1

Good Practice Guide CT

Lonnie Andersen, DTI

Lorenzo Carli, Novo Nordisk

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Content 1 Objective ...................................................................................................................................................... 3

2 Overview ...................................................................................................................................................... 4

2.1 Scanner (3.1 page 6) ............................................................................................................................ 4

2.2 Sample Preparation (3.2 page 6) ......................................................................................................... 4

2.3 Fixture Specifications (3.3 page 7)....................................................................................................... 4

2.4 Number of Parts (3.4 page 8) .............................................................................................................. 4

2.5 Scan Parameters .................................................................................................................................. 5

2.6 Measurements..................................................................................................................................... 5

2.7 Uncertainty .......................................................................................................................................... 5

3 Good Practice Guide Reference .................................................................................................................. 6

3.1 Calibration and Maintenance of Scanner ............................................................................................ 6

3.1.1 Calibration and Maintenance ...................................................................................................... 6

3.2 Sample Preparation ............................................................................................................................. 6

3.2.1 Temperature Acclimatization ...................................................................................................... 6

3.2.2 Sample Cleaning .......................................................................................................................... 7

3.2.3 Identification of Multiple Samples .............................................................................................. 7

3.3 Fixture Specifications ........................................................................................................................... 7

3.3.1 Fixture Material ........................................................................................................................... 7

3.3.2 Fixture Handling .......................................................................................................................... 8

3.4 Number of Parts .................................................................................................................................. 8

3.4.1 Height, Length and Thickness Ratio............................................................................................. 8

3.4.2 Magnification ............................................................................................................................... 9

3.4.3 Sample Interaction .................................................................................................................... 11

3.4.4 Position Dependency ................................................................................................................. 13

3.4.5 Fixture Level............................................................................................................................... 14

3.4.6 Fixture Angle .............................................................................................................................. 15

4 Uncertainty ................................................................................................................................................ 16

4.1 Assumptions and Approximations ..................................................................................................... 16

4.2 Task Specific Approach ...................................................................................................................... 17

4.3 Example: How to determine the uncertainty of the outer diameter measurement of an industrial

plastic item from Novo Nordisk A/S. ............................................................................................................. 18

4.3.1 Uncertainty Budget - General Procedure: ................................................................................. 18

4.3.2 Calculation of Uncertainty Budget ............................................................................................ 22

4.4 Comments ......................................................................................................................................... 25

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1 Objective The objective of the good practice guide (GPG) is to provide a guide to achieve the best possible

accuracy in dimensional CT scanning, and thereby decreasing the uncertainty of the CT scan.

The guide deals with some of the aspects faced when using CT-scan in an industrial setting, trying to

optimize scan time, without decreasing the dimensional accuracy or at least considering the effect of

the choices made. This document does not provide a detailed uncertainty budget, but should rather

be seen as a guide as to which parameters to consider and investigate, when faced with increasing

the number of samples per scan to decrease the total scan time, and the parameters that could affect

the scan result in general.

The Guide is comprised of three sections:

Overview: A list of the parameters that should be considered when initializing a scan. Use this

guideline to ensure the best possible result for every scan.

Reference: A section with references to the different points in the overview if more detail is

needed.

Uncertainty: A simple and very general uncertainty budget. Can be used as a starting point

when estimating the uncertainty of the scans.

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2 Overview The following points should be considered when performing CT scans of one or more samples.

2.1 Scanner (3.1 page 6) Scanner should be routinely calibrated and scale corrected.

2.2 Sample Preparation (3.2 page 6) Acclimatization of samples for at least 4 hours.

Clean Samples: o Metal samples: Alcohol on lint-free Kleenex o Polymer (etc.): Clean for dust with oil free compressed air.

Use markers to clearly identify sample position in fixture when scanning more than one part.

If proper acclimatization is not possible, systematic errors stemming from temperature should be corrected.

2.3 Fixture Specifications (3.3 page 7) Use low-density polymer fixtures machined to fit the part: Insulation foam, dental wax, etc.

