Training program for the metric specification of imaging sensors


ACTA IMEKO 
ISSN: 2221-870X 
December 2022, Volume 11, Number 4, 1 - 6 

 

ACTA IMEKO | www.imeko.org December 2022 | Volume 11 | Number 4 | 1 

Training program for the metric specification of imaging 
sensors 

Raik Illmann1, Maik Rosenberger1, Gunther Notni1 

1 Technische Universität Ilmenau, Gustav Kirchhoff Platz 2, 98693 Ilmenau, Germany  

 

 

Section: RESEARCH PAPER  

Keywords: Measurement education; measurement training; engineering education; hands-on pedagogy; image sensor characterization 

Citation: Raik Illmann, Maik Rosenberger, Gunther Notni, Training program for the metric specification of imaging sensors, Acta IMEKO, vol. 11, no. 4, 
article 10, December 2022, identifier: IMEKO-ACTA-11 (2022)-04-10 

Section Editor: Eric Benoit, Université Savoie Mont Blanc, France  

Received August 26, 2022; In final form December 2, 2022; Published December 2022 

Copyright: 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. 

Corresponding author: Raik Illmann, e-mail: raik.illmann@tu-ilmenau.de  

 

1. INTRODUCTION 

Optical coordinate metrology is an essential part of industrial 
automation and inspection processes. Therefore, this subject 
area should play an essential role in today's engineering education 
in courses such as mechanical engineering, electrical engineering, 
computer science or engineering informatics. Thus, the question 
arises, how to efficiently teach essential contents, which are 
necessary for a successful handling of this topic in engineering 
practice. The requirements are that both the basics and the 
relevance have been understood, and that the systems 
engineering integration can be implemented on the basis of the 
learned knowledge and transferred into a functional system. 

Group work and the targeted intervention of a supervisor play 
an essential role here. Not only in order to close existing 
knowledge gaps in a targeted manner, but also in order to train 

the cooperation in teams with corresponding social competence, 
which is inevitable in practice. 

The central topic of the program is the metric characterization 
of imaging sensors. With regard to practice, two essential 
technological aspects can be taught through this. First, it is 
crucial for the implementation of a test system to be able to 
evaluate and classify geometric product specifications (GPS) 
characterized by the manufacturer of an image sensor, i.e., 
ultimately to be able to understand its test procedure. Secondly, 
this makes essential principles of image signal processing 
accessible and also provides a practical and comprehensible 
application case, which proves the usefulness of the methods and 
thus offers the motivation directly on the basis of the concrete 
example. The standard DIN EN ISO 10360 [1] is used as the 
basis for the methodical procedure; for coordinate measuring 
machines with optoelectronic sensors, the VDI standard 2617 [2] 
is used specifically. It describes the inspection of coordinate 

ABSTRACT 
Measurement systems in industrial practice are becoming increasingly complex and the system-technical integration levels are 
increasing. Nevertheless, the functionalities can in principle always be traced back to proven basic functions and basic technologies, 
which should, however, be understood and developed. For this very reason, the teaching of elementary basics in engineering education 
is unavoidable. The present paper presents a concept to implement a contemporary training program within the practical engineering 
education on university level in the special subject area of optical coordinate measuring technology. The students learn to deal with the 
subject area in a fundamentally oriented way and to understand the system-technical integration in detail from the basic idea to the 
actual solution, which represents the common practice in the industrial environment. The training program is designed in such a way 
that the basics have to be worked out at the beginning, gaps in knowledge are closed by the aspect of group work and the targeted 
intervention of a supervisor. After the technology has been fully developed theoretically, the system is put into operation and applied 
with regard to a characterizing measurement. The measurement data are then evaluated using standardized procedures. A special part 
of the training program, which is to promote the own creativity and the comprehensible understanding, represents the evaluation of 
the modulation transfer function of the system by a self-developed algorithmic program section in the script-oriented development 
environment MATLAB, whereby students can supportively fall back on predefined functions for the evaluation, whose implementation 
however still must be accomplished. 

