VDI/VDE 2643 Part3 2008:10

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Optical 3D-measuring systems Multiple view systems based on area scanning

Preliminary note

The content of this guideline has been developed in strict accordance with the requirements and recommendations of the guideline VDI 1000.

All rights are reserved, including those of reprinting, reproduction (photocopying, micro copying),storage in data processing systems and translation, either of the full text or of extracts.

The use of this guideline without infringement of copyright is permitted subject to the licensing conditions specified in the VDI notices (www.vdirichtlinien.de).

We wish to express our gratitude to all honorary contributors to this guideline.

Introduction

Optical 3D measuring systems are used as universal measuring and test equipment. Every user must be sure that the optical 3D measuring system used comes up to the performance required. In particular, the maximum permissible error must not be exceeded. In the long run, this can be ensured only through comparable acceptance criteria and reverification of the equipment at regular intervals. The responsibility for this lies on the one hand with the manufacturer of the equipment and on the other hand, with the user of the optical 3D measuring system.

Acceptance testing and re-verification of optical 3D measuring systems of different design, level of automation and size must be rapid and easy to carry out using low-cost artefacts. For this purpose, length standards and artefacts are suitable which are measured with the measuring system just as usual objects to be measured.

The present guideline gives practical acceptance test and re-verification procedures to assess the precision of imaging optical 3D measuring systems providing area-based sampling. In addition to guideline VDI/VDE 2634 Part 2, it defines necessary supplements for the measurement of objects using multiple images.

The series of guidelines VDI/VDE 2634 consists of the following parts:

Part 1 Imaging systems with point-by-point probing

Part 2 Optical systems based on area scanning

Part 3 Multiple view systems based on area scanning

1 Scope

The present guideline is applicable to optical 3D measuring systems based on area scanning which operate on the triangulation principle and determine the object to be measured from several different images. The measuring systems can be configured so that the application-specific requirements are met. The sensors consist of several components, e. g. one or several imaging probes (cameras) and one or several projection systems imaging structures onto the object surface to be measured, or a system for illuminating existing surface textures. Examples of such sensors are measuring systems on the basis of fringe projection or moiré techniques as well as area-based photogrammetry or scanning systems.

This guideline applies to the measurement of 3D objects using multiple images. Unlike in testing in accordance with VDI/VDE 2634 Part 2, components of the measuring system may be moved relative to each other during the measurement. This can be achieves by re-positioning of the sensor and/or of the object to be measured. The different single images of the measured object are transformed into a uniform object coordinate system, e. g. by

• transformation of the single images through suitable reference markers
• matching of all single images into the total point cloud via the geometry of the object (matching without reference markers)

Systems in which the sensor or the measured object is positioned by measuring translational and/or rotational axes such as sensors on coordinate measuring machines according to guideline VDI/VDE 2617 Part 6.2 are not covered by this guideline.

In the present guideline, methods and artefacts for acceptance testing and regular reverification of optical 3D measuring systems are specified. The methods are similarly suitable for

• acceptance testing of optical 3D measuring systems
• re-verification of optical 3D measuring systems (within the meaning of “control of measuring and test equipment” according to standards DIN EN ISO 9000 to DIN EN ISO 9004)

The requirements to be met by the artefacts used for acceptance testing and re-verification are specified and some of them are described as examples. Artefacts within the scope of this guideline are linear, planar and spatial arrangements of probing elements, for example optically probable planes or spheres. Artefacts must have been calibrated with regard to their dimensions and form.

To assess the accuracy of the measuring systems quality parameters are specified. The limits for these parameters are specified by the manufacturer for acceptance testing of the optical 3D measuring systems, and by the user as far as re-verification is concerned.

The quality parameters serve to specify the optical 3D measuring systems as well as to compare different measuring systems.

As these values are dependent on the mode of operation and on the operating conditions, it is advisable to state and specify particular modes and conditions of operation for acceptance testing and reverification so that comparability of the test results is ensured. The quality parameters cannot easily be used for any measurement task whatever.