Avoid point compression of fixture – increases density -> noise

Use a fixture angle of at least 10°

2.4 Number of Parts (3.4 page 8) Use height/length/thickness ratio to utilize scan volume optimally while not compromising

the voxel size.

If more samples are scanned test the effect of:

o Decreasing the magnification (i.e. less voxels per sample).

o Sample interaction.

o Position dependency.

o Fixture level.

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2.5 Scan Parameters Choosing the right scan settings can be very difficult, and for the purpose of this guide we

therefore assume that the operator has had some sort of training in how the scanner works

and how to set up the parameters for a good scan.

Most scanners are somewhat robust when parameters are kept within a reasonable range,

see Figure 17 p. 20.

Avoid hard filters when scanning polymer material.

The same parameters should always be used when scanning the same sample for industrial

purposes (not when checking for reproducibility).

Investigate the effect of beam hardening correction when scanning high density materials (do

reconstruction with and without beam hardening correction and compare to CMM

measurements)

2.6 Measurements Use a recommended software package, to ensure the highest possible accuracy.

Ensure that the alignment system, ie the coordinate system used for the registration, is

robust.

Make sure that the extracted features are robust (highest possible fit point density and

relevant fitting method).

If a measurement template is copied from one scan to another, inspect the automatically

generated fit points and if necessary adjust.

2.7 Uncertainty CMM measurements of the scanned part, or a calibrated work piece like reference is needed

to determine the uncertainty.

Reproducibility of scanner should be determined by carrying out at least 15 different scans

while:

o Changing the operator

o Scanning on different times during the day

o Varying the X-ray parameters.

Drift should be measured by doing continuous scans on a calibrated reference such as the

“Birthday cake”

Repeatability of measurements should be determined by carrying out at least 10 repeated

measurements on the same scan, repeating the entire measurement strategy each time.

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3 Good Practice Guide Reference 3.1 Calibration and Maintenance of Scanner

3.1.1 Calibration and Maintenance The CT scanner should be scale corrected and the length scale in calibration control to

ensure optimal results. The specification of the calibration control depends on the

specifications from the manufacturer.

Recommendation

Regular calibrations should be performed, and the scanner specific calibration plan

should be followed.

3.2 Sample Preparation

3.2.1 Temperature Acclimatization The sample should be acclimatized to room temperature (20±1°C) to prevent

temperature variations. This is especially important when CT scanning is used for

metrology purposes due to material shrinkage. Most scanners used for metrology

purposes will have temperature control, minimizing the effect of temperature during

scanning.

Furthermore, many plastic parts will be affected by humidity, which should be

considered as well.

Recommendation

i. Measurements should be performed in a temperature and humidity

controlled environment if possible.

ii. At least 4 hours is recommended, for acclimatization, but it depends on the

sample material and size.

iii. If less time is allowed for acclimatization, or if environment does not have

sufficient climate control, material shrinkage or expansion can occur resulting

in a systematic error, which should be corrected for using the following

equation:

𝐿𝑐𝑜𝑟 = 𝐿𝑚𝑒𝑎𝑠 + ∆𝐿

where

∆𝐿 = 𝛼 × (𝑇 − 20℃) × 𝐿,

α is the thermal expansion coefficient of the sample, T is the temperature of

the sample during measurement (often this will be the laboratory

temperature), and L is the length measured. If the data is corrected, the

uncertainty of the correction must be included in the uncertainty budget.

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3.2.2 Sample Cleaning To prevent noise on the scan the parts should be cleaned beforehand and handling

should be minimized.

Figure 1: Effect of dust on a polymer scan

Recommendation

If possible clean samples using pressurized air (air gun), ethanol etc. Gloves can be

used to avoid particle transference.

3.2.3 Identification of Multiple Samples Documentation of placement when more than one sample are scanned at a time is

important. Small identification numbers etc. may not be visible when data is loaded.

