO 
ISSN: 2221‐870X 
June 2015, Volume 4, Number 2, 68‐71 

 

ACTA IMEKO | www.imeko.org  June 2015 | Volume 4 | Number 2 | 68 

Modelling of linear test bench for short distance 
measurements 

Lauryna Šiaudinytė  

Institute of Geodesy, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT‐10223, Vilnius, Lithuania 
 

 

 

Section: RESEARCH PAPER  

Keywords: Calibration bench; laser interferometer; linear measurements 

Citation: Lauryna Šiaudinytė, Modelling of linear test bench for short distance measurements, Acta IMEKO, vol. 4, no. 2, article 12, June 2015, identifier: 
IMEKO‐ACTA‐4 (2015)‐02‐12 

Editor: Paolo Carbone, University of Perugia, Italy 

Received October 15, 2014; In final form November 27, 2014; Published June 2015 

Copyright: © 2015 IMEKO. This is an open‐access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits 
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 

Funding: This work was supported by the European Social Fund under the Global Grant measure 

Corresponding author: Lauryna Šiaudinytė, e‐mail: lauryna.siaudinyte@vgtu.lt 

 

1. INTRODUCTION 

The main standard dealing with total stations testing is ISO 
17123. However, this standard focuses on field testing 
procedures. Although a total station is mainly intended for 
outdoor measurements, indoor calibration in controlled 
environmental conditions provides the best way to determine 
systematic errors. However, testing devices under laboratory 
conditions usually come with new issues of which lack of space 
is typically one of the most important. This brings to the need 
of test bench development for the calibration of geodetic 
distance measuring equipment within relatively short distances.  

In many calibration laboratories there are special benches 
designed for tape calibration which could be adjusted for 
electronic distance measuring equipment calibration. Section 2 
reveals applied instrumentation for indoor distance 
measurements of various calibration laboratories. 

Proposed possibilities for the development of a short 
distance linear calibration bench using the existing basis of 
special supports for cyclic error determination are presented 
further in this paper. The new calibration bench of aluminium 
construction is cost saving and lightweight compared to 
stainless steel. Within 13 meters of the bench it is possible to 
determine systematic errors and therefore to increase accuracy.  

 
Automation of the carriage will reduce the measurement 

uncertainty caused by human interaction.  

2. DISTANCE MEASURING INSTRUMENTATION 

Preservation of the primary length standard - the meter - is 
the main role of length metrology. It also has to ensure the 
infrastructure needed for dimensional and positional 
measurements traceability to the meter. 

The meter is defined as the length of the path traveled by 
light in vacuum during the time interval of 1/299 792 458 of a 
second. An interferometer is an instrument providing standard 
distance measurements. There are a few main types of laser 
interferometers used in laboratory measurements – homodyne 
and heterodyne laser interferometers are the most commonly 
used. Homodyne interferometers are based on the interference 
of two beams (one split beam) of the same frequency. The 
optics of homodyne interferometers is similar to Michelson 
interferometers, however it produces a lower signal due to a 
high noise ratio compared to the heterodyne interferometer. 
Heterodyne interferometers are based on two beams with 
different frequencies (low and high), different polarization 
mixed with each other and in non-linear combination creating 
two new frequencies (heterodynes). The double frequency 

ABSTRACT 
To perform the calibration of total stations under  laboratory conditions,  lack of space  is a common  issue. The paper presents the 
analysis of applied solutions for short distance measurements and assumptions of the construction development of a linear test bench 
for cyclic error determination. Various aspects of improvement are explained in the paper, and the preliminary design of a linear test 
bench being developed at Vilnius Gediminas Technical University is presented.  



 

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interferometers measure the relative displacement of two 
reflectors by splitting the beam. 

Then two beams are directed to different retro-reflectors 
and the resulting signals are returned to a photodetector [7]. 
The working principle of the laser interferometer is shown in 
Figure 1. Heterodyne interferometers are very sensitive and 
usually more accurate than homodyne interferometers.  

