Content uploaded by Subbareddy Darukumalli
Author content
All content in this area was uploaded by Subbareddy Darukumalli on Mar 03, 2021
Content may be subject to copyright.
euspen’s 20th International Conference &
Exhibition, Geneva, CH, June 2020
www.euspen.eu
Axial calibration of an on-machine focus variation surface texture and form sensor
Subbareddy Darukumalli1,2, Teguh Santoso1, Wahyudin P. Syam1, Franz Helmli2 and Richard Leach1
1Manufacturing Metrology Team, University of Nottingham, UK.
2Alicona Imaging GmbH, Dr Auner Straße 21a, 8074 Raaba, Austria.
E-mail: s.darukumalli@bruker.com
Abstract
To address the increase in tight tolerance requirements for small parts produced by precision manufacturing, on-machine optical
areal surface topography instruments are emerging. To calibrate these instruments and estimate their measurement uncertainty,
their metrological characteristics need to be determined according to ISO 25178 part 600. In this paper, the amplification coefficient
and linearity deviation metrological characteristics in the vertical axis of a prototype compact on-machine focus variation areal
surface texture and form measurement sensor are determined. With a series of experiments in different positions of the vertical axis
using calibrated materials measures with heights from 0.2 µm to 1000 µm, we determine the amplification coefficient and linearity
deviation for the vertical axis. In addition, with a procedure derived from ISO 10360 part 8, the maximum permissible unidirectional
stationary error of the vertical axis is determined.
Metrological characteristics, axial calibration, on-machine metrology, focus variation
1. Introduction
Advances in precision manufacturing technologies lead to an
increase in the tight tolerance requirements of small parts. To
measure such tolerances to sub-micrometre accuracy and avoid
the measurement instrument’s influence on the measured
features, in contrast to the traditional contact measurement
instruments, commercial non-contact optical areal topography
instruments are emerging. On-machine areal topography
instruments are becoming popular because surface texture and
form errors can be used as the fingerprint of the manufacturing
process [1].
Focus variation microscopy (FVM) areal topography measuring
instruments provide measurement data using an optical setup
along with a high-precision encoder for measurement axis
position measurement [2]. To calibrate a FVM instrument, a
series of standardised metrological characteristics must be
determined [3], where calibration is defined as “an operation,
under specific conditions, in a first step required to establish a
relation between the quantity values with measurement
uncertainties provided by measurement standards and
corresponding indications with associated measurement
uncertainties and in a second step, uses this information to
establish a relation for obtaining a measurement result from an
indication” [4]. In practice, calibration of the instrument refers
to a series of operations required to establish the contribution
of the metrological characteristics to the measurement
uncertainty associated with the instrument measurements [5,6].
In this paper, we address the metrological characteristics
associated with the on-machine focus variation sensor
measurement axis in section 2, the experimental design and
measurement procedure are explained in section 3,
measurement data and analysis are presented in section 4 and
finally the conclusions and future work are given in section 5.
2. Metrological characteristics
The metrological characteristics used for FVM instrument
calibration include: amplification coefficient, linearity deviation,
residual flatness, measurement noise, lateral period limit and xy
mapping error [5,6]. In this paper, we address the amplification
coefficient, linearity deviation and maximum permissible
unidirectional stationary error associated with the on-machine
FVM sensor measurement axis (z-axis) using calibrated material
measures. These characteristics are defined as:
• Amplification coefficient is the slope of the linear
regression curve obtained from the response curve
[5,6].
• Linearity deviation is the maximum local difference
between the line from which the amplification
coefficient is derived and the response function [5,6].
• Maximum permissible unidirectional stationary error
is determined using a method
derived from the ISO 10360-8 maximum permissible
error determination procedure ( where indicates
the measurement direction, for stationary, ODS for
optical distance sensor and for maximum
permissible error) by the measurement of height steps
in a single field of view [7].
3. Experimental design
The compact on-machine FVM sensor used is presented in
reference [8] and has a magnification 20× (0.4 numerical
aperture, working field of view 0.59 mm × 0.59 mm and sampling
distance approximately 0.30 µm) objectives lens, together with
ring light illumination. The working range of the z-axis is 15 mm.
Single step height artefacts were measured in five positions
within the working range of the instrument and the
measurement positions were chosen to cover the total working
range. Each step height artefact has measured at 90%
(13.5 mm), 70% (10.5 mm), 50% (7.5 mm), 30% (4.5 mm) and
10% (1.5 mm) of the instrument working range [9].
As shown in Table 1, eight different step height artefacts with
nominal heights from 0.2 µm to 3000 µm were chosen for the
measurements. The nominal 3000 µm step height was built with
two gauge blocks and calibrated with a focus variation
instrument with a calibrated axial response [7]. The 0.2 µm to
7.5 µm step height artefacts were calibrated at PTB using an
interference microscope according to VDE/VDI 2655, the 24 µm
and 50 µm step heights were calibrated at PTB using a traceable
stylus instrument and the 1000 µm step height artefact was
calibrated at a DKD calibration laboratory using a gauge block
measurement system.