Recommendation

Use the same setup in the scanner or use marks of high density on the fixture to

indicate the direction of numbering.

3.3 Fixture Specifications In order to get the best possible scan, or have the possibility of scanning multiple samples at once a

well-designed fixture is very important. Having a fixture, which is invisible on the scan, makes data

analysis much easier due to less noise. Furthermore, a well-designed fixture makes it possible to scan

multiple samples at once decreasing the total scan time.

3.3.1 Fixture Material The fixture material should have a very low absorption coefficient compared to the

scanned material (transparent) to avoid noise on the scan.

Recommendation

Insulation material, dental wax etc. are good candidates for plastic parts

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3.3.2 Fixture Handling Avoid handling which could increase the density of the fixture material, i.e.

compression. Increasing the density by compression often result in noise on the scan,

which is difficult to remove afterwards.

Recommendation

Handle fixture with care.

3.4 Number of Parts

3.4.1 Height, Length and Thickness Ratio When scanning samples with one dominating dimension, the number of samples per

scan can be easily optimized without compromising the voxel size.

Figure 2: Increasing the number of samples without compromising the voxel size. h is the height of the sample, w is the width, and v is the tilting angle.

The image shows a case where the voxel size will be largely dependent on the height

of the sample. In this case adding more samples in the other directions, makes it

possible to scan more samples without compromising the voxel size.

When applying this, one should consider that subsequent clipping could be difficult

due to tilting of the samples (resulting in material overlap in the clipping box), and

one layer might be the best solution in this case.

Recommendation

Use the dominant measurement to optimize the number of samples in the less

dominant measurement.

Considerations:

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i. If clipping is needed one layer of samples, (i.e. three in the above example) is

preferable. Avoid visual overlap between the samples due to tilting.

ii. Test effect of part interaction and placement in fixture.

3.4.2 Magnification When adjusting the scan magnification to scan one or more samples two things

should be considered:

i. If the effective volume of the samples is increased the magnification is

decreased and the voxel size increases – See Figure 3.

Figure 3: Relationship between voxel size and source-to-object distance (SOD) (magnification) for the Metrotom 1500.

ii. The highest magnification (i.e. the smallest voxel size) does not always

correspond to a better accuracy. In fact, geometrical errors of the axis, the x-

ray cone angle and other error sources related to the detector can affect the

3D reconstruction. Figure 5 below shows a measurement of an outer

diameter and inner diameter at different source-to-object distances (SOD)

(i.e. different magnifications), while keeping all other settings constant, to

illustrate the error.

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.0 100.0 200.0 300.0 400.0

Vo

xel S

ize/

µm

SOD/mm

Voxel size vs SOD

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Figure 4: The sample used in the tests. Red arrow indicate the outer diameter (Dnom = 15.820 mm) and blue the

inner diameter (dnom = 4.377 mm) measured.

Figure 5: Test of the effect of magnification using two different dimensional measurements. The deviation from the nominal value is shown as the relative deviation (deviation divided by nominal

value)

It can be observed, that the relative deviations compared to CMM

measurements do not increase linearly with the voxel size. Thus, sub-voxel

accuracy is achieved (0.1-0.2 voxels at low magnifications). The largest

relative deviation is seen at the smallest voxel size, which could indicate a

calibration problem at the smaller voxel sizes. Such deviations in voxel size

should be investigated further to ensure the correct voxel size is used.

Recommendation

The effect of increasing the voxel size should be tested to determine how this effects

the uncertainty of the measurement.

0.000

0.050

0.100

0.150

0.200

0.250

0.300

40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0

Rel

ativ

e D

evia

tio

n

Voxel Size (µm)

Effect of Voxel Size

Outer Diameter D Inner Diameter d

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Test three different magnification: magnification with only one part,

magnification with desired number of parts, and a magnification in the middle

of the two.

Use CMM measurements to determine deviation.

3.4.3 Sample Interaction When scanning several samples at a time, sample interaction should be considered.

The number of parts will increase the amount of material that the X-ray must

penetrate. This means that the X-ray energy must be increased, which in turn can

result in noise effects on the scan.

