WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --This Is How PI Does Measuring - Part II
Positioning Accuracy, Repeatability, and similar Measurements: Measurement Procedure and Data Preparation at PI

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

Page 1 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --1 Qualification of Positioning
Axes
Measurements are carried out on prototypes, individual
products and series-production products to qualify the
positioning axes produced by PI (Physik Instrumente). In thecase of series-production products, valid specifications arederived based on these measured values and then published in
the datasheets. These specifications describe the fundamental
positioning characteristics for a product type, such as e.g.
positioning accuracy, angular error in multiple axes, andunidirectional and bidirectional repeatability.
It is important particularly in the design of customer-specificsolutions that there is a common understanding of what the
specifications are because it is only in this way that the design
can be clearly defined.
This document describeswhich measurements are carried out and whichmeasurement methods are used,which standards are considered to this process,how the data acquired from the measurements is
prepared,
how measurement results are derived from the data andwhat terminology is used to describe them.

In addition, this document provides a brief overview of themeasurement protocol and the measurement results that arereported and how both are structured.

ISO 230 series of standards with respect to the measurements
described in this document.
A major disadvantage of the stated standards for thequalification of micropositioning and nanopositioning systems
is the fact that they were actually designed for larger turning
lathes, milling machines, and similar products. Therefore, theexplanations and detailed descriptions for the methods
described in these standards are not always applicable for thequalification of products that are produced for high-precision
micropositioning and nanopositioning. If it was not possible totransfer the ideas from these standards directly to thequalification of PI products, the measurement rules describedin these standards were modified.
This means that the measurement rules used at PI are not a
direct copy of the stated standards but rather they include
specific adaptations and, in particular, enhancements of themwith the aim of being able to test micropositioning andnanopositioning axes in the best way possible.
PI actively takes part in the current ASME B5.64
standardization committee which works on the developmentof a measuring standard for micro and nanopositioning
systems.

2 Applicable Standards andSpecial Features of Precision
Positioning

3 Basic Measurement Procedureand the Measuring Equipment
Used

The measurement rules described here are mainly based on
the ISO 230 series of international standards, whereby thestandards ISO 230-1 (2012-03) and ISO 230-2 (2014-05) areprimarily relevant, as well as the American standard ASME
B5.54 (2005). This standard is to a large extent identical to the

3.1

General Measurement Procedure

The positioning axes produced by PI are designed and specified
for a defined travel range.

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Page 2 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --Definitions: The travel range is the range within which
the controller can move the system to different
positions. The measuring range lies within this travel
range or corresponds to the maximum travel range. The
end points on each measuring range are always
approached unidirectionally. All other measurement
points can be approached bidirectionally. The
classification "unidirectional" indicates a measurement
series in which the movement to a target position isalways carried out in the same direction, while"bidirectional" indicates that the movement to a target
position is from both directions (forwards andbackwards).
In order to determine a measurand, positions within the travel
range are approached bidirectionally and a measurement istaken at the position. This is not possible at the end points ofthe travel range because these points represent the end of thenumerically controllable range and these positions can only bereached coming from one direction. The so-called bidirectional
measuring range excludes the end points and is thereby always
a bit shorter than the entire measuring range.
The data measured unidirectionally at the end points of themeasuring range are only used for determining selected
measurands. For example, this data is used to determine thestroke, which ensures that the positioning axes can also be
traversed along the specified path.
The positions within the measuring range at whichmeasurement data are recorded are named target position Pi.
As standard, target positions at the measurement points at theends of the measuring range (two points) and another 18
points distributed equidistantly along the measuring range aremeasured, which makes 20 target positions in total.
The axes are traversed to these target positions to record themeasurement data in a meandering pattern (see Figure 1) andthe positioning data is recorded using suitable measuring
equipment. The entire bidirectional cycle is completed fivetimes as standard so that it is possible to record five sets ofunidirectional measurements in both directions.

standstill and only then is the measurement data recorded
using corresponding measuring equipment.

Illustrative representation of the cycle used to record themeasurement data.

