Resolution

With image processing sensors, the structural resolution can be influenced within wide limits by the choice of magnification (high magnification results in high resolution). This adjusts the pixel size, which is important for resolution. At the same time, however, the size of the overall image and thus the measuring range "in the image" also changes – a high number of pixels leads to a correspondingly large measuring range. The relative structural resolution results from the ratio of pixel size to measuring range. It corresponds to the reciprocal value of the number of pixels in the respective orientation and is currently (as of 2019) in the order of 1/1000 to 1/5000 for conventional sensors. With a relative structural resolution of 1/1000, for example, only features significantly larger than 0.1 mm can be resolved and measured in a measuring field of 100 mm in length.

For optical distance sensors, a distinction can be made between the axial resolution in the orientation of the optical axis (not quite aptly referred to as "vertical" or "in the z-direction") and the lateral ("horizontal") resolution in the measuring plane. The guidelines of the VDI/VDE 2617 series[9] describe methods for determining and reverification testing of the structural resolution for lateral measuring sensors (Sheet 6.1) and for distance sensors (Sheet 6.2), which are based on the determination of the modulation transfer function. Edges or sinusoidal gratings of different wavelengths are used as test specimens. For distance sensors, other structure standards such as bores, gaps, pins or spheres may also be defined by the manufacturer.

For tactile and X-ray tomography sensors, the distinction between axial and lateral resolution is not useful. However, the methods known from optical sensors can be used in an adapted form. In addition, VDI/VDE 2617 Sheet 13 (also VDI/VDE 2630 Sheet 1.3) describes an alternative method for X-ray tomography sensors. This is based on determining the size of the smallest measurable structures, such as spheres or spherical arrangements. However, a binding standardisation for resolution does not yet exist due to a lack of practical experience. The methods described above are only recommendations. In the DIN EN ISO 10360[10] series of standards, these methods are also recommended for optical distance sensors (Part 8). This is not currently planned for tactile (Part 5) and laterally measuring optical sensors (Part 7). In practice, the structural resolution of tactile sensors can be easily estimated using the radii of the sensing spheres.

For the application of X-ray tomography for inspection tasks (e.g. cavity detection), the structural resolution of the volume data (voxel) is described using the modulation transfer function. The characteristic value calculated in this way in the unit "line pairs per mm" defines an inspection limit for the recognisability of a structure, but does not allow any sufficient conclusions to be drawn about the measurability of features. In traditional X-ray tomography in the German-speaking world, the term spatial resolution is used for this characteristic value of structural resolution, which is not entirely accurate.

The spatial resolution of coordinate measuring machines is determined by the resolution of the scale systems used (here always spatial resolution) and the spatial resolution of the sensors. In the case of image processing and X-ray tomography sensors, the spatial resolution of the sensors is initially also determined by the pixel or voxel size of the camera or X-ray detector and the structural resolution of the other system components[8]. However, grey value interpolation (subpixeling, subvoxeling) increases the spatial resolution significantly above the structural resolution. This is the only way to achieve a sufficiently high spatial resolution of the overall system with acceptable measuring ranges of the sensors.

It should be noted that the spatial resolution must be much smaller than the desired measurement uncertainty. This means, for example, that with a measurement uncertainty of a few micrometres, a spatial resolution of the sensor of well below 1 µm is required. This results in relatively small sensor measuring ranges (a maximum of a few 100 mm). The measurement of complex parts with larger measuring ranges therefore requires the sensors to be positioned using the coordinate measuring machine axes. This corresponds to the already described measurement "on the image" or Raster Tomography.