Figure 6 show the difference between the outer diameter D and the inner diameter d

when the sample is scanned alone in the four different positions (D1 to D4 and d1 to

d4) and together with three other samples. Measuring more parts shows a systematic

underestimation of all measurements except d2 and d4, when compared to reference

measurements due to mutual interaction. However, the deviation is within the

repeatability of the scanner.

Figure 6: The effect of scanning one vs four samples. The result show the effect of scanning one sample alone in four different positions compared to scanning it with three other samples in the same positions. D1-D4 is the outer diameter measured in the four positions; d1-d4 is the inner diameter. All measurements are compared to the CMM value and shown as the relative deviation (Figure 5).

The same tendency was seen on the roundness measurement, where the roundness was

higher when scanning one sample vs four (Figure 7), however this could not be compared to

the CMM measurements.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

D1 D2 D3 D4 d1 d2 d3 d4

Rel

ativ

e D

evia

tio

n

Sample Nr and Measurement

One Sample vs Four

1 Sample 4 Samples

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Figure 7: The effect of scanning one sample vs four. Measurements are done on the large diameter.

Recommendation

When deciding to scan several samples the effect of one sample versus several should

be tested. If a systematic error is present this should be corrected for, and the

uncertainty of the correction should be included in the uncertainty budget, see

section 4.3.1 p. 18.

0.028

0.029

0.030

0.031

0.032

0.033

0.034

0.035

0.036

R1 R2 R3 R4

Ro

un

dn

ess /

mm

Sample Nr and Measurement

One Sample vs Four

1 Sample 4 Samples

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3.4.4 Position Dependency Scanning more samples can introduce position deviations due to different detector

areas, position relative to the X-ray beam, and height in the fixture due to the tilting

angle. If the detector is good then ideally there should not be a dependency, however

if the detector is not that good then there can be an effect.

Figure 9 show the relative deviations from reference values of four samples scanned in

four different positions in the fixture. No apparent systematic error is seen, at this

detector level.

Figure 8: Top view position of samples in fixture, showing rotation of samples to test for position dependency.

Figure 9: Investigation of the effect of fixture positions. Each sample is compared to the respective CMM measurement. The deviation is shown as the relative deviation compared to the CMM value.

Recommendation

The quality of the detector and how it affects the deviation from fixture positions

should be investigated when scanning more than one sample. The above example

0

0.02

0.04

0.06

0.08

0.1

0.12

1 2 3 4

Rel

ativ

e D

evia

tio

n

Position Nr

Effect of Position

Item 1 Item 2 Item 3 Item 4

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(Figure 8 and Figure 9) can be used as an inspiration to such a test setup. If a

systematic error is present this should be corrected for, and the uncertainty of the

correction should be included in the uncertainty budget, see section 4.3.1 p. 18.

3.4.5 Fixture Level Different vertical positions use different areas of the detector (see Figure 10). Figure 11

shows the difference between using a fixture level where the detector is known to be

“good” (middle 2,4) and where it is known to be “bad” (upper 1,3).

Upper position

Middle position

Figure 10: Different detector areas used.

Figure 11: Effect of Level corresponding to different detector areas.

Recommendation

The effect of the height level should be investigated to rule out detector errors. If

there are certain levels where the detector does not perform optimally, these should

be avoided when scanning.

0.000

0.010

0.020

0.030

0.040

0.050

1 2 3 4

Dev

iati

on

/ m

m

Position

Effect of Fixture Level

Middle position Upper position

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3.4.6 Fixture Angle Tilting the samples reduces the noise in the scan from flat surfaces and limits the

longest distance the X-ray must travel through the material in unsymmetrical

samples. The graph in Figure 12 shows the results of 4 different items, where the

outer diameter (D) was measured with a CMM. The samples were then scanned with

a fixture tilted in different angles. The effect of the tilting angle does not seem to be

very large on the sample scanned, however, this is something that will depend on the

geometry of the sample, and should therefore be tested.

