Analysis of Combined Probing Measurement Error and Length Measurement Error Test for Acceptance Testing in Dimensional Computed

Tomography

Fabrício BORGES DE OLIVEIRA, Markus BARTSCHER, Ulrich NEUSCHAEFER-RUBE Coordinate Metrology Department, Physikalisch-Technische Bundesanstalt (PTB)

Braunschweig, Germany, Phone: +49 531 592 5258, Fax: +49 531 592 5305, e-mail: fabricio.borges@ptb.de, markus.bartscher@ptb.de, ulrich.neuschaefer-rube@ptb.de

Abstract Industrial X-ray Computed Tomography (CT) has evolved as an alternative measurement method to tactile and optical coordinate measurement systems (CMSs). Acceptance testing e.g. according to ISO 10360 standards is a common method to assess locally and globally CMS errors as probing measurement errors P and length measurement errors E, respectively. This paper explores in an experimental approach aspects of performing combined, i.e. simultaneous, P and E acceptance tests in the field of dimensional CT. This combined test approach was proposed in ISO standardization in early 2014. Prospective benefits of combined P/E testing are the potential reduction of time and costs. However, the combined P/E test is a completely new concept in the field of coordinate metrology and needs to be analyzed for its metrological characteristics. Thus, this work – performed within the framework the European Marie Curie project INTERAQCT – discusses this new approach on the basis both of real CT scans and simulations and tries to create input for the international standardization of dimensional CT. Keywords: Standardization, Marie Curie project INTERAQCT, Acceptance testing, combined P/E test, dimensional computed tomography (CT), length measurement error E, probing error P 1. Introduction

In the last decade, industrial X-ray Computed Tomography (CT) has evolved as an alternative measurement method to classical (i.e., tactile and optical) Coordinate Measurement Systems (CMSs). Consequently, to further increase the trust in CT measurements, both manufacturer and users of industrial CT are highly interested in standardized tests for these systems. Acceptance testing is part of the main scope of the well-established international ISO 10360 series of standards, up to now focused on classical CMSs. A common approach to assess local and global CMS errors is performing probing measurement error P and length measurement error E testing, respectively. This paper explores in an experimental approach advantages and disadvantages of performing combined, i.e. simultaneous, P and E acceptance tests in the field of dimensional CT. This combined test approach was proposed in ISO standardization for CT (CT task force of ISO technical committee (TC) 213 working group (WG) 10 beginning of 2014. Two important prospective advantages of combined P/E testing are the potential reduction of time and costs. However, the common P/E test is a completely new concept in the field of dimensional metrology, i.e. in coordinate metrology, and needs to be analyzed for its metrological characteristics. Thus, the paper discusses this new approach and tries to create input for the international standardization of dimensional CT. Therefore, this paper starts with a general description of acceptance testing for CMS, describing its principles. Then, the paper describes the reference standards used for the new proposal of combined P and E test as well as an experimental setup for both CT scans and simulations. In the following section, a description of the evaluation procedure including a new patch-based approach for CT measurements is given. Finally, results and conclusions are discussed closing the paper.

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2. Acceptance testing of dimensional CT