mailto:raik.illmann@tu-ilmenau.de


 

ACTA IMEKO | www.imeko.org December 2022 | Volume 11 | Number 4 | 2 

measuring machines by measuring calibrated test samples. This 
involves checking whether the measurement deviations are 
within the limits specified by the manufacturer or user.  The test 
samples must be such that their properties do not decisively 
influence the parameters to be determined. The characterization 
is carried out on the basis of the principle described in [2] a circle 
measured at five different positions. For this purpose, a 
calibrated chrome standard and a through-light unit are used. 
After completion of the measurements, the results are to be 
statistically evaluated in accordance with the standard. In 
addition, the determination of the modulation transfer function 
(MTF) is intended to provide an assessment of the resolving 
capability of the overall system and to train an in-depth 
algorithmic understanding of 2D image processing. 

2. THEORETICAL BACKGROUND 

2.1. Problem description 

The metrological problem with which the students are to be 
confronted is described in Figure 1. A calibrated sample with a 
circular ring (object) is placed as a normal on a light source. The 
circular ring passes (as a negative) through an optical system 
which consists of lenses and apertures. The image that is 
consequently created on the sensor surface deviates from the 
original image due to optical and mechanical influences. In 
addition, geometric quantization during scanning within the 
image sensor produces a further measurement deviation. All 
deviations in sum result in a total measurement deviation which 
has to be determined. Further it can be observed that with a 
change of the position of the object (5 different positions in [2]) 
due to the influences of the optics and mechanics the measured 
diameters of the circular rings differ. This also has to be 
quantified. 

2.2. Analysis of measurement uncertainty 

All image processing algorithms are already implemented in 
software, so that the diameter of the circular ring is output as the 
result of the measurement. The algorithms for edge detection are 
subpixel-based and very complex, therefore a more detailed 
description is not provided within this paper so reference is made 
to special literature [3]. More crucial for the metric testing of the 
image sensor system is the consideration of the measurement 

uncertainties. According to the formulas 1-3 the total 
measurement uncertainty can be determined.  

The measurement uncertainty describes the deviation 
behaviour of the overall system. The total value of the 
measurement uncertainty is determined by the errors of the two 
essential assemblies, the mechanical and the optical measuring 
device, and results from: 

𝑈total = √𝑈mech
2 + 𝑈opt

2  . (1)  

Both mechanical and optical measurement uncertainty can be 
further divided into systematic and random measurement 
uncertainty. They result from: 

𝑈mech = √𝑈sys,m
2 + 𝑈random,m

2  (2)  

and 

𝑈opt = √𝑈sys,o
2 + 𝑈random,o

2  . (3)  

The systematic measurement uncertainty is usually specified 
by the manufacturer and is determined from comparative 
measurements with calibrated standards. Within the training 
program these are given to the students. 

The random measurement uncertainty, on the other hand, is 
determined by several measurements carried out in the training 
program under the same environmental conditions and with the 
same test specimen. The standard deviation can now be 
calculated from the measured values obtained. 

𝜎 = √
1

𝑛 − 1
∑(𝑥𝑖 − �̄�)

2

𝑛

𝑖=1

 . (4)  

The random measurement uncertainty 𝑈random,MS of the 

measurement series 𝑈zuf,MR is now obtained, using the 95.4% 
confidence level. 

𝑈random,MS =
2 𝜎

√𝑛
 . (5)  

 

Figure 1. Schematic system description. 



 

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However, since the mechanical and optical measurement 
uncertainties in the measurement result cannot be separated 
directly with the available setup, the evaluation is simplified 
somewhat at this point and only predefined systematic deviations 
are included in the calculation of the total measurement 
uncertainty. 