If no restrictions as to the modes and conditions of operation are made, the specified limits of the
quality parameters must be complied with for all potential modes and conditions of operation. If specified restrictions are not complied with, exceeding of the pertinent limit of the quality parameters is possible and admissible.

By modes of operation possibilities of adjusting and configuring the optical 3D measuring system are to be understood such as, for example:

• type of illumination and intensity
• measuring volume and sensor measuring volume
• type, number and arrangement of optical probes used
• type and duration of image acquisition and image evaluation
• data pre-processing (filter parameters, elimination of outliers, thinning of point cloud in overlapping regions, curvature-dependent thinning, etc.)

By operating conditions the external factors influencing the optical 3D measuring system are understood. These are, for example:

• preparation of object to be measured (e. g. spraying)
• temperature and temperature gradient
• humidity
• vibration (mechanical)
• electromagnetic interferences
• illumination of environment
• dust

2 Symbols

Quality parameters

\({PF}\) probing error (form)

\({PS}\) probing error (size)

\({E}\) length measurement error

\({SD}\) sphere spacing error

\({FD}\) plane spacing error

Limits

\({{MPE}_{XX}}\) limit for quality parameter XX (maximum permissible error)

This means, for example: \({{MPE}_{PS}}\) is the limit for \({PS}\) .

Auxiliary quantities

\({D_a}\) measured diameter of test sphere
\({D_r}\) calibrated diameter of test sphere
\({{L}_{ka}}\) measured sphere spacing
\({{L}_{kr}}\) calibrated sphere spacing
\({L_a}\) measured value of test length
\({L_r}\) calibrated value of test length
\({L_0}\) spatial diagonal of measuring volume specified by manufacturer
\({L_S}\) spatial diagonal of sensor measuring volume specified by manufacturer
\({E_E}\) length measurement error on short gauge block

3 Principle of acceptance testing and re-verification

Acceptance testing and re-verification of the measuring system are ensured by measurement of calibrated artefacts. These must be made in such a way that their properties does not have any appreciable effects on the quality parameters to be determined. It is checked whether the measurement errors lie within the limits specified by the manufacturer or by the user.

In addition to acceptance testing and re-verification in accordance with VDI/VDE 2634 Part 2, it is also
checked what effects re-positioning of the sensor or of the object to be measured exert on the quality parameters. The measuring system must be capable to combine several clouds of measuring points which have each been determined in different positions and alignments of the sensor into a single superior object coordinate system.

This capability of the measuring system is tested. To account, if possible, for all uncertainty influences, the artefacts are to be probed in such a way that in the single images their position relative to the sensor is always a different one.

The measuring volume recorded each time by a sensor in a single image is the sensor measuring volume. It is generally smaller than the total measuring volume which is composed of all single images.

The dimensions of the artefacts are related to the spatial diagonal of the measuring volume or to a cuboid inscribing the sensor measuring volume to the maximum possible extent. Form and size of the sensor measuring volume are to be stated by the manufacturer.

4 Acceptance test

The acceptance test serves to verify whether the measuring system complies with the limits for the quality parameters specified by the manufacturer or agreed by contract. Prior to the performance of the tests stated in Section 4.1 to Section 4.3, the preparations specified in the manufacturer’s operating instructions are to be made such as, for example:

• switching-on and preparation of the measuring system for the measurement operation
• configuration and qualification of the sensor
• fixing of artefacts so that they are sufficiently stable

The necessary data are to be stated by the manufacturer. During the tests the ambient and operating conditions specified by the manufacturer must be complied with.

Filtering and data pre-processing of the measurement values are admissible only to the extent to which they may be defined as boundary condition for the quality parameter to be tested or to which they may be carried out in normal operation of the device, as, among other things, they exert an influence on the resolution of the sensors. The type of filtering and the form of data pre-processing must be documented.