The main principle of acceptance testing, according to ISO 10360 series of standards, is to perform an overall test of the entire performance of the CMS. Mainly, the test should create trust upon the technology by means of helping to achieve traceability to the SI-unit metre and enabling comparability with other CMSs [1]. Therefore, the test is to be performed as an integrated system and it should evaluate the system using every process step of the measurement chain (i.e. as a black box). Also, it should be economic and feature satisfactory reliability (satisfactory test value uncertainty [2]). However, the acceptance test by itself does not provide complete traceability for general measurements of industrial parts. For this purpose a statement regarding the measurement uncertainty is required, which is by intent not covered by the acceptance testing procedure. A last important objective of the acceptance testing and the underlying specifications (which are tested using the acceptance test procedure) is to provide comparability between different CMSs – as well for CMSs of the same type and sensing principle and as well to CMSs which employ different measurement and sensing technologies. The acceptance test shall reflect the standard use of the CMS and shall cover all dominant error behaviour of the CMS under study. Therefore, real-life effects and e.g. the request for simple geometry reference standards in the test design shall be taken into account. Besides, the difficulty to achieve comparability with other CMS when using real-life specimen and due to its complexity and variety, the use of real-life specimen in the scope of acceptance testing is limited. Another important principle of acceptance testing is to assess both global and local performance – i.e. error – characteristics of CMSs. The local error behaviour is tested as a probing error test (P-test) assessing the diameter and form deviation of a calibrated sphere (Figure 1). The global system behaviour is tested as a length measurement error (E-test) using reference standards for lengths (e.g. hole plates, step gauges, ball plates, etc.). The hole plate reference standard has shown to be an useful tool to evaluate the E-test of CT systems, due to its high number of possible features and the different radiation absorption lengths along the hole plate. Moreover, the hole plate standard is in accordance with ISO 10360 concepts, due to the fact that it features 5 independent lengths in 7 different directions. Besides, it has economic design and satisfactory test value uncertainty can be achieved. However, a recent test study in ISO TC 213 WG10 in 2013 and 2014 has shown that there is material influence present [3]. Length measurements can be evaluated as bi- and/or unidirectional measurements, see Figure 1. Recent resolutions of ISO TC 213 WG 10 state that bi-directional measurements are mandatory for the acceptance testing. On the other hand, uni-directional measurements are optional [3]. Either uni- or bidirectional measurements can be evaluated using patches to create a representative point. This approach – which entered into ISO 10360 methodology with ISO 10360-8 for optical distances sensors [4] – enables more stable results when measuring length by reducing the influence of the sensor noise as well as the patch approach improves comparability between CMSs with different sensor technologies, mainly due to the high density of points obtained by CT and to the morphological filtering being present in tactile probing. On the other hand, the use of patches has intrinsic low pass filtering properties and can hide local effects of the system, which might be relevant for the CMS user/tester. However, in the current international standard for optical distance sensors unsolved issues exist, e.g., the patch geometry is described in a non satisfying way. For CT-based CMS technology, acceptance testing is relatively new. The first national guideline was released in 2011, when the German engineers association VDI/VDE published

the first framework for acceptance testing for CT – the guideline VDI/VDE 2630-1.3 [5]. The guideline VDE/VDI 2630-1.3 tries to map approaches of ISO 10360-2 to CT [6]. The work in the series VDI/VDE 2630 has started in 2004. In the international standardization level, the acceptance testing framework for CT started later. In 2010, the International Standards Organization (ISO) working group ISO TC 213 WG10 created the technical task force committee committed to develop acceptance testing for CT – creating in future ISO 10360-11. The current status of ISO standardization work for CT can be seen in more details in [1]. In the context of ISO 10360-based acceptance testing for CT, a combined probing and length test (i.e. simultaneous, P and E acceptance tests) was proposed in 2014. This paper explores in an experimental approach advantages and disadvantages of performing such a combined P and E acceptance test in the field of dimensional CT as well as the impact of patches for CT-based length measurements.

Figure 1. global behaviour assessment – E-test tested as uni- and bidirectional length measurements (here for the case of cylindrical geometry); Local behaviour assessment – P-test tested as probing dispersion using 95% of the points and probing size error using all point, 25 representative points

based on 25 patches and all probed points (here for the case of spherical geometry)

3. Combined P/E testing

Both experimental CT scans and CT simulations for combined P/E were performed. In the experimental CT scans, a calibrated hole plate and a calibrated sphere were used as reference standards for studying the combined P/E test. Additionally, simulations of CT scans using the BAM software aRTist [8] were performed where the simulation parameters are comparable to the performed CT scans (e.g. material composition, shape, dimensions and setup parameters). Both CT scans and simulations include the case of independent P and E tests, too. Length measurement- and probing measurement-based analyses were carried out for both CT scans and simulations.

