## 1 Introduction
In their configuration, typically a stylus (having a probing sphere at its free end, and usually fixed to a rigid centre plate/boss at the other end) is suspended by a type of flexure structure, for instance, flexure strips [4; 15], slender rods [14; 18], flexure hinges [11] or membranes [16]. When the probing sphere is touched and deflected by a workpiece, the flexure structure is deformed due to the probing force. By measuring the deformation via various sensing techniques, for example by means of capacitive sensors [4; 15], piezoresistive sensors [16], inductive sensors [11], laser focus sensors [14], a Michelson interferometer combined with an autocollimator [17], or even by means of low-cost DVD pick-up heads [18], the translational motion of the probe sphere in 3D can be derived. Some of the probes [15; 16] are realized based on the micro-electro-mechanical systems (MEMS) technique, which offers a much smaller dynamic mass (20 mg) and thus enables a potentially higher measurement speed. Although being the mostly used probing technique in micro-CMMs and offering outstanding measurement performance (3D uncertainty typically in the order of tens of nanometres), tactile probes have several limiting aspects. The first aspect concerns the probing force and the probing stiffness. A design trade-off needs to be made between the stiffness and the flexibility of the probing element, for instance to avoid damaging the sensitive parts on the one hand, and to overcome the surface forces or inertial loads on the other hand. To overcome this trade-off, the University of Nottingham (UK) has recently developed a probe whose stiffness is variable due to the use of a switchable suspension structure [19]. The second limitation is related to the contact measurement mode. This method hasseveral drawbacks--such as possible surface damage, unwanted adhesion to surfaces, or measurement bias due to the inertia force. In addition, the contact mode microprobes usually apply styli with a limited aspect ratio to achieve a better measurement stability. To mitigate these problems, non-contact mode micro-CMM probes have been developed [21; 22; 23]. In the non-contact measurement mode, the probes are vibrated and the change of the vibration amplitude due to the probe sample's interaction is usually applied for measurements. For instance, [PERSON] et al. [21] developed a high-aspect-ratio microprobe using a probe shank with a diameter of 7 \(\upmu\)m having an aspect ratio of 700:1. During the measurements, its probe shank is oscillated in a standing wave. The motion of the free end of the probe shank forms a virtual probe tip to serve as the contact point, thus no spherical ball is required. [PERSON] et al. [22] developed a novel vibrating tactile probe for which six piezoelectric actuators and sensors are fabricated using electro-discharging machining on the three legs of its triskelion design. However, the shape and stability of the motion trajectory of the non-contact probing tip are a critical issue. [PERSON] et al. [23] reported that the shaft moved in an elliptical motion in their design. Therefore, a compensation method is applied by measuring the stylus' displacement using position sensitive detectors (PSDs). However, the PSDs are bulky and consequently limit the available measurement space. The third limitation concerns the measurement loop. The measuring sensors of most of the tactile probes are typically located at the suspending membrane or at the flexure strips and measure the signal, which is being transferred via the probing styli. Consequently, the deformation of the probing styli is \"invisible\" in the sensor's readout, which leads to measurement errors. Such a problem becomes much more serious for probes with a smaller styli diameter (\(d\)) and a longer styli length (\(l\)) as the deformation is inversely proportional to \(d^{4}\) and proportional to \(l^{3}\)[20]. To tackle these problems, a tactile optical probe--well known as the fibre probe today--has been developed at the Physikalisch-Technische Bundesanstalt (PTB) [24].