  A method is presented for calibrating the higher eigenmodes (resonance modes)
of atomic force microscopy cantilevers that can be performed prior to any
tip-sample interaction. The method leverages recent efforts in accurately
calibrating the first eigenmode by providing the higher-mode stiffness as a
ratio to the first mode stiffness. A one-time calibration routine must be
performed for every cantilever type to determine the power-law relationship
between stiffness and frequency, which is then stored for future use on similar
cantilevers. Then, future calibrations only require a measurement of the ratio
of resonance frequencies and the stiffness of the first mode. This method is
verified through stiffness measurements using three independent approaches:
interferometric measurement, AC approach-curve calibration, and finite element
analysis simulation. Power-law values for calibrating higher-mode stiffnesses
are reported for three popular multifrequency cantilevers. Once the higher-mode
stiffnesses are known, the amplitude of each mode can also be calibrated from
the thermal spectrum by application of the equipartition theorem.