3.1 Reference standards

A calibrated hole plate machined by erosion in aluminium (AlSiMgMn/ 3.2315/ EN AW-6082) and a calibrated silicon nitride sphere were used to investigate whether an impact on P-test and/or E-test when performing combined P/E test exists. The hole plate a has size of 48 mm × 48 mm × 8 mm and features 28 holes (4 mm diameter and cylindricity less than 5 µm) designed in such way that it features 5 independent lengths in seven main different directions (Figure 2 (a)), in accordance with ISO 10360-2:2009 concepts [6]. The design of

this plate was developed by NMoreover, a silicon nitride sphwas used, see Figure 2 (b). It suitable for CT probing test anReference measurements of tha special full diamond probe opollution effects during the hquality of tactile CMS meaperforming scanning measuraluminium surfaces (aluminmeasurements). In the reference measurementdifferent heights were probedflexibility on the measurands, etc. Therefore, comparable mmeasurements can be achieved

Figure 2. (a): Aluminium hole p(b): Silicon nitride tactile CMS p

Figure 3. Reference meas

1 Single-point: use of single point to2 Multi-point: use of several points 3 Patches: use of several points in re

y NMIJ/AIST and PTB, and is described in msphere with a carbon fibre shaft (i.e., classical C

features 8 mm in diameter and a sphericity o analyses. the hole plate and sphere were performed usinge of 2 mm in diameter. The diamond probe w

e hole plate measurements. These effects easeasurements, especially when using ruby

surements or the massive multiple single-inium particles remain on the probe an

ents of the hole plate, several scanning circued within the holes (Figure 3). This calibratiods, i.e., it enables the use of single-point1, mul measurements between the reference meased.

e plate 48 mm x 48 mm x 8 mm, designed by NMIJ/S probe; image shows characterisation of the dark s

using a (red) standard ruby probe

easurements scheme of the hole plate using circumf

t to measure distance ts to obtain a element, e.g. a circle to perform centre to c region of small spatial size to create a representative po

(a)

more details in [1]. al CMS tactile probe)

of less than 0.3 µm,

ing tactile CMSs and was used to prevent asily can impair the y probes and when

-point probing on and disturb tactile

cumferential lines in tion approach allows ulti-point2, patches3,

easurements and CT

IJ/AIST and PTB [1], k silicon nitride probe

mferential lines

o centre measurements

point

(b)

3.2 Experimental setup

CT scans

For the CT scans, the hole platcombined setup (Figure 4). Aindependently. For the combicentred to the axis of the rotaryScans of three different sphe2.9 mm and 5.7 mm were used135 times the voxel size of thelateral displacement of the sphMagnification factor of 4.7 timscaling correction has been peapplied scaling correction exclFuthermore, soft beam hardenfor the independent hole pmeasurements, no beam hardeand dimensions of the sphere.value profile of the reconstruparameters can be found in measurements. Each CT scan l

Figure 4. Hole plate and silicoshaft)

Table 1. CT

Voltage in kV

Current in µA

Exposutime in

180 84 2

CT simulation

CT simulations of the comb(version 2.4.0) of the Bundesansee Figure 5 (a). This softwareand is – in its recent version(Figure 5 (b)), but also to perfopresent in CT scanning can be

late and the sphere were scanned in the same m. Also scans of the hole plate and the spherbined setup, the hole plate was place tilted b

tary table according to the ISO proposal of the here to plate distances were carried out. Distsed, which corresponds approximately to 11 tithe measurement, respectively. Due to the mechphere relative to the hole plate occurred, too. times (corresponding to a voxel size of 42 µm) performed to improve the accuracy of CT meaxcludes an additiona error which is otherwise ovening correction were applied for the combine plate measurements. However, for the inrdening correction was applied, due to the ma

. The beam hardening effects were verified bstructed volume of the sphere measurement. in the Table 1. The same CT parameters n lasts approximately 3 h 40 min.

icon nitride sphere (as part of a tactile CMS probe w) mounting setup for the combined P/E test