Table 1 List of used step height artefacts.
Artefact
Calibrated height/µm
Uncertainty/µm at k
= 2
Step height 1
3000.46
±0.50
Step height 2
1000.00
±0.10
Step height 3
49.75
±0.25
Step height 4
23.97
±0.15
Step height 5
7.51
±0.15
Step height 6
2.4
±0.15
Step height 7
0.75
±0.15
Step height 8
0.24
±0.10
As we are using the prototype version of the FVM, before
starting the measurement, the instrument was adjusted for field
curvature correction by estimating the form error and by
removing it using the software settings for the used objective
lens. All measurements are performed with the same
measurement settings. Measurements were performed in a low
noise laboratory environment.
Table 2 Estimation of measurement uncertainty budget.
Measu
red
step
height/
µm
Calibration
certificate
uncertainty
/µm
Estimated
instrument
uncertainty
/µm
Measurem
ent
procedural
uncertainty
/µm
Computed
Test
uncertainty
/µm
1000
0.1
0.2
0.017
0.233
50
0.25
0.2
0.165
0.360
24
0.15
0.2
0.068
0.259
7.5
0.15
0.2
0.044
0.253
2.4
0.15
0.2
0.031
0.251
0.75
0.15
0.2
0.008
0.250
0.24
0.1
0.2
0.011
0.223
As shown in Table 2, the estimated measurement uncertainty
at each measurement step was noted and the maximum
standard deviation of the squared sum of these values is
computed as the measurement test uncertainty, i.e. ±0.360 µm.
This includes the measured step height uncertainty value from
calibration certificate using a traceable instrument, the
estimated uncertainty of the measuring instrument and
measurement procedure, including the profile analysis (which
includes the direction of the profile selection, profile width,
orientation of the profile width, choosing the rectangle area to
apply the levelling to the workpiece coordinate system, and
choice of the measuring points for the step height
measurement). It is difficult to measure the expansion
coefficient of the instrument at this stage of the prototype
development; therefore, the expansion coefficient is not
considered for the uncertainty estimation.
The measurement procedure of the step height value
determination is explained below and an example procedure is
shown in Figure 1.
Figure 1. The procedure of the step height measurement analysis
The measurement procedure for the calibration is as follows.
1. Clean the measurement artefact and place it at the
focus plane.
2. Select the desired measurement position from the
live view and configure the appropriate software
settings for measurement.
3. The measured areal data is analysed using
commercial software provided by Alicona (Alicona
Measure Suite).
4. The measured data is levelled to the workpiece
coordinate system.
5. A profile width is chosen to cover most of the
measurement area.
6. Step height is extracted from the chosen profile area.
7. With a derived method from the ISO 5436-1 [10], step
height artefact profile analysis procedure, the step
height value is computed for single step height
measurement.
4. Results and analysis
A total of forty measurements were performed with the eight
step heights measured at five different positions. Due to the
measurement test uncertainty caused by the prototype optical
setup and illumination, the 3000 µm step height measurement
does not contain enough high quality measurement data
(measurement data contains many missing points, as it is unable
to choose the profile area without holes for profile analysis) to
do the profile analysis. Due to the small field of view of the
working objective lens, the bottom plane of the step height is
unable to focus properly with ring light illumination which leads
to the missing points in the measured data. Therefore, the
results from the 3000 µm step were not taken into consideration
for further analysis.
To estimate the repeatability of the measurement, at one
measurement position, each step height is repetitively
measured five times. The repeatability value is computed as the
standard deviation of the mean of the measured values at the
same measurement position, and was found to be 0.012 µm.
Table 3 Measurement error by comparing the measured height step
values to the reference values at different measurement positions.
Measured
Step height
90%
Error/
µm
70%
Error/
µm
50%
Error/
µm
30%
Error/
µm
10%
Error/
µm
1000 µm
0.052
0.075
0.1
-0.044
-0.056
50 µm
-0.082
-0.072
-0.059
-0.021
-0.032
24 µm
0.001
-0.13
-0.033
0.005
0.106
7.5 µm
-0.015
-0.091
-0.105
-0.048
-0.016
2.4 µm
-0.049
-0.088
-0.078
0.014
-0.011
0.75 µm
0.002
-0.011
0.007
-0.019
-0.009
0.24 µm
-0.011
0.001
0.002
-0.005
0.006
Step height measurement errors were computed by
comparing the step height measurements with their reference
values and errors are plotted in Figure 2. A maximum error of
0.13 µm was reported at 70% of the working range for the 24 µm
artefact and the minimum error of 0.001 µm was reported at
70% of working range for the 0.241 µm artefact. As shown in
Table 3, the measurement errors show that all the measured
values were in the range of the reference uncertainty values of
the measured artefacts.
