Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach
Journal of Applied Physics 98(11): 114904
Dynamic atomic force microscopy (AFM) offers many opportunities for the characterization and manipulation of matter on the nanometer scale with a high temporal resolution. The analysis of time-dependent forces is basic for a deeper understanding of phenomena such as friction, plastic deformation, and surface wetting. However, the dynamic characteristics of the force sensor used for such investigations are determined by various factors such as material and geometry of the cantilever, detection alignment, and the transfer characteristics of the detector. Thus, for a quantitative investigation of surface properties by dynamic AFM an appropriate system identification procedure is required, characterizing the force sensor beyond the usual parameters spring constant, quality factor, and detection sensitivity. Measurement of the transfer function provides such a characterization that fully accounts for the dynamic properties of the force sensor. Here, we demonstrate the estimation of the transfer function in a bandwidth of 1 MHz from experimental data. To this end, we analyze the signal of the vibrations induced by snap-to-contact and snap-off-contact events. For the free cantilever, we determine both a parameter-free estimate [empirical transfer function estimate (ETFE)] and a parametric estimate of the transfer function. For the surface-coupled cantilever the ETFE is obtained. These identification procedures provide an intrinsic calibration as they dispense largely with a priori knowledge about the force sensor.