If, in normal operation of the measuring device, the evaluation is based on polygonized measurement
data (e. g. STL data), triangulated measurement data are also to be used for the determination of the quality parameters, as by thinning of the measuring points in overlapping regions or regions of only small surface curvature, the resolution is influenced as well. Likewise, the insertion of new, calculated (triangular) points can result in additional error influences on the probing and length measurement error.

The artefacts and the measuring system must have assumed the mean temperature of the measuring volume. If the mean temperature of the artefacts and of the measuring system significantly differ from the reference temperature in accordance with DIN EN ISO 1, suitable temperature corrections are to be made providing such corrections are also applied in normal operation of the device.

4.1 Quality parameter: probing error

By the quality parameter “probing error”, the error behaviour of the measuring system in a small portion of the measuring volume is described. In addition to the testing of the probing error according to VDI/VDE 2634 Part 2, it is also tested here whether the measuring system is capable of transforming several single images captured independently of each other into a common coordinate system.

The probing error essentially consists of two influences: on the one hand, the errors of a single measurement in the sensor measuring volume of the optical measuring system itself and on the other, the errors due to the transformation of the single measurements (e. g. recognizable from gaps in the overlapping region of transformed single images). A distinction is made between the probing error \({PF}\) (form) and the probing error \({PS}\) (size). Testing of the probing error is based on the measurement of the form and diameter of a test sphere.

For the determination of these two quality parameters the relevant mode of operation is also to be stated. If this is omitted, the two parameters are valid for all admissible modes of operation of the measuring system.

4.1.1 Definition of quality parameters

The quality parameter referred to as probing error \({PF}\) (form) is the range of the radial distances of the measuring points from a calculated fitting sphere. The fitted sphere is determined by the least-squares method with free radius.

The quality parameter called probing error \({PS}\) (size) is the difference between the measured and the calibrated diameter of the sphere.

4.1.2 Artefacts

To determine the probing errors \({PF}\) and \({PS}\) , spheres made of ceramics, steel or another suitable material with a diffusely scattering (not a volume-scattering) surface are used. To account for the area scanning characteristics of the systems, the spheres should have a diameter of ${(0,02{\cdots}0,2) {\cdot}L_S} $ . If, for technical reasons, other diameters must be used, these are to be stated and documented.

The form error of the test sphere must be distinctly smaller than the quality parameter to be tested. The roughness of the sphere surface should be negligibly small. For the artefact a calibration certificate must be available.

The material and the surface treatment of the test sphere are to be stated, as different materials may lead to different values for the probing error. If the manufacturer does not specify the material and the surface of the artefact, these can be chosen arbitrarily.

4.1.3 Procedure

For the joint determination of the probing errors \({PF}\) and \({PS}\) , the test sphere is measured on a ran- dom basis in at least three arbitrary positions within the measuring volume.

The test sphere must be recorded from different directions. This can be done by re-positioning of the measuring system and/or of the object to be measured (sphere with additional structures optionally situated in the space, e. g. photogrammetry markers or additional form features) as is also realized in practice. The sphere surface should be captured as completely as possible.

In each position the sphere should be measured from at least five different sensor positions (Figure 1 ). Restrictions as to the maximum number of sensor positions do not exist.

Figure 1 . Example of position and probing direction of the sensor relative to the test sphere

As far as this is possible with the measuring system, the sensor must each time be so aligned when re-positioned that the test sphere comes to lie in different locations in the sensor measuring volume. According to VDI/VDE 2634 Part 2, uniform distribution of the sphere positions over the whole sensor measuring volume is to be aimed at (Figure 2).

When using filters or algorithms, for outlier reduction or thinning-out point clouds, the alterable parameters must be stated. If this data is not stated, the quality parameters may be determined without filter. It is to be taken into account that the filter methods which are used in practical measurement can also be applied to verify the probing error.Different values for the probing error may have to be determined for different filter settings needed by the user.

