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This paper presents different possibilities of determination of cantilever deflection using the beam theory and finite element method. It is proved that the cantilever can be described as an elementary beam with the force point within the neutral fibre, and its deflection can be determined according to Euler-Bernoulli beam theory. The determined analytical relationship between the inclination angle of the cantilever beam and displacement of its end is used for further calculations of the output signal of the atomic force microscope (AFM) position detector optical lever. Such position detectors as an interferometer, optical lever, and focus sensor are compared for application in an AFM. Analytical and numerical position detector models are developed here for determination of characteristic curves of detector output signals and their sensitivities. The comparison shows that the interferometer is by far the most sensitive and the optical lever is similarly sensitive to the focus sensor. Furthermore, a combined deflection-detection system that contains a homodyne Michelson interferometer and an optical lever is discussed.

Existing long-range nanopositioning and nanomeasuring machines are based on three independent linear movements in a Cartesian coordinate system. This in combination with the specific nature of sensors and tools (further on summarized as tool) limits the addressable part geometries. This article contributes to the enhancement of multiaxial machine structures by the implementation of rotational movements while keeping the precision untouched. A parameter based dynamic evaluation system with quantifiable technological parameters has been set up and employed to identify general solution concepts and adequate substructures. First evaluations show high potential for sample scanning mode variants considering linear movements of the object in combination with angular movements of the tool, considering a goniometer setup in specific. The evaluation system is further enhanced by the implementation of data based on comprehensive design catalogues, uncertainty calculations and CAD-model based footprint analysis for specific setups. To support the selection, detailed parameter sets are generated containing explicit moving ranges, uncertainties, resolutions, reproducibilities and costs. This approach is also applied to the rotation of the object. The results are compared to the tool rotation and mixed versions. After all, the knowledge gained, is formed into general rules for the verification and optimization of design solutions for multiaxial nanopositioning machines.