2.3. Modulation transfer function 

There are several approaches to determine the modulation 
transfer function (MTF). The main approaches are part of the 
teaching in parallel to the designed training program and are 
presented in the lectures. A simple and practically easy to 
understand method is described in [4] and [5]. Thereby, the 

intensity differences (contrasts, 𝐼max − 𝐼min) of a search ray 
orthogonal to a rectangular signal are evaluated. If instead of the 
rectangular signal a sinusoidal signal is assumed, the contrast 

transfer function 𝐶𝑇(𝑓) goes directly over into the modulation 
transfer function 𝑀𝑇𝐹(𝑓). Basically, the contrast ratios of the 
pattern in the image  𝐾(𝑓)  

𝐾(𝑓) =
𝐼max − 𝐼min
𝐼max + 𝐼min

 (6)  

have to be put into the ratio to the contrast in the object space 

𝐾′(𝑓). 

𝐾′(𝑓) =
𝐼max
′ − 𝐼min

′

𝐼max
′ + 𝐼min

′
 . (7)  

Plotted over the sampling points of the spatial frequency f as 
reciprocals of the line distances defined by the object, the MTF 
can thus be approximated  

𝐶𝑇(𝑓) =
𝐾′(𝑓)

𝐾(𝑓)
≈ 𝑀𝑇𝐹(𝑓) . (8)  

For the calculations according to (6), (7) and (8), all values can 
be determined from the measurements, which is why these 
formulas must also be implemented by the students in the 
practical part. Complex examples for modulation transfer 
functions of spectral sensors are given in [6]. 

3. MEASUREMENT SYSTEM DESCRIPTION 

3.1. Measurement system 

The system used for the experiment is shown in Figure 2. It 

consists of a monochromatic camera , a telecentric objective 

, a light table for measurement using the transmitted light 

method , a halogen-based light generator , and a stand 

construction in column design . 

3.2. Measurement targets 

Two samples are used for the training program. The first 
sample is shown in Figure 3 (left). In the sample, the metric 
dimensions are represented by circles. These circles are moved 
to the 5 positions described and the diameter of the 
corresponding circular ring is measured there in each case. The 
Second sample is a U.S. Air Force (USAF) test chart shown in 
Figure 3 (right), based on which the modulation transfer function 
is determined. 

4. TRAINING PROGRAM CONCEPT  

The training program is shown as a flow chart in Figure 4 and 
is described in detail below. 

4.1. Preparation and general aim  

The overall aim is to teach and consolidate the theoretical 
aspects. The theoretical basics are taught in preparation of the 
students in self-study. At the beginning of the training program, 
the supervisor checks the essential basics necessary for 
understanding the subject matter. Here it must be paid attention 
particularly on the part of the supervisor to recognize lack of 
understanding and to recognize possibly by further questions the 
actual knowledge conditions of the participants individually. 
Often misunderstandings or misinterpretations of the facts 
occur, which must be corrected. Interdisciplinary action should 
also be taken here, and basic mathematics or mechanics should 
also be addressed. Essentially, the following topics should have 
been learned at the end of the program: 

 

Figure 2. Measurement setup. 

   

Figure 3. Measurement targets. Circular rings chrome glass (left), USAF 
(right). 

 



 

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• knowing and understanding terms [1] 

• understanding the necessity of characterisation 
concerning engineering tasks 

• understanding measurement setup (incl. optics) 

• understanding the measurement procedure 

• reflection and deduce the causes of uncertainties in the 
measurement system 

• evaluating und visualize the data 

• encouraging the understanding of algorithms. 

It is also important that the supervision always refers to the 
method of application and integration of the systems and 
components in the engineering practical task. In this way, the 
important practical relevance is continuously maintained. After 
verification of qualification and the elimination of 
misunderstandings, instruction is given in the measurement 
setup and operation of the software. 