Figure 2. Example of different positions of the same test sphere in the sensor measuring volume (fields of view of sensor)

4.1.4 Evaluation

For the determination of the quality parameters for each individual position of the test sphere a com-
mon fitting sphere is calculated from all single images using the least-squares method. From the measurement result obtained the signed radial deviations of the probing points from the fitting sphere are determined. In accordance with VDI/VDE 2634 Part 2, maximally 3 ‰ of the measuring points may be rejected when the fitting sphere is calculated. This is then to be stated and documented. The range of the (remaining) radial deviations is the quality parameter called probing error PF. The difference between the fitted diameter \({D_a}\) and the calibrated diameter \({D_r}\) of the test sphere is the quality parameter referred to as probing error \({PS}\):

\[PS = D_a - D_r \]

4.1.5 Assessment

The specification of the probing errors is complied with if the values determined for the quality parameters exceed the associated limits \({MPE_{XX}}\) in none of the measurement positions.

Here, the expanded uncertainty \({U}\) of the test method is to be accounted for (cf. DIN EN ISO 14253-1).

\[|P_x| {\le} MPE_{XX}| - U \quad for \thinspace the \thinspace manufacturer \]

\[|P_x| {\le} MPE_{XX}| + U \quad for \thinspace the \thinspace customer \]

Even if the specifications are exceeded in maximally one position of the test sphere, the measurements in this position must be repeated three times. If in all repeat measurements the measured valuesmreach or do not reach the limits, the acceptance test is successful

The limiting values for the quality parameters are to be complied with under all conditions permitted by the manufacturer. This applies in particular with regard to the surface properties of the artefacts and the filter parameters.

4.2 Quality parameter: sphere spacing error

In analogy to VDI/VDE 2634 Part 2, the quality parameter “sphere spacing error” serves to test the capability of the measuring system of performing length measurements from several different single images. Due to averaging effects, the probing error is not completely contained in the sphere spacing error. For the determination of the length measurement error in accordance with DIN EN ISO 10360, the procedure described in Section 4.3 is therefore to be chosen.

4.2.1 Definition of quality parameter

The sphere spacing error is obtained as the difference between the measured value and the cali-
brated value of a spacing of the centres of two spheres. Unlike in VDI/VDE 2634 Part 2, the measured spacing is derived from the measurementvalues from several area scannings. The limiting value SD of the admissible sphere spacing error is the quality parameter sphere spacing error. It is determined as a quantity independent of length and must be complied with in the whole measuring volume specified.

4.2.2 Artefacts

For the determination of the sphere spacing error, artefacts with spherical elements to be probed (e. g. handle-shaped, cf. Figure 1 in VDI/VDE 2634 Part 2) made of steel, ceramics or other suitable materials are used. The spheres should be ${(0,02{\cdots}0,2) {\cdot}L_S} $ in diameter. The surfaces of the spheres to be probed are diffusely scattering (not volume scattering).

The material and the surface treatment of the test spheres are to be stated, as different materials may lead to different values for the sphere spacing error.

If the manufacturer does not specify the material and the surface of the artefact, these are freely selectable.

The calibration uncertainty of the artefact must bedocumented and distinctly smaller than the maxi-
mum permissible sphere spacing error stated by the manufacturer for the measuring system to be tested (cf. DIN EN ISO 14253-1). Both the spacings and the form of all probed elements of an artefact must have been calibrated and the roughness of the elements to be probed should be negligibly small.

4.2.3 Procedure

The sphere spacing error \({SD}\) specified by the manufacturer must be complied with in the whole measuring volume for any arrangement of the artefact. Its determination is carried out on a random basis in seven different positions. It is recommended to arrange and measure the artefact as represented in Figure 3.

Figure 3. Recommended arrangement of artefacts when determining the sphere spacing error

As far as permitted by the measuring system, testing should be carried out with a measuring volume in the form of a cuboid which is greater than the sensor measuring volume. Unless agreed otherwise, the spatial diagonal of the measuring volume should at least have twice the length of the sensor measuring volume.

