Scanning probe microscopes are very well used for characterization at the nanometer scale. To ensure the measurement coherency and the accuracy of the results, those microscopes need to be periodically calibrated. It's done thanks to reference standards whose dimensional characteristics are measured by a metrological atomic force microscope (mAFM) for example. The aim of this thesis work is to develop in France the first metrological atomic force microscope in order to calibrate the reference standards that are used in scanning probe microscopy. Displacement range is about 60 μm in the horizontal plane and 15 μm along the vertical axis. Dimensional measurements of the tip-sample relative position are achieved with four differential interferometers whose laser wavelengths are calibrated in order to perform direct traceability to the length standard. The tip sample relative position uncertainty is about one nanometer for the whole range. The conception of this metrological AFM is lead through four main design rules: (i) the minimization of Abbe errors, (ii) the optimization of the metrological loop, (iii) the reduction of thermal effects during the measurement process and (iv) the optimization of ambient interferometrical measurement.