Using these measurements, the positioning error is calculated
for every target position. These positioning error xij↑ or xij↓
thus correspond to the difference between the current
position actually reached Pij and the target position Pi. The
corresponding positioning error is calculated for every cycle j
at the target position i as follows:𝑥𝑥𝑖𝑖𝑖𝑖 = 𝑃𝑃𝑖𝑖𝑖𝑖 − 𝑃𝑃𝑖𝑖The symbols ↑ and ↓ indicate the direction from which thetarget position was reached.

3.2

Measuring Equipment

The measurement data is usually recorded using
interferometers to determine the linear deflection andautocollimators to determine the angular error.

The entire measurement process only uses static
measurements. This means that the axes are traversed to atarget position, the moving platform is allowed to come to a

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
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Page 3 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --A typical measurement setup, from left: an autocollimator tomeasure angular errors, a positioning axis on which two reflecting
mirrors are mounted, and an interferometer setup to measure thedisplacement.

This type of setup is shown in Figure 2. An interferometer isused from one direction to determine the linear displacementof the axis being tested, while an autocollimator is used todetermine the angular error from the opposite direction at thesame time. The positioning axis is equipped with two reflector
mirrors, which are used by the interferometer andautocollimator for their measurements. The measuring
equipment used by PI is described in more detail in the
Whitepaper “This is how PI Does Measuring - Part I”.

3.3

Correction of the Raw Data

3.3.1 Correction of the Abbe Error
An Abbe error occurs when an angular error has caused anerror in the linear measurement (e.g. positioning accuracy).

Abbe errors for both angles α, β: red = measuring beam, lα and lβ
describe the distance to the axes with respect to theinterferometer's measuring point. A correction is made to arrive
at a point located at the surface of the moveable platform.

This is illustrated in Figure 3: Due to the tilt of the moveable
platform, there is an angular error when the beam from theinterferometer hits the measurement mirror. The effect on thelinear measurement value depends on the distance between
the mirror and the platform. There is thus an error in themeasurement value that can be corrected accordingly andeliminated from the data.
Depending on the setup of the measuring equipment relative
to the moveable platform, there can be an Abbe error in one
or two directions.
To calculate the correction, the linear measurement values areadjusted based on the angular data measured using the
autocollimator. The distance between the moveable mirror
and the surface of the moveable platform is determined andused for the calculation. This distance is also stated in themeasurement protocol. Therefore, the measurement protocol
shows whether or not a tilt correction of the measurement
data has been carried out.
The angular and linear measurements are carried out
separately from one another at PI. This means that the linear
and angular errors can be distinguished from one another andare reported separately.
If an Abbe error has been corrected during the test procedure,
the surface of the moveable platform is used as the reference
surface. The correction is calculated based on this surface.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
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Page 4 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --Using this information, the resulting positioning error for
points at any distance to the platform can also be calculated.

4 Data Analysis

3.3.2 Correction of Thermal Drift

The calculation rules and the corresponding calculation
formulae used to evaluate the measurement data arepresented here.

It is not always possible to fully compensate for the influenceof thermal fluctuations by monitoring and managing theambient conditions. This is especially the case for positioning
axes with resolutions and accuracies down to thesubnanometer range. Even the smallest change in temperatureduring the measurement procedure can cause changes inposition due to thermal expansion of the measurement setup
or measuring equipment. Also mechanical tension in themeasurement setup and the resulting relaxation processes
lead to such changes in position. If the highest level of accuracy
is required, these effects can have a massive influence on themeasurement results. Therefore, it may be necessary tocorrect for these thermal effects.
The measurement data is corrected based on the following
assumptions:The positioning axis that is being tested does not itself
change over time, except for the mechanical changes
resulting from changes in temperature.
If the temperature were stable, the first measurement
point would always be measured at an identical position.
Thermal drift is not position-dependent but rather timedependent.

To make the correction, a straight line is calculated through thefirst measurement points of repeated sets of measurements
taken one after another. This straight line (temporal) can thenbe subtracted from the measurement data for one set ofmeasurements. This makes it possible to compensate forthermal drift.
The protocol indicates whether or not a correction has been
carried out for thermal drift.

