arXiv:1002.4284v2 [cond-mat.mes-hall] 3 Mar 2010 1 Thermal fluctuation of the cantilever position sets a fundamental limit for the precision of any Scanning Force Microscope. In the present work we analyse how these fluctuations limit the deter- mination of the resonance frequency of the tip-sample system. The basic principles of frequency detection in Dynamic Scanning Force Microscopy are revised and the precise response of a typical frequency detection unit to thermal fluctuation of the cantilever is analysed in detail. A general relation for thermal frequency noise is found as a function of measurement bandwidth and can- tilever oscillation. For large oscillation amplitude and low bandwidth, this relation converges to the result known from the literature, while for low oscillation amplitude and large bandwidth we find that the thermal frequency noise is equal to the width of the resonance curve and therefore stays finite, contrary to what is predicted by the relation known so far. The results presented in this work fundamentally determine the ultimate limits of Dynamic Scanning Force Microscopy. Thermal frequency noise in low oscillation amplitude Dynamic Scanning Force Microscopy J. Colchero, M. Cuenca, J.F. Gonz´ alez Mart´ınez, J. Abad, E. Palacios-Lid´ on and J. Abell´ an Abstract Facultad de Qu´ımica, Departamento de F´ısica, Universidad de Murcia, E-30100 Murcia.