Figure 12: Test for influence of tilting angle.

a. Recommendation

Tilting effect is highly dependent on the sample. The general recommendation is to

use a tilt angle of at least 10°, and if scanning very unsymmetrical samples, or flat

samples, the tilting angle should be investigated (Figure 12).

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0° 10° 30° 45°

Rel

ativ

e D

evia

tio

n

Tilting Angle

Effect of Tilting Angle

Sample 1 Sample 2 Sample 3 Sample 4

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4 Uncertainty

There are numerous factors and parameters that affect CT uncertainty (see Figure 13), making its estimation quite challenging. For this reason, a task specific approach is recommended in industry where some assumptions and approximations are needed to simplify the problem. Figure 13 is color coded according to the contributions to the uncertainty budget (see table 1).

Figure 13 Ishikawa diagram illustrating factors influencing the uncertainty in CT.

4.1 Assumptions and Approximations The color coding in Figure 13 is used to illustrate how the many contributions to the uncertainty

budget of CT measurements can be simplified. These general approximations are made:

1. Green: The parameters in the green area are pooled into the contribution from

reproducibility (up).

2. Purple: The parameters in the purple area are considered in the measurement uncertainty

(um) related to the method

3. Red: The parameters in the red area are considered as a part of the uncertainty from the

temperature fluctuations (utemp). If there are known environmental factors which are not

controlled, these should be included as a separate contribution.

4. Blue: The parameters in the blue area can be included in the uncertainty due to drift (udrift).

5. Yellow: The parameters in the yellow area will depend on the object scanned. In this case

these parameters are not considered as an individual contribution, however if the object is of

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high density or is made from multiple materials this effect should be included in the

uncertainty budget.

It is assumed that the number of parts, filter, fixture, scan parameters etc. are chosen

beforehand following the suggestions described in the guideline, and they will be kept

constants whenever performing repeated CT scan of the same item over time.

4.2 Task Specific Approach The estimation of measuring uncertainty for CT scanning depends on the specific task under

consideration and cannot be generalized to any item, strategy, software etc.

Systematic errors must be corrected choosing one of the following approaches:

1. Perform reference measurements on different equipment (CMM, optical scanner,

profilometer etc.).

2. Scan a reference object under similar experimental conditions as the parts under

considerations.

In both cases, use the results to compensate for CT measurements.

Random errors must be estimated and included in the uncertainty budget. The following error

sources should be taken into account (at least):

Table 1: Random errors that should be included in the uncertainty budget.

Symbol Uncertainty Description Distribution Quantification

ucal Calibration Uncertainty of reference

measurements or calibration certificate

Gauss,1 𝑈𝑐𝑎𝑙

𝑘

udrift Drift Drift in calibrated work

piece between calibration dates.

Gauss,1

𝑆𝑇𝐷𝑐𝑎𝑙 𝑟𝑒𝑓

utemp Temperature

(object+environment) Temperature effects U*, 2

𝛼 × 𝐿 × ∆𝑇

√2

up Reproducibility Reproducibility of the

scanner.

Rectangular

, 3

𝑆𝑇𝐷𝐶𝑇 𝑅𝐸𝑃

√3

um

Software repeatability (alignment +

measurement)

STD of repeated measurements on the

same scan. Gauss, 1 𝑆𝑇𝐷𝑅𝐸𝑃 𝑀𝐸𝐴𝑆

ub Bias Reference measurements Gauss, 1

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* The temperature has been chosen as a U-shaped distribution, due to known fluctuation. Using a U-

shaped distribution the extreemes are taken into account (worst case scenario) and the contribution

is not underestimated. A rectangular distribution could be used if this is not the case.