CT setup parameters for the combined P/E test

osure e in s

Frames/ projection

Filter Cu in mm

Number of projections

4 0.5 1640

mbined P/E test were performed using the sanstalt für Materialforschung und –prüfung (Bare has been constantly developed and extendedions – capable not only to perform simulatioerform simulation of entire CT scans. Most of tbe modelled in this software.

mounting setup, i.e. here were performed

by 45º, slightly off he combined P/E test. istances of 0.5 mm, times, 69 times and

echanical mounting, a

m) and a 2D grid-like easurements [7]. The overlaid on the data. ined setup as well as independent sphere

material composition by plotting the gray . The CT scanning

s were used for all

with a carbon fibre

of

Voxel size in µm

42

e software “aRTist” (BAM) in Berlin [8], ded in the last decade tion of radiographies f the physical effects

The simulated measurements were carried out for different relative positions between hole plate and sphere, where the beam path concerning the material penetration length was changed, see Figure 6, i.e. (a) the sphere was “hidden” by the hole plate in a high number of projections (i.e. the beam had maximum material thickness to penetrate); (b) the sphere was “hidden” by the hole plate in a high number of projections, however lower material thickness due to the holes in the beam path hitting the sphere; and (c) the sphere was always “visible” to the beam. Comparable parameters as described in the CT scans section were used for the CT simulation (e.g. material composition, shape, dimensions and setup parameters). However, there are some physical effects which were not simulated in this study, e.g. beam hardening correction and mechanical misalignments; these parameters explain differences between real scans and simulations to some extent.

Figure 5. Simulated combined mounting setup (a), graphical interface of simulated radiography using software aRTist (b)

Figure 6. Simulation experimental setups for combined P/E test; (a) sphere beam path with a big amount of material to penetrate; (b) sphere beam path with a less amount of material to penetrate, due

to the holes; and (c) sphere beam path hole plate free.

3.3 Evaluation

The evaluation of the acceptance test is based on absolute (i.e. compared with reference measurements) length measurement and probing measurement-based analyses. In order to have CT data comparable with tactile CMS measurements, the same data points obtained by tactile CMS reference measurements were fitted in the CT volume, after performing a surface determination step using the commercial CT analysis software VG Studio Max 2.2.6. There are two possibilities of performing surface determination in such combined scenario, e.g. using the same threshold starting value for both length and probing evaluations or performing different threshold starting values focused on each material (i.e. aluminium and silicon nitride). Preliminary tests have been carried out and have shown that

(a) (b)

the surface determination step plays a critical role in the combined P/E test. The test is intended to be mono-material, but it is multi-material, indeed. However, in this paper as a starting point the same surface determination was used for both length measurement- and probing measurement-based analyses. Bidirectional length measurements were carried out based on single- or multi-point (i.e. patches) and unidirectional multi-point measurements (i.e. centre to centre measurements). All the length-based analyses in the hole plate were carried out for the longest distance in each direction, see Figure 7.

Figure 7. Longest distances on each direction of the hole plate – E-test

At the middle plane of the hole plate, least-squares circles with unconstrained radii and positions were fitted for the unidirectional centre to centre measurements. For the bidirectional single-point measurements, least-squares cylinders with unconstrained radii and positions were fitted, combination and intersection between two cylinders leads to the position where the single-point shall be taken. Additionally, bidirectional multi-point measurements (i.e. patches, see Figure 8) were performed. Points within a sphere-shaped region with radii of 35 µm, 70 µm, 100 µm, 200 µm and 1000 µm, respectively, were used to calculate a patch-based Chebyshev best-fitting cylinder (this fitting element is usually applied to create the middle symmetry cylinder for a minimum zone cylinder based form analysis – MZC). The centre of gravity of the patch points and the centre of the patch-based cylinder provide interim points for creating the representative point. The two interim points define a line which intersects the Chebyshev best-fitting cylinder. This intersection point defines finally the representative point. Chebyshev best fitting was used in this approach due to its flexibility. Tests were carried out for the usual least-square (LS) fitting, however, for smaller patches, Chebyshev best fitting presented better and more stable results than least-square fitting. Additionally, the patch procedure is in conformance with the new ISO directive issued in early 2015: No information from other patches shall be used when extracting the representative point of a patch. This measurement procedure was performed using scripting mode in the commercial coordinate metrology inpsection software GOM Inspect Professional V7.5 SR2.