3.3.3 Linear Correction of Raw Data
If only the deviation from an ideal straight line is of interest foran evaluation, the raw data have to be initially corrected
linearly. This means that a regression line is subtracted fromthe positioning error xij with respect to the commanded target
position Pi. This is calculated according to the method of leastsquares.

4.1

Basic Data for the Positioning Error

Firstly, the unidirectional positioning error is determined atevery measured target position for both directions 𝑥𝑥𝑖𝑖 ↑ and𝑥𝑥𝑖𝑖 ↓. This data is then used to calculate the mean positioning
errors 𝑥𝑥̅𝑖𝑖 ↑ and 𝑥𝑥̅𝑖𝑖 ↓ for both directions at every individual
position:
𝑥𝑥̅𝑖𝑖 ↑=𝑛𝑛1
� 𝑥𝑥𝑖𝑖𝑖𝑖 ↑
𝑛𝑛
𝑗𝑗=1

and
𝑥𝑥̅𝑖𝑖 ↓=𝑛𝑛1
� 𝑥𝑥𝑖𝑖𝑖𝑖 ↓𝑛𝑛
𝑗𝑗=1

Using the mean positioning error at the points 𝑥𝑥̅ 𝑖𝑖 ↑ and 𝑥𝑥̅𝑖𝑖 ↓,which only measure the two individual directions (forwards
and backwards), the mean value is determined. This is themean bidirectional positioning error at every individual
position 𝑥𝑥̅𝑖𝑖 :𝑥𝑥̅𝑖𝑖 =

𝑥𝑥̅𝑖𝑖 ↑ +𝑥𝑥̅𝑖𝑖 ↓2

The calculated values can be used to plot a mean curve thatshows the mean errors of the axis across the entire travel range(see Figure 4).
The mean values show the systematic deviation. Other
variables for a positioning axis can be attributed to statisticaldeviations. For this reason, the standard deviations at therespective target positions Pi are determined separately for theforwards and backwards directions. This is carried out using
the following formulae:

The measurement protocol indicates whether or not a linear
correction has been carried out.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
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Page 5 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --The mean bidirectional positioning error M is the
maximum deviation (peak-peak) of the mean curveas described above, meaning the mean positioning
error of the axis.

𝑛𝑛

12
𝑠𝑠𝑖𝑖 ↑= ���𝑥𝑥𝑖𝑖𝑖𝑖 ↑ −𝑥𝑥̅ 𝑖𝑖 ↑�𝑛𝑛 − 1
𝑗𝑗=1

andThis is shown in red in Figure 5.

𝑠𝑠𝑖𝑖 ↓= �𝑛𝑛

1
2
��𝑥𝑥𝑖𝑖𝑖𝑖 ↓ −𝑥𝑥̅ 𝑖𝑖 ↓�𝑛𝑛 − 1
𝑗𝑗=1

These five datasets together provide a good overview of thesize of the statistical deviations and how the positioning axis
behaves over the measuring range. Figure 4 shows an example
overview of the complete data. Other variables can becalculated on this basis.
The mean bidirectional positioning error M

If a correction line (see 3.3.3) has been subtracted from theraw data when calculating M, this value is designated as ML .

4.3

The positioning error for an axis for both the forwards andbackwards directions

The Backlash B

To determine the size of the error between the positioning
processes in the forwards and backwards directions, themaximum positioning backlash B is calculated. It represents
the maximum deviation between the forwards and backwards
directions.
𝐵𝐵 = 𝑚𝑚𝑚𝑚𝑚𝑚 [|𝑥𝑥̅𝑖𝑖 ↑ −𝑥𝑥̅𝑖𝑖 ↓|]4.2

The Mean Bidirectional Positioning Error
M

This is shown in red in Figure 6.