There are environmental factors such as temperature, 
pressure and humidity influencing linear measurements. The 
most important factor of length measurement accuracy is 
temperature. The sensitivity of interferometric systems to 
varying temperature can significantly influence the 
measurement results because of linear expansion of materials 
affecting the stability of the structural geometry. Precision 
measurement systems are usually placed in a controlled 
environment with a constant temperature of 20.0 °C ± 0.2 °C. 
To meet such requirements the interferometric system should 
be placed in a special chamber with many parameter measuring 
sensors to maintain an effective thermal and pressure isolation. 
These sensors as well as temperature fluctuation can bring in 
the uncertainty in such precise length measurements [3]. 
Another important uncertainty source in dimensional metrology 
is the abbe error which occurs due to the difference between 
the axis of the measurement object and the axis of the 
measuring device. This error can also be caused by the motion 
of the measurement object [6]. 

2.1. Applied solutions for indoor calibration 

In the National Metrology Institute of Germany 
(Physikalisch-Technische Bundesanstalt) there is a 50 m long 
geodetic base which is also a comparator established for the 
calibration of length measuring instruments where the principle 
of Michelson’s interferometer is used as a length standard. The 
carriage is mounted on the rails fixed along the 50 m base. The 
stationary part of an interferometer is placed on a stable base in 
front of the rails. The laser beam is split into two paths 
generated by a reflector consisting of three mirrors arranged on 
the surface of a cube, and fixed to the moving carriage. The 
zero point of the interferometer in respect of the rangefinder is 
determined by means of a gauge block. The measurement error 
of the distance measuring device can be determined by 
comparison with the distance measured by an interferometer 
and a calibrated instrument [10]. In KRISS the 50 m long bench 
was developed for the calibration of surveying tapes. The main 
components of this system are the interferometer and the 
carriage moved by the servo motor attached to it along steel 
rods and controlled by a computer through wireless 
communication. The interferometer axis is set in the center 
between the rails where the tape is placed. There is an optical 
system with the microscope installed in the moving carriage to 

detect the graduation of the tape. The distance measured by the 
interferometer is compared to the distance determined by the 
tape being calibrated [4]. 

50 m long benches are very common in metrology institutes, 
however, such distance may cause additional uncertainty. It is a 
challenging task to align all the components and install the 
precision rail system while avoiding inclination and geometric 
alterations due to thermal expansion or compression.  

Therefore, the Finish Centre for metrology and accreditation 
developed a shorter – 30 m long distance calibration bench. For 
stability this bench was built (constructed) two floors under the 
ground. Concrete pillars are placed at every 2.8 m and a 31.5 m 
monolithic concrete beam on top of them. There are two 
separate bases established in both ends of the bench for the 
reference equipment and instruments under calibration. The 
rails are mounted on additional supports and the carriage 
moving along the rail is equipped with laser interferometer 
optics for both distance and angle measurements as well as a 
microscope with CCD camera for linear position detection. 
This interferometric bench is suitable for a laser tracker, a total 
station and tape calibration. The expanded uncertainty (k = 2) 
of the length scale is 2.6·10-6 m for a 30 m displacement [9]. 

Although smaller benches can fit laboratory premises better, 
there is a need to calibrate total stations in longer distances 
because they are designed to be used outdoors by measuring 
longer stretches. To extend measuring distances in the 
laboratory a special mirror system can be used. To double or 
triple the measuring distance a zigzag path can be created for 
the beam to travel by using mirrors mounted on certain points 
and rotated at a certain angle. Such method allows avoiding 
reflector mounting outside the laboratory [5]. 

Due to the space issue at Vilnius Gediminas Technical 
University it was decided to create a 13 m long linear bench for 
short distance measurements and cyclic periodic error 
determination.  

3. THE LINEAR BENCH 

The linear bench under development at the Institute of 
Geodesy of the Vilnius Gediminas Technical University is 
suitable for the calibration of geodetic electro-optical 
equipment. The main instrument used in survey is a total 
station. This instrument is exceptional because of its ability to 
measure horizontal and vertical angles as well as distances 
simultaneously. An Electronic Distance Meter (EDM) is 
embedded in the total station for the distance measurements. 
This instrument is typically based on the phase difference 
measuring principle for distance measurements. The measuring 
signal modulated on the carrier wave in the emitter travels a 
distance D from the total station A to reflector B and back to 
the instrument receiver. In the receiver the difference between 
transmitted and received signals are measured and compared. 
Point A and point A' shown in Figure 2 are the same however 
the returned wave has been opened out. In an EDM the double 
distance length (2D) is measured by a difference in phase angles 
of two sinusoidal waves (transmitted and received). This 
distance can be expressed in terms of wavelength of the 
measuring unit [8]:  

mmnD  2               (1) 

where λm is the wavelength of the measuring unit, n is an integer 
number of wavelengths travelled by the wave, Δλm is a fraction 
of the wavelength travelled by the wave.  

