# State of the Art of Tactile Micro Coordinate Metrology
## 3 Stage and Metrology Systems Design  
The second critical element of an accurate micro CMM is the 3D translation stage with the metrology system. In order to achieve smallest uncertainties, the Abbe principle must be strictly fulfilled, _i.e._, the reference scale must be in line with the measured length and thus always pointing  
Figure 1: METAS tactile probe for micro parts (housing removed). towards the probe element for all positions of the stage, which imposes severe design restrictions. For classical CMMs with large measurement volumes, this cannot be realized due to limited space and disproportional cost. Two major classes of metrology systems can be distinguished, _i.e._, laser interferometer and incremental scale based systems. Abbe free stages with interferometers use a moving frame with mirrors onto which usually the workpiece is placed, as it is shown for the two-dimensional case in Figure 2 (left). Plane mirror interferometers are used to measure the displacement of the mirror frame with respect to the metrology frame with the probe. To build an Abbe free measurement stage using incremental scales is somewhat more complicated because the scales need to be connected with both frames and therefore require additional bearings. Figure 2 (right) shows a possible solution in 2D, as proposed by [PERSON] _et al._[22]. Whereas measurement stages with incremental scales are more robust for industrial environment and potentially cheaper, they have the disadvantage, that the additional bearing between the two frames is part of the measurement loop and thus induces an additional uncertainty contribution. Incremental scale based measurement stages have been proposed by TUE [22], which was later on commercialized by Zeiss for the micro coordinate machine F25 [8] (the instrument F25 is no longer part of the product portfolio of Zeiss). In this design, the Abbe principle is respected for the \(x/y\)-stage, while for a \(z\)-displacement of the probe out of the \(x/y\)-plane an Abbe offset must be taken into account. The F25 provides a measurement volume of 100 mm \(\times\) 100 mm \(\times\) 100 mm. A similar design, but with all three axes in Abbe, has been realized by TUE [23] for the TriNano micro CMM and is commercialized by XPRESS [13]. One of the first Abbe free interferometric stages for coordinate metrology was realized at NPL: a conventional CMM was used for the 3D movement of a cube corner supporting the mirrors for reflecting the interferometer beams [9]. TU Illmenau designed an ultra-precise 3D stage with Zerodur(r) (Schott AG, Jena, Germany) frame and a multi-axis interferometer including angular motion (yaw) measurement for their nano-positioning and nano-measuring machine NMM [24], which is commercialized by SIOS [25]. The Hefei University of Technology built two prototype micro CMMs, both with roller bearing stages driven by piezo motors and laser interferometers for stage position sensing [26; 27]. An original ultra precision stage development at Philips CFT [28] has been installed at METAS and was the basis for a new development by IBS [29] leading to the Isara 400 machine [30]. Figure 2: Principle of measurement stages (2D case for simplification of drawing). **(left)** Laser interferometer scales and moving workpiece stage with reference mirror frame; **(right)** Incremental scales and moving probe stage with additional bearings between frames. The ultraprecision stage of the METAS micro CMM [4; 28] has vacuum preloaded air bearings. The stages are driven by Lorenz actuators and their motion is measured and controlled by three plane mirror heterodyne interferometers. The original V-configuration of the guideways with wedges as shown in Figure 3 makes the stage very compact and stiff. The working volume of the stage is 90 mm \(\times\) 90 mm \(\times\) 38 mm. According to Figure 2 (left) the probe head remains in a fixed position connected to the metrology frame while the stage is moving the workpiece during measurements.