Figure 2. Measurement error plot: the green lines indicates the
maximum permissible error limit from the measurement errors and the
orange lines indicates the maximum permissible error limit including the
measurement test uncertainty for the measurement axis.
As we can see in the measurement error plot, all the
measurement errors lie between the -0.13 µm and 0.13 µm and
the estimated measurement test uncertainty is 0.360 µm. The
maximum permissible unidirectional stationary error of the
measurement axis (derived from the ISO
10360-8 maximum permissible length measurement error
procedure [8]) is computed as the sum of the measurement test
uncertainty, maximum error value and a length coefficient. This
is given by
(where L is the
length of the sample in millimetres).
The amplification coefficient is determined by fitting a line to
the determined step heights using the least-squares method [5].
Linearity deviation is computed as the maximum local difference
between the line from which the amplification coefficient is
derived and the response function. At the different working
ranges of the measurement axis, the amplification coefficient
and linearity deviation values are computed and listed in Table
4.
Table 4 Amplification coefficient and the linearity deviation at the
different positions of the measurement axis.
Measurement
position/mm
Amplification
coefficient
Linearity
deviation/μm
90 % ~ 13.5
1.0000
0.129
70% ~ 10.5
1.0001
0.208
50% ~ 7.5
0.9998
0.168
30% ~ 4.5
0.9998
0.077
10% ~ 1.5
0.9998
0.110
The amplification coefficient of the whole measuring range is
computed as the mean of the amplification coefficient at
different measurement positions, i.e. 0.9999. This shows that
the measurement axis response is close to the ideal response
curve with less than 0.0001% of deviation.
The maximum linearity deviation 0.208 µm is reported at 70%
of the working range and the minimum linearity deviation
0.077 µm is reported at 30% working range of the measurement
axis. The linearity deviation of the whole working range of the
measurement axis is computed as the absolute maximum of the
linearity deviations at different measurement positions, i.e.
0.208 µm.
5. Conclusion
In this paper, the amplification coefficient, linearity deviation
and maximum permissible unidirectional stationary error of an
on-machine focus variation sensor measurement axis are
determined using single-step height artefacts. The results show
that the mean amplification coefficient is 0.999 and the linearity
deviation is 0.208 µm. The measurement error values show that
all the measured values are in the uncertainty range of the
measured artefacts.
In this experiment, the measurements were carried out with a
prototype version of the optical setup to evaluate the
performance of the measurement axis. In the near future, we
are planning to determine the whole sensor metrological
performance with the fully developed optical setup, which is
corrected for aberrations and distortions.
Acknowledgements
This work has received funding from the European Union
Horizon 2020 Marie Skłodowska Curie ITN projects PAM^2 and
MICROMAN under the grant agreement numbers 721383 and
674801.
References
[1] Gao W, Haitjema H, Fang F Z, Leach R K, Cheung C F, Savio E, Linares
JM 2019 On-machine and in-process surface metrology for precision
manufacturing. Ann. CIRP 68 843-866
[2] Danzl R, Helmli F and Scherer S 2011 Focus variation–a robust
technology for high resolution optical 3D surface metrology. Strojniški
Vestnik – J. Mech. Eng. 245–256
[3] ISO/DIS 25178-700 2020 Geometrical product specification (GPS) --
Surface texture, Areal -- Part 700: Calibration, adjustment and
verification of areal topography measuring instruments (International
Organization for Standardization)
[4] ISO/IEC GUIDE 99 2007 International vocabulary of metrology —
Basic and general concepts and associated terms (VIM) (International
standard)
[5] ISO 25178-606 2015. Geometrical product specification (GPS) --
surface texture, areal -- Part 606: nominal characteristics of non-contact
(focus-variation) instruments (International Organization for
Standardization)
[6] ISO 25178-600 2018 Geometrical product specification (GPS) --
surface texture, areal -- Part 600: metrological characteristics for areal-
topography measuring methods (International Organization for
Standardization)
[7] Zangl K, Danzl R, Helmli F, Prantl M 2018 Highly accurate optical
µCMM for measurement of micro holes Proc. CIRP 75 397-402
[8] Darukumalli S, Santoso T, Syam WP, Helmli F, Leach R K 2019 On-
machine optical surface topography measurement sensor based on
focus variation 19th Int. Conf. euspen, Bilbao, Spain
[9] Giusca C L, Leach R K, Helery F 2012 Calibration of the scales of areal
surface topography measuring instruments: part 2. Amplification,
linearity and squareness Meas. Sci. Technol. 23 065005
[10] ISO/CD 5436-1 2000 Geometrical product specifications (GPS) -
surface texture: profile method; measurement standards - Part 1:
material measures (International Organization for Standardization)