Figure 1. Working principle of a laser interferometer.  



 

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The fraction of the wavelength travelled by the wave (Δλm,), 
when the phase angle of the transmitted wave is φ1 and the 
phase angle of the received wave is φ2, is expressed as follows: 

 
mm 




2
12                        (2) 

Deterioration of the inner system components over time can 
influence the measurement results. Therefore, instruments have 
to be tested regularly to determine short periodic or cyclic 
errors. The cyclic error is sinusoidal with a wavelength equal to 
the unit length of the instrument. 

3.1.  The former stand for cyclic error determination 

A 15 m geodetic baseline for EDM short distance calibration 
at the Vilnius Gediminas Technical University was established 
in collaboration with the Finish Geodetic Institute in 2001. In 
total 16 stands were attached to the grooved profile which was 
fixed to a stabilized wall. One stand was established especially 
for EDM mounting and the other 15 for reflector mounting. 
All the stands were aligned, levelled and established at a pitch of 
1 m.   

The basement location of this laboratory led to a stable 
construction of this bench.  After establishment this bench was 
calibrated by the Finish Geodetic Institute. A Wild Distomat 
DI 2002 and a Wild Theomat T2002 tachometer along with a 
Wild GPH1AP reflector were calibrated at the Nummela 
Standard Baseline and used for distance measurements.  In total 
70 lengths were measured performing repetitive measurements 
from stands 0, 2, 5, 7, 8. Calibration results are shown in Table 
1. 

 These indoor facilities can be used for all electronic distance 
measuring equipment. The EDM of laser scanners are also 
calibrated using this cyclic error determination baseline. The 
target is placed on the established stands and scanned. Each 
scanned target consists of a cloud of approx. 39 000 points 
which are used to determine the coordinates of the target 
centres. Then the measured distances are compared with the 
calibrated distances between the cyclic error determination 
baseline stands [1]. 

3.2. The linear bench under development 

Distance measurement equipment has long been tested and 
controlled by implementing non automated measurements and 
measuring objects at certain well-known distances. At the 
Institute of Geodesy such principle has been used by 
implementing multiple fixed indoor stands for short distance 
measurements and cyclic error correction, as well as several 
fixed outdoor pillars were used for long distance measurement 
control. Nonetheless, implementation of such instrumentation 
requires a lot of human interaction in the process which slows 
down the process considerably and introduces multiple 
operator related errors. Additionally, since modern electronic 
measurement equipment (distance meters, total stations etc.) 
can determine an enormous amount of measurement data with 
very high resolution, the implementation of fixed pillars for 
error determination is not fully correct. The distances between 
fixed stands might include possible systematic errors which are 
left uncovered by such a calibration. The issues like the 
calibration step under laboratory conditions are neither covered 
in the international standards (i.e. ISO). 

Implementation of automated measurement and control of 
the process would allow to increase both the speed and the 
accuracy of the measuring process. However, automated 
systems are available mostly for short distances. Although the 
mentioned automation brings in lots of benefits to the 
measurement process, it still remains costly, complex and not 
always affordable for some organizations. Therefore, the 
Institute of Geodesy is developing a linear test bench consisting 
of standard components and cost effective aluminum profiles. 

The test bench implements the distance meters’ cyclic 
correction stand composed of multiple firmly mounted 
supports as the base for the linear movement rail. The rail itself 
is a standard aluminum profile made for steel roller bearing 
linear guides to roll the mounted moving car. Implementation 
of aluminum profiles ensures a lower total mass relevant due to 
implementation of inherited components of the base. However, 
some inaccuracies due to the lower stiffness are unavoidable. 
The profile rail is connected supports (with a step of 2 meters) 
and precisely levelled. Preliminary design of the linear 
calibration bench and its components (a – moving carriage, b – 
rails, c – supports, d – reflector for total station measurements, 
e – corner cube fixed to the moving carriage to create the path 
for the split laser beam, l - distance between the firmly mounted 
supports, 1 meter) is shown in Figure 3.  

