## 1 Introduction  
Following the progressive miniaturization of today's manufacturing processes, more and more micro- and nanoparts with a complex geometry are applied to numerous industrial products, such as those in the automotive, medical, robotics and telecommunications fields. Full 3D measurements of these micro- and nanoparts with uncertainties down to 100 nm or even below are increasingly in demand [1; 2]. For instance, spray holes of fuel injection nozzles are to be fabricated with diameters of less than 100 \(\upmu\)m for a better fuel atomization. Measurements of the diameters and of the form and inner surface quality of the spray holes are of crucial importance. The microgears with modules from 1 \(\upmu\)m to 1 mm are key components of, e.g., microrobotics and medical devices. Nondestructive measurements and the quality control of both the mould and the replicated gears are of great importance. Today various techniques are available for full 3D measurements of microparts. One of the most important development trends in industrial dimensional metrology, having the potential to fulfil the requirements to measure complex microparts, is multi-sensor coordinate metrology. This combines the speed of optical measurements with the accuracy and 3D capability of tactile measurements and, more recently, the ability to measure interior features using X-ray computed tomography (CT) [3]. Improved metrological capabilities are needed to ensure the measurement traceability and reliability of the various measurement techniques. To offer the highly accurate full 3D metrological capability of microparts, a generation of micro-coordinate measuring machines (micro-CMMs) has been developed in the last two decades [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. The first micro-CMM was developed by [PERSON] et al. [4] at the National Physical Laboratory of the United Kingdom in the year 1999. In its configuration, they applied a mirror corner near the CMM probe as reference mirrors and utilized three laser interferometers and three autocollimators to measure the probe position with respect to the metrology frame. This novel design greatly reduced the Abbe offset, thus offering high 3D measurement accuracy (estimated as 50 nm at the 95% confidence level) over a measurement volume of 50 mm \(\times\) 50 mm \(\times\) 50 mm. Almost at the same time, [PERSON] et al. [5] developed a micro-CMM where linear scales are applied to measure the position of the probe tip fully in compliance with the Abbe principle in the \(x\)- and \(y\)-directions with a motion volume of 100 mm \(\times\) 100 mm \(\times\) 50 mm. The design was later commercialized by the Zeiss company in their micro-CMM F25 (unfortunately, F25 is now no longer in the product portfolio of Zeiss). A similar design idea has recently been realized in the micro-CMM \"TriNano\" with all the three axes measured with the Abbe principle [6]. In the year 2000, [PERSON] et al. [7] developed a nanopositioning and nanomeasuring machine (NMM) with a motion volume of 25 mm \(\times\) 25 mm \(\times\) 5 mm. They applied three miniature laser interferometers and two autocollimators to measure six degrees of freedom (DOFs) of the motion stage with respect to the Zerodur metrology frame, which is fully in compliance with the Abbe principle in all three axes. Using a similar principle, [PERSON] [8] built the CMM \"Isara\" with a measurement volume of 100 mm \(\times\) 100 mm \(\times\) 40 mm. Recently, a larger version (\"Isara 400\") has been developed by IBS Precision Engineering BV with a motion volume of 400 mm \(\times\) 400 mm \(\times\) 100 mm [9]. Various micro-CMM probes have also been developed [4; 11; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Most of them are mechanical tactile probes working in the contact mode [4; 11; 15; 16; 17; 18; 19].