## 2 Instrumentation Developments
### 3D Tactile-Optical (Fibre) Probe  
The principle of a 3D fibre probe is illustrated in Figure 3a. The microprobe consists of an optical glass fibre which acts as the stylus, with a small spherical tip attached to the end. The tip is mounted in the focal plane of the imaging system of an optical coordinate measuring machine (CMM). It is mirror-coated on the lower hemisphere in order to achieve reflectivity. The fibre is fixed to an optical CMM by a three-curved prong leaf spring of low stiffness. This arrangement ensures the flexibility of the probe in all axes. The determination of the tip position in the axes horizontal to the optics (\(x\)- and \(y\)-directions) is similar to the well-known 2D fibre probe. The image of the illuminated stylus tip is located in the camera image of the optical CMM by correlation techniques. The stylus position along the \(z\)-axis is  
Figure 2: **(a)** 3D structure of the piezoresistive micro probe; **(b)** layout of the piezoresistance sensors (Wheatstone bridges) at the back of the membrane; **(c)** photos of the fabricated sensor chip and of the micro-3D-CMM probe as a whole. A one euro coin illustrates the size of the probe; and **(d)** a double triangle design realized for improving the isotropy of stiffness. Figures **(a)–(c)** are reproduced with permission from [36], Copyright IOP Publishing Ltd., 2009.  
determined by an optical distance sensor, e.g., based on the Foucault knife-edge principle [38], which measures the height of the upper end of the fibre. Apart from the 3D measurement function, also the design of the fibre probe has been further improved [25]. For instance, in order to achieve a better isotropic probing stiffness, the design of the leaf spring which suspends the stylus has been optimized by FEM calculations. The original and the optimized designs are shown in Figure 3c,d, respectively. With this improved design, the ratio between the stiffness values in vertical and in horizontal direction could be reduced down to 1.4:1 for standard probes (tip diameter: approximately 250 \(\upmu\)m). Furthermore, to eliminate any shadowing effects by the workpiece, a stylus with two spheres has been developed as shown in Figure 3e,f. In such a configuration, the lower sphere is applied to probe the workpiece, whereas the upper sphere is applied for measurements. The displacement ratio between the two spheres was calibrated prior to use. As an advantage, the imaging of the upper sphere is not limited by the workpiece and therefore no shadowing effect occurs. The simplest realization--which consists of a stylus with both spheres arranged vertically with one above the other--is shown in Figure 3e. The distance between the two spheres can be up to a few millimetres. This allows measurements in holes, without the upper sphere being obstructed by the sidewalls of the hole, and thus without reducing the measurement accuracy by this optical effect. However, it is to be mentioned that larger distances between the two spheres lead to larger measurement deviations due to the smaller displacement of the upper sphere. Therefore, the distance between the spheres should be as small as possible, depending on the measurement application. Another advanced design of the dual-sphere stylus is the L-shaped configuration, as shown in Figure 3f. The stylus consists of a single fibre with two spheres, whereby the fibre is bent below the upper sphere. With such a probe, structures with undercuts can be measured. Here, the bent angle and the length of the bent part can also be adapted to the measurement task. The 3D fibre probe is capable of achieving a typical probing speed of 0.1 mm/s to 3 mm/s. The specified probing errors are:  
Figure 3: (**a**) Schematic diagram showing the measurement principle of a 3D fibre probe; (**b**) photo of a 3D fibre probe measuring a ruby sphere (\(\Phi\) 2 mm); (**c,d**) the designs of the leaf spring before and after improvement, respectively; (**e**) an alternative design with a dual-sphere stylus; and (**f**) an alternative design with an L-shaped stylus [25].