The moving carriage of the bench is an aluminum body plate 
moving on precise ball bearings. A motorized linear air bearing 
would be the main component ensuring a smooth motion of 
the carriage. Therefore, vertical and horizontal straightness as 
well as rotational motion errors have to be determined before 
using the carriage for the calibration of length measuring 
instruments [2]. 

Implementation of aluminum here is preferable due to the 
decrease of moving mass its inert influence on the rail profile. 

Figure 2. Principle of phase shift measurement.  

Table 1. The results of distance measurements between the stands. 

Stand 
number 

Measurement result 
Y±U95% (k=2) 

0‐1    1000.2 mm ± 0.5 mm 

0‐2    2000.6 mm ± 0.2 mm 

0‐3    3001.4 mm ± 0.3 mm 

0‐4    4001.4 mm ± 0.4 mm 

0‐5    4999.2 mm ± 0.3 mm 

0‐6    5999.2 mm ± 0.5 mm 

0‐7    7000.8 mm ± 0.3 mm 

0‐8    7997.9 mm ± 0.3 mm 

0‐9    9000.8 mm ± 0.5 mm 

0‐10  10001.0 mm ± 0.5 mm 

0‐11  10999.2 mm ± 0.5 mm 

0‐12  12000.4 mm ± 0.5 mm 

0‐13  12998.9 mm ± 0.5 mm 

0‐14  14000.4 mm ± 0.5 mm 

0‐15  15005.1 mm ± 0.5 mm 

A'

B

B

A

A

nλm ∆λm

DD

Φ1=0° Φ2=90



 

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The movement of the car is automated by step motors (with 
coarse distance determination) and the car can be positioned at 
practically any linear position within the distance of the bench. 
The precise position of the car is determined by a stationary 
fixed Renishaw interferometer with its mirror mounted on the 
moving car. 

For the uncertainty evaluation it is important to consider 
the following aspects. Since the aluminum profile is supported 
at a pitch of 1 m, the deflection of the profile is 0.03 mm in 
every stretch with a bending stress of 0.74 N/mm2 because of 
both carriage and reflector weights, which is up to 10 kg. EMD 
measurements are mostly affected by environmental conditions 
which can be minimized by performing measurements in a 
laboratory. However, stabilizing the temperature and 
atmospheric correction is obligatory according to ISO 17123:5 
because temperature, pressure and humidity affect the velocity 
of the signal. It is also very important to perform slope and 
zero point corrections. Zero point errors are related to electrical 
delays, the differences between the electronic and mechanical 
center of the instrument. The scale error which is caused by 
internal frequency errors also has an impact on measurement 
results. The abbe error is one of the main error sources in these 
linear measurements because of nonlinearity of the carriage 
base plate and the rails. To sum up, the alignment of reflector 
and total station, abbe error and the motion of the carriage are 
the main uncertainty sources.  So far the research showed that 
an expanded uncertainty of 3.0·10-6 m for 13 m displacement 
can be achieved, however, the system needs to be stabilized and 
further multiple measurements in various displacements will be 
provided with mentioned uncertainty components in further 
research. 

4. CONCLUSIONS 

The assumptions of using fixed cyclic error determination 
stands as a base for the development of a linear calibration 
bench with an automated moving carriage are presented in this 

paper. The advantages of this proposed bench are the 
lightweight of the used materials as well as a cost saving 
solution. However, it is more complicated to precisely control 
the environment where the calibration is performed. 

The main purpose of this linear bench is to reduce human 
interaction in the process and to determine cyclic and other 
distance measurement errors by performing measurements at a 
desired distance within the length of the bench. 

ACKNOWLEDGEMENT 

This research is funded by the European Social Fund under 
the Global Grant measure (project No. VP1-3.1-ŠMM-07-K-
01-102). 

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Figure 3. Preliminary design of the linear bench.