The mean bidirectional positioning error M is the difference
between the maximum and minimum values for the meanbidirectional positioning errors at the points 𝑥𝑥̅𝑖𝑖
𝑀𝑀 = 𝑚𝑚𝑚𝑚𝑚𝑚( 𝑥𝑥̅𝑖𝑖 ) − 𝑚𝑚𝑚𝑚𝑚𝑚 ( 𝑥𝑥̅𝑖𝑖 )Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
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Page 6 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --Accordingly, the maximum bidirectional repeatability is the
maximum value of the repeatability values at the target
positions:
𝑅𝑅 = 𝑚𝑚𝑚𝑚𝑚𝑚 [𝑅𝑅𝑖𝑖 ]This is shown in red in Figure 7.

The maximum positioning backlash B

A mean backlash can also be determined on this basis. This
indicates the size of the mean deviation between the forwards
and backwards directions. To determine the mean positioning
backlash 𝐵𝐵�, the sum of the mean values for the backlash at allindividual positions is determined as follows:𝐵𝐵� = �𝑚𝑚

1
�(𝑥𝑥̅𝑖𝑖 ↑ −𝑥𝑥̅𝑖𝑖 ↓)�
𝑚𝑚
𝑗𝑗=1

The backlash B indicates how the positioning axis
behaves if the direction is reversed.

4.4

Unidirectional and Bidirectional
Repeatability R

Another important characteristic of a positioning device isrepeatability.
To calculate the repeatability, the bidirectional positioning
repeatability 𝑅𝑅𝑖𝑖 is first calculated for one position. It is
calculated as follows:
𝑅𝑅𝑖𝑖 = max[𝑠𝑠𝑖𝑖 ↑ +𝑠𝑠𝑖𝑖 ↓ +|𝐵𝐵𝑖𝑖 |; 2𝑠𝑠𝑖𝑖 ↑; 2𝑠𝑠𝑖𝑖 ↓]with𝐵𝐵𝑖𝑖 = 𝑥𝑥̅𝑖𝑖 ↑ −𝑥𝑥̅𝑖𝑖 ↓The bidirectional repeatability indicates how "well"each individual target position will always be "hit"from different directions.

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The maximum bidirectional repeatability R, as well as,
for example, R1 for the first target position

The maximum unidirectional positioning repeatability
𝑅𝑅 ↓↑ is the maximum value of the standard
deviations of the unidirectional repeatability for apositioning axis:
𝑅𝑅 ↓↑= ± 𝑚𝑚𝑚𝑚𝑚𝑚 [𝑠𝑠𝑖𝑖 ↑; 𝑠𝑠𝑖𝑖 ↓ ]The maximum unidirectional repeatability
indicates how large the maximum
deviation at any target position can bewhen approaching the position from thesame direction.

The value for the unidirectional positioning
repeatability is given as a ± value.
The average unidirectional positioning repeatability
𝑅𝑅� ↓↑ is calculated as follows:
1 𝑚𝑚
1∑𝑖𝑖=1 𝑠𝑠𝑖𝑖 ↑ + ∑𝑚𝑚
𝑖𝑖=1 𝑠𝑠𝑖𝑖 ↓𝑚𝑚𝑚𝑚
�𝑅𝑅 ↓↑= ±2

It is the average of the unidirectional repeatabilities
in both directions.

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WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --4.5

The Bidirectional Positioning Accuracy A

4.7

The bidirectional positioning accuracy A is ameasurand that combines all of the errors that arise
and thus represents the maximum error that canoccur during positioning.
The bidirectional positioning accuracy is the range that is
calculated by combining the bidirectional systematicdeviations with the statistical deviations:
𝐴𝐴 = 𝑚𝑚𝑚𝑚𝑚𝑚 [𝑥𝑥̅𝑖𝑖 ↑ +𝑠𝑠𝑖𝑖 ↑; 𝑥𝑥̅𝑖𝑖 ↓ + 𝑠𝑠𝑖𝑖 ↓] − 𝑚𝑚𝑚𝑚𝑚𝑚 [𝑥𝑥̅𝑖𝑖 ↑ − 𝑠𝑠𝑖𝑖 ↑; 𝑥𝑥̅𝑖𝑖 ↓ − 𝑠𝑠𝑖𝑖 ↓]The Linearity L
The linearity describes the maximum deviation fromthe measured values for an ideal straight line.