The greatest length to be tested must at least be 2/3 the length of the spatial diagonal of the measuring volume. The smallest length to be tested should not be smaller than 2/3 the shortest length of side of the measuring volume.

If possible, probing of the two spheres of the artefact in one image should be avoided. The measurement of the spheres is carried out using measuring points distributed as uniformly as possible over the whole surface.

When using filters or algorithms, respectively, for outlier reduction or thinning-out of point clouds,
the parameters which can be varied by the user must be stated. If these data are not given, the quality parameters can also be determined without a filter being used. It is to be taken into account that the filter methods as applied in practical measurement are also used for testing the sphere spacing error. Should the user need different filter settings, it might be necessary to determine different values for the sphere spacing error.

4.2.4 Evaluation

For the determination of the sphere spacing error the centres (positions) of the spheres probed are to be calculated for each tested length from the probing points for all single images by fitting by the least-squares method with free radius. According to VDI/VDE 2634 Part 2, maximally 3 ‰ of the measuring points may be rejected when calculating the fitting sphere. This is then to be stated and documented. The spacing of the sphere centres is the value \({L_{ka}}\) as indicated for the tested length.

The sphere spacing error \({SD}\) is obtained as the difference between the measured value \({L_{ka}}\) and the calibrated value \({L_{kr}}\) of the tested length in accordance with

\[SD = L_{ka} - L_{kr} \]

4.2.5 Assessment

When comparing the sphere spacing error \({SD}\) with its limit \({MPE_{SD}}\) , the expanded uncertainty \({U}\) of the test method is to be accounted for (cf. DIN EN ISO 14253-1) as follows:

\[|SD| {\le} MPE_{SD}| - U \quad for \thinspace the \thinspace manufacturer \]

\[|SD| {\le} MPE_{SD}| + U \quad for \thinspace the \thinspace customer \]

The quality parameter “sphere spacing error” is complied with if in terms of the amount, no sphere spacing error exceeds the limit for the maximum permissible sphere spacing error \({MPE_{SD}}\) considering the measurement uncertainty. If this limiting value is exceeded maximally once, the relevant measurement must be repeated three times and in these measurements the limiting value in question must not be exceeded another time. Otherwise, the acceptance test is not successful.

The limiting value for the quality parameter is to be complied with under all conditions permitted by the manufacturer. This applies in particular with regard to the surface properties of the artefacts and the filter parameters.

4.3 Quality parameter: length measurement error

By quality parameter “length measurement error” the three-dimensional error behaviour of the measuring system over the whole measuring volume is described. This error behaviour is due to superposition of various single errors such as, for example, systematic errors not corrected for, adjusting errors when linking various images of the object measured as well as random errors.

The length measurement error described here is different from the sphere spacing error described above. Due to the great number of admissible points to be probed when determining the spherespacing error, the probing error is not completely contained in the quality parameter due to averaging effects in the calculation of the fitting sphere and thus is not comparable with that of the measurement of gauge blocks. This is why to length measurement errors which are calculated from more than two probed points per length, the fraction of the probing error is to be separately added.

4.3.1 Definition of quality parameter

According to DIN EN ISO 10360, the quality parameter length measurement error E is the error with which the length of a material measure can be determined with the measuring system if the measurement is carried out by bidirectional probing of two opposite points from opposed directions on nominally parallel faces vertical to one of the two surfaces. The spacing between these points is the tested length. If the length measurement error cannot be determined as described above but, for example, by multiple-point probing of gauge blocks or by measurement of ball bars, this must be expressly stated by the manufacturer. Comparability of the results must be ensured by suitable measures (cf. also Section 4.3.4.).

When the length measurement error is determined,it is to be documented how the determination has been carried out, as on different test set-ups different values may be obtained for the quality parameter.

4.3.2 Artefacts

For the determination of the length measurement error, artefacts with material measures of length such as ball bars with two or more spheres, ball beams (summarily referred to as ball bars in the following), gauge blocks, step gauges (in the following called gauge blocks), ball plates and other artefacts with parallel faces or spheres are used as elements to be probed.