Figure 8. Description of the applied patch analyses for bidirectional multi-point length measurements

Probing error analyses were performed for form and size of the test sphere. Form analysis is evaluated as probing dispersion value (PForm.Sph.D95%::CT) and probing form error (PForm.Sph.1x25::CT). For size analyses, probing size error “all” (PSize.Sph.All::CT); and probing size error (PSize.Sph.1x25::CT) [9],[1] are evaluated. For an explanation of notation see e.g. [10] and [1]. The probing dispersion value is determined as the smallest width of a spherical shell that includes 95% of all data points. Probing size error “all” is measured as the difference of the diameter of a unconstrained least-squared fit of all points measured on a sphere and its calibrated diameter. Probing form error is the error of indication within the range of the Gaussian radial distance can be determined by a least-square fit of 25 representative points on a test sphere. Probing size error is the error of indication of the difference between the diameter of a least-square fit of 25 representative points on a test sphere and its calibrated diameter. These 25 representative points shall provide comparability between CT and classical tactile CMS, due to the noise present in CT and to the morphological filtering present in tactile probing. However, a well defined procedure on how to assess these characteristics in CT is not finally established yet and is required to create an accepted testing scheme. The following 8 steps method was adopted in this contribution for probing form error and probing size error evaluation (Figure 9):

1. Fit unconstrained least-squares (LS) sphere to all data points 2. Select 25 patch centres on this LS sphere (e.g. ISO 10360-5 pattern [11]) 3. Construct 25 cones symmetric to the selected patch centres starting the cone apex from main LS sphere centre 4. Intersect all data points point cloud with each cone resulting in 25 sub-point clouds 5. Construct 25 LS spheres to the 25 sub-point clouds created before 6. Construct 25 lines through sphere centres created in step 5. and respective patch points’ centre of gravity 7. Intersect the 25 lines with the respective 25 sub LS spheres resulting in 25 points 8. Analyse the 25 points for form and diameter using unconstrained LS fitting

Figure 9. Description of the applied analyses of probing form error and probing size error

All sphere fitted points were exported as ASCII files by the measurement software (VGStudio MAX 2.2.6) and the following P-test analyses were carried out with a MATLAB® dedicated application, developed at PTB [12]. 4. Results

CT scans were obtained with different sphere to hole plate distances and lateral positions (top part of Figure 10), for multi-point unidirectional centre to centre length, bidirectional external single-point and multi-point (i.e., patches) length measurements. The results of dimensional and geometrical evaluations allows to investigate whether there is an influence on the combined P/E acceptance test presented in Figure 10 (a), (b) and (c).

Figure 10. CT Scan results: sphere to plate distance 0.5 mm; 2.9 mm; 5.7 mm; (a) unidirectional multi-point centre to centre length measurement error results; (b) bidirectional single points based length

measurement error results; and (c) results of probing error analyses for the four probing error characteristics (cf. main text)