To calculate the linearity, the measured values at the target
positions P0 to Pm+1 are used. A straight line is taken that passes
through the end points of the measuring range and is
subtracted from the calculated deviations. These calculated
errors are then designated xlij.
Accordingly, the positioning linearity L is calculated as follows:𝑛𝑛1
𝐿𝐿 = 𝑚𝑚𝑚𝑚𝑚𝑚 �� � 𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 ↑��𝑛𝑛This is shown in red in Figure 8.

𝑗𝑗=1

This is shown in red in Figure 9.

The bidirectional positioning accuracy A

To ensure the consistency of the bidirectional repeatability,
the calculation for the bidirectional positioning accuracy uses
only one standard deviation and not two standard deviations.

4.6

The Stroke S

Determination of the positioning linearity L

This can be used to calculate the percentage linearity Lp (inpercent) where Lm denotes the measuring range:

The testing of a positioning axis shall prove that the entire
travel range can be used, which means that the axis being
tested can reach every numerically controlled target position if
the travel range was also selected as the measuring range. For
this purpose, the mean values for the positions at the end
points of the measuring range are determined. The difference
between these values is the stroke S of the positioning axis.

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𝐿𝐿𝑝𝑝 = 100 ∙

𝐿𝐿
𝐿𝐿𝑚𝑚

Page 8 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --4.8

The Hysteresis H

The hysteresis H of an axis is the maximum difference of
forwards and backwards values at all target positions:
𝑛𝑛

𝑛𝑛

𝑗𝑗=1

𝑗𝑗=1

1
1
𝐻𝐻 = 𝑚𝑚𝑚𝑚𝑚𝑚 �� � 𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 ↑ − � 𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 ↓��𝑛𝑛𝑛𝑛
The calculation of H is carried out in the same way as thecalculation of the backlash B.
Accordingly, the percentage hysteresis Hp (in percent) is
calculated as follows
𝐻𝐻𝑝𝑝 = 100 ∙

𝐻𝐻
𝐿𝐿𝑚𝑚

5 Annex 1: The Coordinate
Systems Used and Designationsof the Axes of Motion
In general, PI uses a right-handed coordinate system todesignate the axes of motion. The linear axes are thus labeledwith X, Y, and Z and the rotational axes with A, B, and C. The
rotational axes are assigned according to the linear axes, e.g. A
is the rotational axis around the linear axis X.
In places where further clarification is necessary, the rotationalaxes are also labeled with an explicit reference to the linear
axes, e.g. A (rot X). To illustrate how the axes are designated,the coordinate system is once again shown in Figure 10.

Right-handed coordinate system

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WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --6 Annex 2: Mechanical Crosstalkof a Movement and
Designation of the Error
In the case of mechanical positioning axes, it is usually not justthe positioning error in the direction of motion that is relevant
but also the mechanical crosstalk of a linear motion in theother linear and rotational directions. To determine thismechanical crosstalk, linear measurements orthogonal to thedirection of motion and corresponding angle measurements
are carried out. Here, a measurement is carried out according
to the motion profile of the measurement procedure describedin chapter 3.1. The same methods as for the positional data areused to analyze these data. However, the analysis does not
subtract the actual position from the target position but uses
the raw data.
Straightness and flatness are calculated from the meanbidirectional positioning error after a linear correction ML has
been carried out.

Nomenclature of errors in the various axes for a linear motion.

It is still important to note here that the rotational error cantransfer to a translational error at the functional point incertain circumstances, depending on where the zero point forthe parasitic tilt lies.

The nomenclature used at PI for these different errors is thus
as follows:

The errors themselves have a clear nomenclature. The various
measurable errors for linear motion are shown in Figure 11.

X

Axis of the commanded linear motion

EAX
EBX
ECX

Angular error around the X-axis (roll)
Angular error around the Y-axis (pitch)
Angular error around the Z-axis (yaw)E <Axis designation where the error has been measured><commanded axis>

EXX Positioning error of the X-axis
EXXL Positioning error of the X-axis, minus regression line
EYX Straightness error in the direction of the Y-axis(straightness)
EZX Straightness error in the direction of the Z-axis (flatness)
If two axes are moving (e.g. X and Y), it is still possible for a
combined parasitic motion to occur in the Z-axis. This error iscalled the out-of-plane error.
Similar errors can also be found on rotational positioning axes.
Accordingly, Figure 12 shows the various measurable errors forrotational motion.