If ball bars and ball plates are used, the probed elements should be ${(0,02{\cdots}0,2) {\cdot}L_S} $ in diameter.

The material of the artefacts is to be stated, as different materials may lead to different values being obtained for the length measurement error. If the manufacturer does not lay down specifications for the material and the surface of the artefact, these will be freely selectable.

The calibration uncertainty of the artefact must be documented and distinctly smaller than the maximum permissible length measurement error specified by the manufacturer for the measuring device to be tested (cf. DIN EN ISO 14253-1). Both the spacings and the form of all probing elements of an artefact necessary for testing must have been calibrated and the roughness of the probing elements should be negligibly small.

4.3.3 Procedure

The length measurement error E stated by the manufacturer must be complied with in the whole measuring volume for any arrangement of the artefact. Its determination is made on a random basis in seven different positions. It is recommended to arrange and measure the artefact as shown in Figure 3.

As far as permitted by the measuring system, testing should be carried out using a cuboid-shaped measuring volume greater than the sensor measuring volume. Unless agreed otherwise, the spatial diagonal of the measuring volume should have at least twice the length of the sensor measuring volume.

The greatest length to be tested must at least be 2/3 the length of the spatial diagonal of the measuring volume. The smallest length to be tested should not be smaller than 2/3 the shortest length of side of the measuring volume. The measurement of the tested length in only one image shall be avoided, if possible.

When using filters or algorithms, respectively, for outlier reduction or thinning-out of point clouds, the parameters that can be varied by the user must be stated. If these data are not given, the quality parameters may also be determined without filter.

It is to be taken into account that the filter methods used in practical measurements are also used for testing the length measurement error. If the user needs different filter settings, different values for the length measurement error may have to be determined.

For the determination of the length measurement error, a distinction must be made between measu- rements using only gauge blocks and measurements carried out with ball bars and ball plates.

If gauge blocks are used, the two measuring faces of the gauge block are, if possible, recorded in the middle of the measuring face. This can be achieved by selection of that point from a cloud of measuring points that is nearest to the centre. For the evaluation of the length measurement error, it is expressly prescribed that only one single measuring point be used.

[!NOTE]

For the evaluation of the plane spacing error \({FD}\) , a plane through all measuring points on a measuring face of the gauge block may be determined by fitting and the spacing of the two planes identified along a reference straight line.

If ball bars and ball plates are used, the measurement is performed in analogy to Section 4.2. The measurement of the spheres is carried out with the aid of measuring points distributed over the whole surface of the sphere as uniformly as possible.

Compared to the measurement of single points on planes, the measurement of sphere positions is accompanied by an averaging effect and possibly a compensation for systematic probing errors. To provide comparability, it is possible to additionally measure a short gauge block with each measured length by the above method and to determine a correction value for the pertinent measured length. The orientation of the gauge block is selected approximately parallel to the respective measuring line of ball bar or ball plate. Alternatively, the correction value can also be obtained from the measurements of the probing error. The respective correction value is subsequently taken into account when the determination of the length measurement error is evaluated (cf. Section 4.3.4). If bars with only two spheres are used, the tested length can also be derived from two single measuring points on the outer caps. It is to be ensured here that theouter caps are probed from opposite directions.

4.3.4 Evaluatio

The evaluation depends on whether gauge blocks, ball bars or ball plates are used as artefacts.

If gauge blocks are used to determine the quality parameter, the tested length is calculated from the spacing of two measuring points on opposite gauge block faces. The difference between the tested length \({L_a}\) (indicated value) and the calibrated central length \({L_r}\) (correct value) of the gauge block (DIN EN ISO 3650) is the length measurement error \({E}\) :

\[E = L_a - L_r \]

[!NOTE]

For the plane spacing error fitting is applied to calculate a plane for each tested length from all probing points of a gauge block face. The surface normal of one of the two fitting planes defines the direction of a straight line running through an optional measuring point on one of the gauge block faces. The points of intersection of this straight with the two fitting planes are calculated. The spacing of these points of intersection is the measured value of the tested length. The difference between the tested length measured and the calibrated central length of the gauge block is the plane spacing error \({FD}\) . It serves for information only and may be helpful to identify systematic length-dependent measurement errors. The results furnished by the plane spacing error are similar to those provided by the sphere spacing error.