4.2. Measurement process 

The measurement is performed according to the instructions 
given in [2]. Regarding the training program, the meaningfulness 
has already been discussed in the basics and does not provide any 
knowledge gain for the student in the actual sense at this point. 
At this point, only the practical data is acquired, with which the 
evaluation and interpretation can be done afterwards. In the first 
step the 10 single measurements of the circular rings are carried 
out at 5 positions, which are reached by shifting the measuring 
object in the object field by means of the X-Y-stage. The 
software required for image acquisition is provided for the 
student and can be operated intuitively, and the circle diameters 
are also determined in this software. After determining the circle 
diameters, these values are saved in the background in a file, 
which can later be pulled into the evaluation software. The 
Second measurements is the capture of the USAF test chart, 
which is captured as a single image and then saved as an image 
file. 

4.3. Evaluating the measurements  

The evaluation of the measurement data is generally the most 
important and most insightful part of the training program. Here, 
the students learn how to evaluate data in an environment that is 
frequently encountered in practice. Both the measurement data 
of the circular diameters and the development of the MTF are 
implemented in the MATLAB environment. 

In general, the necessary program text is available as cloze text 
and must be completed by the students at the essential points. 
This also promotes the algorithmic understanding of a sequential 
process. The first insight is the differentiation of the data types. 
The measurement data of the circle diameters are purely vectoral 
and 1-dimensional, the image data as 2-dimensional field. In 
addition, the image data are available as 8Bit integer, the 
measurement data are of the data type "double". For the 
evaluation of the circle data a script is available, which must be 
supplemented at some commented places only by the function 
for the computation of the standard deviation. Essential 
necessary standard functions and their arguments to be passed 
with syntax must be researched by the students themselves via 
the internal help and implemented in the main program. 
Experience shows that most students have enormous methodical 
deficits exactly at this point for independent problem solving.   

Figure 4. Measurement target 1. 



 

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4.3.1. Determination of the measurement uncertainty 

The data obtained in the measurement serves as the basis for 
determining the measurement uncertainty. These are available in 
a csv-file (comma separated value) stored in the background by 
the image processing software and can be transferred to 
MATLAB with a function for reading in. Afterwards the data 
have to be validated. Unfortunately, problems occur again and 
again due to the comma-dot separation at the decimal point in 
the exchange with German-language software, which should be 
explicitly pointed out here. In the last step the calculation of the 
measurement uncertainty by standard deviations etc. takes place 
and are to be completed here after the appropriate equations by 
the students in the program text. 

4.3.2. Determination of the MTF 

More detailed understanding is required to calculate the MTF. 
It should be noted that within the training program only the MTF 
of the entire system is to be determined. Of course, this would 
also be possible for each individual component in the beam path. 
However, the goal is to get a pragmatic overview of the resolving 
power of the entire system. In addition, the time required should 
also be kept within reasonable limits. The necessary data are 
available as a single image, which must first be read in. 

In the next step, the relevant signals must be extracted from 
the image data set as one-dimensional signals. This is done 
manually by defining the start and end points of the search 
beams. Afterwards, the students represent these signals as a 
simple plot for illustration purposes. To write the necessary 
functions would go beyond the scope of the training program, 
therefore these functions are predefined. 

After extracting the vectoral data, the students calculate the 
MTF according to the relationships presented in the basics. Here 
it is also important to understand the signal properties of the 
overall image (contrast ratios) and to calculate them with 
appropriate functions from the field. Also, here the necessary 
program text is available as gap text. Calculations for 
visualization of the search rays in the image etc. have been 
predefined. As a result, the MTF is plotted graphically. 

4.4. Reflexion and interpretation of the data 

The main focus of the training program is the graphical 
representation of the evaluated data. For each result a plot is to 
be created, which illustrates the data. Figure 5 shows an 
exemplary graphical representation of the statistical values of 10 
single measurements at the 5 relevant positions. The graph shows 
the histogram and the distribution function fitted in it (red 
curve). On the basis of the compression of the curve the meaning 
of the standard deviation as a scattering parameter of the data 
can be read off immediately. The knowledge gain is secured by 
the graphic connection of the data thus finally and is to be 
summarized a protocol.  

All results are finally discussed with the supervisor on the 
basis of the graphs. Thus, the learning result is secured by the 
renewed repetition and purposeful discussion of substantial 
qualitative characteristics, particularly in the curves. Experience 
shows that qualitative progressions can be memorized very 
lastingly through graphically illustrated relations. 