The resulting Task Specific uncertainty is:

𝑈𝐶𝑇 = 𝑘√𝑢𝑐𝑎𝑙2 + 𝑢𝑑𝑟𝑖𝑓𝑡

2 + 𝑢𝑡𝑒𝑚𝑝2 + 𝑢𝑝

2 + 𝑢𝑚2 + 𝑢𝑏

2

4.3 Example: How to determine the uncertainty of the outer diameter

measurement of an industrial plastic item from Novo Nordisk A/S.

The following example shows how to use the above uncertainty parameters (Table 1) in the

uncertainty estimation of a specific item.

CMM and CT measurements are performed on eight industrial items from Novo Nordisk A/S, the

outer diameter “D” (see Figure 14) is measured, systematic errors are considered, and if possible,

corrected for and the uncertainty budget is determined.

Figure 14 Drawing of the item used in the uncertainty budget calculation. The blue arrow shows the outer diameter D, with a nominal value of 15.820 mm

4.3.1 Uncertainty Budget - General Procedure: The following steps were performed in the determination of the uncertainty budget.

Step 1: CMM measurements were performed for all the items under consideration, in this case

8 items (see Figure 18).

Step 2: CT scan and measurements were performed following the instructions of this guideline

(see Figure 18). Four samples were scanned at the same time (see Figure 15.)

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Step 3: The reproducibility was tested having 3 different operators make 5 repeated scans (see

Table 2). The outer diameter was measured from each scan (see Figure 17), and the

standard deviation was calculated for each person. The largest standard deviation was

used as the uncertainty contribution due to reproducibility.

Table 2: Scan settings in reproducibility test.

Current (µA) Voxel Size (µm) Voltage (kV)

Operator 1

233 49 180

283 44 160

290 49 180

284 44 160

259 44 160

Operator 2

381 52 190

306 49 180

224 44 160

401 55 200

290 49 180

Operator 3

330 49 180

300 49 180

309 47 170

308 47 170

306 47 170

Figure 15 Four items scanned at the same time.

Figure 16 CAD model of the piece.

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Figure 17: Reproducibility results for the outer diameter based on five different scans by each of the three different operators.

Step 4: Comparison of CT and CMM measurements to compensate for systematic errors (see

Figure 18). The difference between the mean value of the CMM measurements and the

mean value of the CT measurements can be used to correct for the systematic error.

When doing this the uncertainty of this correction must be included in the budget (ub).

Figure 18 CMM and CT measurements comparison.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Operator 1 Operator 2 Operator 3

Rel

ativ

e D

evia

tio

n /

mm

-1

Reproducibility

Serie1 Serie2 Serie3 Serie4 Serie5

15.770

15.775

15.780

15.785

15.790

15.795

15.800

15.805

15.810

1 2 3 4 5 6 7 8

Mea

sure

d v

alu

e /m

m

Item

CT versus CMM

CMM CT AVG CMM AVG CT

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The 8 CMM values were plotted against the 8 CT values and a “least square fit” was

performed. The slope of the curve was used to compensate the systematic errors. The

contribution from part to part variation i.e. the form error of the work piece will also be

taken into account in the bias.

The data was corrected using the following equation:

𝐶𝑇𝑐𝑜𝑟 = 𝐶𝑇 ×𝐶𝑀𝑀

𝐶𝑇,

where 𝐶𝑀𝑀̅̅ ̅̅ ̅̅ ̅ and 𝐶𝑇 are the mean values of the CMM and CT values respectively. The

results of the correction can be seen in Figure 19 and Figure 20.

Figure 19: CMM and corrected CT data.

15.780

15.785

15.790

15.795

15.800

15.805

15.810

1 2 3 4 5 6 7 8

Mea

sure

d v

alu

e /

mm

Item

Corrected CT Data vs CMM Data

CMM CT

22

Figure 20: The CMM data plotted against the CT data. The goodness of fit shows that the correction factor (1.008) fits the data well.

Step 5: Calculate the uncertainty budget for CT measurements.