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Page 10 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --7 Annex 3: Example
Measurement Protocol
The data from the measurements and calculations can beaccessed by outputting them to a measurement protocol. An
example protocol is shown in Figure 13. The protocol is split
into different sections:1.

General description, e.g. of the system components andparameters

2.

Description of the measurement, e.g. axes, measuring
range, measuring parameters, corrections

3.

Measurement results, e.g. the linear deviations

4.

Measurement results, e.g. the angular deviations

5.

Graphical representation of the measurement results

The calculation rules for the measurement values given in 3.
and 4. are described in chapter 4 and can thus be derived fromthe stated formulae. This applies for both linear deviations andangular deviations.

Nomenclature of errors in the various axes for a rotary motion.

EXC
EYC
EZC

Radial error in the direction of the X-axis
Radial error in the direction of the Y-axis
Axial error from C

EAC
EBC
ECC

Tilt error around the X-axis
Tilt error around the Y-axis
Angular positioning error of C

A combined rotatory error, i.e. a radial error motion, is
described as follows:
EXYC

Radial error of C

Accordingly, a combined tilt deviation is referred to as follows:
EABC

Tilt error of C

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WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --

1.

2.

3.

4.

5.

Fig. 13 Example measurement protocol

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Page 12 of 13

WHITEPAPER – This is How PI Does Measuring – Part II-- Dr. Axel Grabowski, Peter Diez, Birgit Schulze --8 Other Documents and Links
Whitepaper This is how PI Does Measuring - Part I
https://www.physikinstrumente.de/fileadmin/user_upload/physik_instrumente/files/WP/PI-WP4011D-MesstechnikMessumgebung.pdf

Birgit Schulze, Product Marketing
Manager for Parallel Kinematics at
Physik Instrumente (PI) GmbH & Co.
KG

ISO 230-1
https://www.din.de/de/mitwirken/normenausschuesse/nwm/normen/wdc-beuth:din21:151552174

https://www.din.de/de/mitwirken/normenausschuesse/nwm/normen/wdc-beuth:din21:206720855
ASME B.5.54 - 2005
https://www.asme.org/codes-standards/find-codesstandards/b5-54-methods-performance-evaluationcomputer-numerically-controlled-machining-centers

9 Authors

Dr. Axel Grabowski, Head of R&D
Department Sensor Technologies at
Physik Instrumente (PI) GmbH & Co.
KG

PI in Brief
For many years, PI (Physik Instrumente), founded in 1970, hasbeen a market and technology leader for high-precision
positioning technology and piezo applications in thesemiconductor industry, life sciences; photonics, and inindustrial automation. In close cooperation with customers
from all over the world and for 50 years now, PI's specialists(approx. 1,300) have been pushing, again and again, theboundaries of what is technically possible and developing
customized solutions from scratch. Technologies from PI
achieve reproducible accuracies in the millionth of a millimeter
range. More than 350 granted and registered patents
underline the company's claim to innovation.
PI develops, manufactures, and qualifies all core technologies
in-house, thereby constantly setting new standards for
precision positioning: Piezoceramic patch transducers andactuators, electromagnetic drives, and sensors working in thenanometer range. As the majority owner of ACS Motion
Control, PI is also a leading global manufacturer of modular
motion control systems for multi-axis drive systems anddevelops customized complete systems for industrial
applications with the highest precision and dynamics.
With six manufacturing sites and 15 sales and service offices in
Europe, North America, and Asia, PI is represented whereverhigh-tech solutions are developed and manufactured.

Peter Diez, Senior Industrial
Engineer in the Measurement andProduction Technology Group at
Physik Instrumente (PI) GmbH & Co.
KG

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WP4032E Positioning Accuracy, Repeatability, and similar Measurements 12/2020 0 Subject to changes. © Physik Instrumente (PI) GmbH & Co. KG 2020

ISO 230-2