Calculation of thermal noise in atomic force microscopy

Thermal fluctuations of the cantilever are a fundamental source of noise in atomic force microscopy. We calculated thermal noise using the equipartition theorem and considering all possible vibration modes of the cantilever. The measurable amplitude of thermal noise depends on the temperature, the spring constant K of the cantilever and on the method by which the cantilever deflection is detected. If the deflection is measured directly, e.g. with an interferometer or a scanning tunneling microscope, the thermal noise of a cantilever with a free end can be calculated from square root kT/K. If the end of the cantilever is supported by a hard surface no thermal fluctuations of the deflection are possible. If the optical lever technique is applied to measure the deflection, the thermal noise of a cantilever with a free end is square root 4kT/3K. When the cantilever is supported thermal noise decreases to square root kT/3K, but it does not vanish.