If ball bar or ball plate are used as artefacts for the determination of the length measurement error, in analogy to Section 4.2.4, the sphere centres (positions) and the radii of the probed spheres are to be calculated from all single images for each tested length by fitting by the least squares method with free radius. The spacing of the sphere centres is the indicated value \({L_{ka}}\) of the tested length. The difference between indicated value \({L_{ka}}\) and correct value \({L_{kr}}\) is the sphere spacing error \({SD}\) .

\[SD = L_{ka} - L_{kr} \]

Correction measures when using ball bars and ball plates

To offset the averaging effect and to compensate systematic probing errors in the measurement of sphere positions compared to the measurement of single points on planes, these influences are to be accounted for additionally. Several procedures are available:

Method A

The simplest way is to use the measurement results from the determination of the probing error. This method serves to estimate the most unfavourable case. It is to be taken into account that the properties (material, size, form, surface) of the respective artefacts, the probing strategy and the point distri- bution must, if possible, be the same for the determination of both the probing error and the length measurement error. The length measurement error E is obtained as the difference between the tested length \({L_{ka}}\) (indicated value) and the calibrated sphere spacing \({l_{kr}}\) (correct value) of the artefact plus the signed probing error \({PS}\) and the probing error \({PF}\).

This relation can be illustrated as follows:

Case 1:

\[(L_{ka} - L_{kr} +PS) \gt 0 \quad \rightarrow \quad E=L_{ka} - L_{kr}+PS+PF \]

Case 2:

\[(L_{ka} - L_{kr} +PS) = 0 \quad \rightarrow \quad E=PF \quad ordder \quad E=-PF \]

Case 3:

\[(L_{ka} - L_{kr} +PS) \lt 0 \quad \rightarrow \quad E=L_{ka} - L_{kr}+PS-PF \]

Using the signum function, the relation reads:

\[E = L_{ka} -L_{kr} +PS + (\text{sgn}(L_{ka} - L_{kr} + PS))PF \]

where

\[PS = (D_a - D_r) \]

For \({L_{ka} – L_{kr} + PS = 0, +PF or –PF }\) must optionally be assumed for \({E}\) .

The values thus determined for the length measurement error are comparable to those of a gauge block measurement. If this method is applied, it is advisable for the sphere measurements to record as many points to be probed for the sphere centre error as possible so that the influence of discrete point probing can be kept small, this influence being completely accounted for through addition of the correction values.

Method B

A more accurate method which, however, is also more costly is to measure not only the ball bar or ball plate but for each length also a short gauge block. The length measurement error E then is obtained as the difference between the tested length \({L_{ka}}\) (indicated value) and the calibrated sphere spacing \({L_{kr}}\) (correct value) of the ball bar or ball plate plus the length measurement error \({E_E}\) which is determined from the associated measurement of the short gauge block:

\[E = L_{ka} -L_{kr} +E_E = SD + E_E \]

If this method is applied it is advisable, too, for the sphere measurements to measure as many probing points for the sphere centre error as possible so that the influence of discrete point probing can be kept small, this influence being completely accounted for through addition of the correction value.

