## 2 State of the Art--Nanopositioning and Nanomeasuring Machines  
In general, different approaches are used in nanopositioning and nanomeasuring technology. These include the sample-scanning mode, mixed-scanning mode and scanning probe mode [12]. In the sample-scanning mode, the measuring tool remains in a fixed position while the sample is moved by a machine table. In the scanning probe mode, the measuring tool is moved in all three spatial directions while the sample to be investigated is fixed.  
In 1890, [PERSON] described an important principle of length measuring technology, where the measuring apparatus is to be arranged in such a way that the distance to be measured forms the straight-line continuation of the graduation, serving as a scale [13; 14]. In this measuring arrangement, length measuring deviations, which are caused by systematic or accidental tilting, are reduced [14].  
This Abbe comparator principle [13] was further developed into the extended three-dimensional Abbe comparator [15; 16]. The nanopositioning machines developed at the Technische Universitat Ilmenau are based on this principle, as this concept offers the possibility of using the high accuracy of the laser interferometer for 3D measurements. Because in the sample-scanning mode the probe as well as the measuring system are attached to a metrological frame, the Abbe comparator principle is fulfilled in all three measuring axes in which the length- and angle measuring systems do not have to be displaced. Based on this concept, the nanopositioning and measuring machine NMM-1 was developed, where three interferometric length measuring systems intersect in the touching point of the probe [17]. This way, the Abbe comparator concept is complied in all three directions of motion. In order to avoid higher-order error influences due to angular tilt, additional angular sensors are mounted. These sensors are detecting the angular tilt, which is compensated for by the drive system.  
Due to the overall concept of the machine, a resolution of 0.1 nm and a measurement uncertainty of 9 nm can be achieved in the measuring range of 25 mm \(\times\) 25 mm \(\times\) 5 mm [8].  
After evaluating and testing the NMM-1, experience was gained and a new nanopositioning and measuring machine--the so-called NPMM-200--was developed, which is also based on the sample-scan mode and allows a significantly larger measuring range of 200 mm \(\times\) 200 mm \(\times\) 25 mm as well as an increase in performance in terms of position resolution [18]. Here, a three-dimensional measurement uncertainty of 30 nm was achieved [4].  
The company _IBS Precision_ developed a machine with a significantly larger measuring range: the nanocoordinate measuring machine ISARA 400 with a positioning range of 400 mm \(\times\) 400 mm \(\times\) 100 mm. However, the mixed-scanning mode is used here, where the machine table and the measuring tool are moved. The Abbe principle is also fulfilled here, due to the arrangement of the interferometric length measuring systems. The ISARA 400 achieves a measuring resolution of 1.6 nm and a measuring uncertainty of 100 nm [19].  
The positioning machines presented have been specially developed to be able to move in all three measuring axes. Particular attention was placed on enabling a high movement range in the \(z\) direction. For very sensitive measuring tools such as tip-based systems, however, it is essential to have a particularly stable \(z\) axis during the movement of the sample stage.  
For this reason, the nanofabrication machine (NFM-100) was developed to demonstrate and investigate the combination of tip-based technology and nanopositioning technology. This machine only moves in the \(x\) and \(y\) direction within a movement range of 100 mm in diameter. In principle, it follows the same principle, i.e., the sample-scanning mode, as the NMM-1 and the NPMM-200 but without allowing movement in the \(z\) direction.