5. INTEGRATION INTO TEACHING 

The present concept will be integrated into teaching as a fixed 
element from the time of publication. However, initial test 
sessions with students for the evaluation of the concept were 
performed before. These preliminary tests with a total of 4 

groups had three main reasons. First of all, it was to be 
determined whether the test could be completed at all by the 
students in the appropriate time. All 4 groups managed to 
complete the task within the set time frame of 3 hours. The 
second reason is to estimate the suitability. The students were 
asked in detail about their assessment after completing the 
program. All groups confirmed that they had understood the 
usefulness of the course and its relation to real practice. 
Furthermore, it was confirmed that the students were neither 
overstrained nor understrained at any time. The first group, 
which had already conducted an experiment on a similar topic in 
a different form a long time ago, represented a special case. This 
group confirmed above all the increase in clarity and confirmed 
that they had become better familiar with the topic due to the 
many integrated qualitative graphical representations of the 
results. The third reason for the preliminary tests is to test the 
stability of the system. This means both the system stability of 
the hardware and the stability of the software. None of the 
groups experienced any problems in this regard. The hardware 
ran stably, did not cause any dropouts, and the software did not 
deliver any errors. 

 

Figure 5. Measurements on 5 positions (target 1). 



 

ACTA IMEKO | www.imeko.org December 2022 | Volume 11 | Number 4 | 6 

6. CONCLUSION 

The present work represents a full methodological treatise on 
the development of a training concept of engineering students in 
the field of optical coordinate metrology and adjacent to the 
image processing. Current and relevant problems are integrated, 
basic problems of image processing are simulated, demonstrated 
and solved. Ensuring expert supervision, but intervening only 
when necessary, underlines the pedagogical concept. The clearly 
identified problems are solved using current tools. The focus is 
also always on creating a graphical picture between data, their 
evaluations and calculations, on the basis of which the results are 
easily discussed and the facts are easily memorized by the 
students through the graphical symbolization. 

Special attention was paid to typical, recurring deficits and 
problems of the students during the creation of the program, 
which is why they were specifically included and problems are 
intentionally implied during the execution of the program. 

ACKNOWLEDGEMENT 

We thank the Technische Universität Ilmenau for the financial 
support to realize this practical course. 

REFERENCES 

[1] ISO 10360 7: Geometrical product specifications (GPS) - 
Acceptance and re-verification tests for coordinate measuring 
machines (CMM) - Part 7: CMMs equipped with imaging probing 
systems, International Organization for Standardization Geneva, 
2011. 

[2] Verein Deutscher Ingenieure, VDI/VDE 2617 Blatt 6.2,: 
Accuracy of coordinate measuring machines - characteristics and 
their testing - guideline for the application of DIN EN ISO 10360-
8 to coordinate measuring machines with optical distance sensors, 
Beuth Verlag GmbH, Berlin, Februar 2021. 

[3] J. Beyerer, F. Puente León (Eds.), Automated Visual Inspection 
and Machine Vision III: 27 June 2019, Munich, Germany (SPIE, 
Bellingham, Washington, USA, 2019). 

[4] T. Luhmann, S. Robson, Close-Range Photogrammetry and 3D 
Imaging, De Gruyter, Berlin, 2019, 3rd edn. 

[5] W. G. Rees, Physical principles of remote sensing, Cambridge 
Univ. Press, Cambridge, 2003, 2nd edn. 

[6] M. Rosenberger, P.-G. Dittrich, R. Illmann, R. Horn, A. Golomoz, 
G. Notni, S. Eiser, O. Hirst, N. Jahn, Multispectral imaging system 
for short wave infrared applications, Proceedings of SPIE, 2022, 
vol. 12094, id. 120940Z, 14 pp.  
DOI: 10.1117/12.2619350  

 
 

https://doi.org/10.1117/12.2619350