In general, no significant variations were observed for the unidirectional centre to centre measurements (Figure 10 (a)) when changing the distance of sphere relative to the plate. However, significant measurement instabilities can be observed for bidirectional single-point based length measurements (Figure 10 (b)). Indeed, a significant influence was observed on the length measurements depending on the lateral position of the sphere relative to the hole plate, mainly concerning to the X-rays path, see Figure 10 (sphere to plate 0.5 mm, 2.9 mm and 5.7 mm). However, it was expected to obtain smaller measurement errors for the larger sphere to plate distances. This effect did not occurred; see distance 1-28 in Figure 10 (b). Furthermore, distance 1-28 shows the biggest influence for the presence of the sphere as the sphere is next to hole 28. But in general there is no significant influence in the length measurements regarding the sphere to plate distance for those distances used in this study, as the distances used were not sufficient large to have a much lower number of projections with the beam hole plate free. The same is true for the probing error analysis (Figure 10 (c)). This effect was confirmed by simulation data. The simulation setup, Position 1, Position 2 and Position 3, can be seen in Figure 6 and the simulation results are presented in Figure 11. However, for probing analyses in Position 3 (Figure 6 (c)) – where the sphere is far away from the central plane – a strong pole artefact due to the cone beam geometry was observed (Figure 11 (c) and (d)). This effect can frequently be observed with many cone beam CT systems when a spherical reference standard is measured far away from the central plane of the detector [1]. Differences between the results obtained by CT scans and simulation are explained by the missing effects (e.g., beam hardening correction, mechanical misalignments) on CT simulations.

Figure 11. Simulation results of the setups described in Figure 6: (a) unidirectional multi-point centre to centre measurements results; (b) single-point based bidirectional measurements results; (c) results

of probing analyses; and (d) observed pole artefact

Figure 12 presents the patch analyses of CT scans. Figure 12 (a) shows the mean value of three repeated measurements, without repositioning the reference standard, for each distance. In general, an improvement was achieved concerning the stability of the results for most of the bidirectional external measured lengths. The improvement can be seen by the decrease of the variation (i.e., maximum value – minimum value of three repeated measurements) while increasing the patch size (Figure 12 (b)).

Figure 12. CT scans – Mean value of the external bidirectional length measurement error - patch analyses for three repeated measurements without repositioning the reference standards (a); and

variation (Max - Min) of 3 repeated measurements for each distances (b)

5. Conclusions and Summary

CT scans and CT simulations were carried out for the new proposal for common P/E acceptance testing for CT and it was analyzed for its metrological characteristics. Also, for the length measurement error analysis a new concept of a patch operator for CT data was presented and analyzed in this paper. Probing- and length-based evaluations were carried out for different distances and lateral positions of the sphere relative to the hole plate. In general, measurement errors could be observed for both length measurement and probing error. For the length measurements a high dependence on the lateral position of the sphere relative to the hole plate was observed, mainly concerning to the X-rays path. However, no significant influence was observed in the length measurements regarding the sphere to plate distance. The same is true for the probing error analysis. This effect was confirmed by simulation data. Regarding the patch analyses, considerable improvement was achieved concerning the stability of the results for most of the bidirectional external measured lengths while applying patches instead of single-point based length measurements. A critical point of the common setup is that the test is intended to be mono-material but it is in reality multi-material. Thus, surface determination plays an important role when performing such a combined P/E testing. Another critical point observed in the tests is the mechanical mounting/stability. The sphere should not be placed in a position where a lot of material in the beam path exists. Finally, common P/E testing appears to be a nice idea from the first look. But it features several intrinsic problems. First of all it is a new concept which changes (increases) the characteristic numbers to be reported. Thus, it is unfair to one (new) measurement technology to urge only this technology (e.g.) CT to state numbers according to this new concept as measurement technologies are in competition to each other and need to be comparable. Secondly, performing this combined setup appears to be delicate for CT. Testing conditions

(a) (b)

strongly depend from the way the test is performed. This is – in general – not acceptable for a standard test recommended for CT in future ISO 10360-11.

Acknowledgements

We would like to thank the EU Marie Curie Initial Training Networks (ITN) − INTERAQCT, Grant agreement no.: 607817, beneficiary no.: 7 for the project funding, more information can be seen on http//:www.interaqct.eu. Also we want to thank our colleagues Jakob Schlie (for the probing analyses application), Jens Illemann (for the discussion and scaling correction application and procedure), Konrad Hierse (for tactile measurement of the Si3N4 sphere), Michael Neugebauer (for the probe selection discussion and for the assistance with the mechanical mounting) and Uwe Langner (for tactile CMS measurement of the hole plate).

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