Compensation for the dynamics effect on nanoscale broadband viscoelasticity measurements using adaptive filtering approach

A large measurement frequency range (i.e., broadband) is desirable in mechanical property measurements; the measurement frequency range, however, is generally limited by the instrument dynamics effect. Such a limit arises due to the convolution of the instrument dynamics with the mechanical response of the material, particularly when the excitation force applied consists of multiple frequencies in the high-frequency range. The contribution of this paper is the utilization of the adaptive filtering approach to compensate for the instrument dynamics effect on nanoscale broadband viscoelasticity measurements using atomic force microscope (AFM). Specifically, the effect of the AFM dynamics convoluted into the measurement data is converted to an additive disturbance through a homomorphic transform, and the measured AFM dynamics response is utilized to generate the reference signal to the adaptive filter. The convergence of the adaptive filter is discussed, and the bound of the adaptive filter coefficient is quantified. The efficacy of the proposed approach is illustrated by implementing it to compensate for the dynamics effect on the broadband viscoelasticity measurement of a polydimethylsiloxane sample using AFM.