Method C

If ball bars with only two balls are used, the tested length can also be derived from two single measuring points such that on each of the two outer ball caps that point is selected whose spacing from the straight line through the sphere centres of the bar is smallest. The length measurement error E then is obtained from the sphere spacing error plus a correction \({E_K}\) calculated from the spacings \({R_1}\) and \({R_2}\) of the two selected points to be measured from the appurtenant sphere centre and the calibrated diameters \({D_{r1}}\) and \({D_{r2}}\) of the two spheres:

\[E = SD + E_K \]

\[E_K = (R_1 - D_{r1}/2) + (R_2 - D_{r2}/2) \]

Limiting values

In accordance with DIN EN ISO 10360-2, the limiting value of the length measurement error \({MPE_E}\) is stated either as a length-dependent quantity \({±(A+L/K)}\) , as maximum value \({±B}\) or as a combination of the two. It must be complied with over the whole measuring volume of the optical 3D measuring system and under all admissible conditions of measurement. For the limiting value for the length measurement error to be completely stated, the operating and ambient conditions referred to must also be given.

4.3.5 Assessment

The assessment is independent of whether gauge blocks or ball bars are used and is the same for all measuring volumes.

When comparing the length measurement error with its limits \({MPE_E}\) , the expanded uncertainty of measurement \({U}\) of the test method is also to be taken into account (cf. DIN EN ISO 14253-1):

\[|E| {\le} MPE_{E}| - U \quad for \thinspace the \thinspace manufacturer \]

\[|E| {\le} MPE_{E}| + U \quad for \thinspace the \thinspace customer \]

The quality parameter length measurement error is complied with if – taking account of the uncertainty of measurement – no length measurement error exceeds the limit for the maximum permissible length measurement error MPE E as regards its amount. If this limiting value is exceeded maximally once, the measurement in which the limit has been exceeded must be repeated three times. In these repeat measurements the limit must not be exceeded again. Otherwise, the acceptance test is not successful.

The limit for the quality parameter is to be complied with under all conditions permitted by the manufacturer. This applies in particular with regard to the surface properties of the artefacts and the filter parameters.

5 Re-verification

The re-verification check and the interim check (in the following referred to as “re-verification”) of optical 3D measuring systems serve to ensure long-term compliance with the quality parameters specified by the user. The comparison of the results of successive re-verifications permits a trend analysis to be made as to the changes in the device properties. As a result, conclusions can be drawn both for preventive maintenance of optical 3D measuring systems and for the re-verification interval. For trend analyses the modes of operation and the operating conditions must be approximately the same.

Prior to re-verification, the optical 3D measuring system is to be taken into operation in accordance with the operating instructions. The ambient conditions must correspond to the operating conditions for the optical 3D measuring system. It is further to be ensured that the arrangement and fastening of the artefacts is sufficiently stable. The artefacts must have assumed the mean temperature of the measuring volume. If the mean temperature of the artefacts or of the system components of the optical 3D measuring system significantly differ from the reference temperature in DIN EN ISO 1, appropriate temperature corrections are to be applied if this is also common practice in normal operation of the measuring system.

5.1 Artefacts

For the re-verification of optical 3D measuring systems, the same artefacts as for acceptance testing are used (cf. Section 4.1.2, Section 4.2.2 and Section 4.3.2).

5.2 Procedure

It is recommended to carry out re-verification of optical 3D measuring systems in analogy to the acceptance test and to test the same quality parameters (cf. Section 4). The user may reduce the number of measurements. If specified values are exceeded, repeat measurements may be conducted under the same conditions as in acceptance testing.

5.3 Evaluation

The evaluation in connection with the determination of the quality parameters is carried out in analogy to acceptance testing. The limiting values forthe quality parameters may, however, be specified by the user in accordance with his requirements.

In case the quality parameters are exceeded, the system is to be qualified functional only with reservations, and suitable steps are to be taken to remedy the deficiencies.

5.4 Re-verification interval and documentation

The re-verification interval must be individuallyfixed by the user of an optical 3D measuring system. It is dependent on the type and number of the system components, the uncertainty of measurement required and the ambient conditions prevailing at the varying locations of the system.

Re-verification of an optical 3D measuring system is to be carried out on the basis of a test schedule to be specified, in dependence on the stability of the system components, and also includes visual inspections (check for damage). After completion of the re-verification, a report is to be drawn up containing the summary test result. In the reverification report all measured values are to be documented.

Bibliography

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