4.3.2 Calculation of Uncertainty Budget With reference to Table 1 and the resulting uncertainty budget, the 6 different contributors must be

evaluated:

ucal: Uncertainty of reference measurements for the 8 items measured on a CMM (Ucal).

udrift: In this example there is a calibrated workpiece, and the contribution from drift can

therefore be neglected.

However, if there is no calibrated workpiece, the following should be considered. The

contribution from drift considers the uncertainty of the CT calibration by scanning the

reference artefact three times. This is basically the uncertainty of scale error correction, and

in this case this is performed by the person performing the calibrations (i.e. Zeiss).

o If calibrations are done in house by the operator, the drift can be calculated by doing

regular scans of a calibrated reference artifact (such as the “birthday cake”). The

standard deviation of these measurements can then be used as a measure of the

drift.

utemp: Depends on the material, the temperature and the dimension being measured. In this

case the nominal dimension is 15.820 mm and the material is PC/ABS. The thermal expansion

coefficient is α = 70.2x10-6 m/(m K). In this case it is assumed that the temperature variation in the

y = 1.0008xR² = 0.7076

15.792

15.794

15.796

15.798

15.800

15.802

15.804

15.806

15.808

15.810

15.778 15.780 15.782 15.784 15.786 15.788 15.790 15.792 15.794 15.796

CM

M m

easu

rem

ent

/ m

m

CT measurement / mm

CT vs CMM

23

laboratory is no more than ± 1K, making ΔT = 1 K (half width). The uncertainty contribution can be

easily calculated using the equation in Table 1. If the temperature fluctuations are measured to be

larger than this the uncertainty contribution from temperature will be larger as well.

up: Estimated from 3 different operators performing 5 different scans by following this guideline.

Scanning parameters were adjusted every time to achieve optimal image quality. Voltage,

current and voxel size where therefore slightly different for all the 15 scans (see Table 2).

um: For a given point cloud, the post-processing operations were repeated 12 times to

investigate the influence of the alignment to the CAD model and measuring strategy.

ub: The standard uncertainty of the correction of systematic errors (i.e. goodness of the fit

for systematic error correction).

The bias was calculated as the standard deviation of the difference between the 8 CMM

values and the corrected CT values (see Fig. 18)

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Table 3: Uncertainty Contributions

Contributor Calculation

(μm) %

contribution

ucal 6𝜇𝑚

2 3.0 50.1

utemp 1.1𝜇𝑚

√2 0.8 3.4

up 2.9𝜇𝑚

√3 1.7 15.6

um 0.5𝜇𝑚 0.5 1.4

ub 2.3𝜇𝑚 2.3 29.5

UCT 2√3.02 + 0.82 + 1.72 + 0.52 + 2.32 8.5

Expanded Uncertainty (k=2)

Figure 21: The percentage uncertainty contribution from each of the six factors.

u_cal u_temp u_p u_m u_b

50.1

3.4

15.6

1.4

29.5

Un

cert

ain

ty C

on

trib

uti

on

%

UNCERTAINTY CONTRIBUTION

25

4.4 Comments Looking at the percentage contribution of each error source (Figure 21 and Table 3), it can be seen that in this

specific case there is not a dominant error contributor. If the expanded uncertainty should be reduced, the

following improvement can be considered:

1. The systematic error compensation, and the resulting bias were based on measurements of eight

items. By increasing the number of measurements a better estimate of the systematic error can be

achieved, thus reducing the bias.

2. The operator was free to choose the optimal scanner parameters (voltage, current, magnification i.e.

voxel size) to perform the task. By finding the optimal parameters for this specific task the variability

of the up contributor can be decreased.

Last but not least, it should be noted that the resulting expanded uncertainty is task specific, and only applies

to measurements of this specific item, using a specific fixture, and only at the experimental conditions

described in the introduction of this section.

When measuring other plastic parts this general approach to uncertainty is still valid, but the results from this

budget cannot be transferred to a different part.

When measuring metal parts for example, the influence of filters, image artefacts like beam hardening, and

effects of scattering and absorption might highly influence the resulting uncertainty.

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