*3.3. Uncertainty of the Systematic Error, ub*

Table 3 lists the standard uncertainty associated with the systematic error of the measurement process (*ub*). It is assessed by the difference between the average value obtained during the measurement process variability (*up*) parameter assessment and the indicated value of the CMM during the dummy calibration process.

The systematic error (*ub*) results show a wide range of values. While some results are within a few microns, others are between 0.1 ÷ 0.2 mm (absolute values). The average value for all the GD/Ts is within 50 μm. At this point, it is not easy to understand and justify the wide range of values obtained for the (*ub*) uncertainty contributor, but it is possibly explained by the higher point quantity and more homogeneous point distribution of the measurements obtained by the 3D optical system compared to the CMM measurements.

At this point, it makes sense to highlight, as in the introduction, that 3D optical systems are a relatively new technology, and their measurement error sources are still being researched. They are affected by many potential uncertainty error sources, such as the light condition, measurement and material properties, system orientation and resolution, ambient temperature, measurement volume, and chromatic effects, which complicate the measurement uncertainty assessment process to a large extent. Nonetheless, as stated previously within the introduction, this study aims to present a point cloud measurement task-specific uncertainty assessment method and its experimental implementation. The obtained expanded measurement uncertainty results are not as important as those of the method presented by the authors.


**Table 3.** (*ub*) uncertainty contributor according to ISO 15530-3 technical specification.

#### *3.4. Expanded Measurement Uncertainty, U*

Table 4 summarises the uncertainty budget for the experimental implementation of the proposed method. It shows the three major uncertainty contributors and the expanded measurement uncertainty result U obtained from Equation (2). It should be noted that the measurement results are not corrected by the amount of systematic effects; therefore, the (*ub*) contributor is considered within the final uncertainty budget.

The uncertainty budget shows that the systematic error contributor (*ub*) is the main contributor to the final result. While the CMM calibration uncertainty (*ucal*) contributor average value falls within 1 μm and the measurement process variability (*up*) average value is less than 10 μm, the systematic error (*ub*) average value falls within 50 μm. Thus, the CMM calibration uncertainty (*ucal*) becomes negligible, which means that the main contributors to the task-specific uncertainty budget are the measurement process variability (*up*) and systematic error contributor (*ub*). As stated before, the measurement result is not corrected by the number of systematic effects which, in this case, are the main uncertainty sources for the measurement with 3D optical systems.


**Table 4.** (U) Expanded measurement uncertainty assessment results. Uncertainty budget.
