High-speed demodulation in multifrequency atomic force microscopy

Atomic Force Microscopy (AFM) has been integral in the field of nanoscale engineering since its invention in 1986 by Binnig et al. By sensing microcantilever tip–sample interactions, atomic scale resolution imaging is achieved which far exceeds the optical diffraction limit. Through gentle mechanical interrogation, high-speed AFM has enabled several biological processes to be captured for the first time. Multifrequency AFM (MF-AFM) methods allow for the study of tip-sample interactions occurring at multiple frequencies. This extends imaging information beyond the topography to a range of nanomechanical properties including sample stiffness, elasticity and adhesiveness. The acquisition of these observables requires tracking the amplitude and phase of additional frequencies of interest. These include higher harmonics of the fundamental frequency, higher flexural eigenmodes and intermodulation products. Regardless of which particular MF-AFM method is employed, they each require the demodulation of amplitude and phase to form observables for the characterization of nanomechanical properties. This thesis begins with the consolidation of demodulators for intermittent contact AFM. The demodulators are unified in a standard modeling framework which includes digital implementation on a standard FPGA platform. Following this, a rigorous experimental comparison of conventional and model-based demodulators is performed with respect to tracking bandwidth, noise performance, robustness to unwanted frequency components and implementation complexity. Several methods are found to achieve single-cycle tracking, however at this tracking bandwidth the majority are unusable due to large demodulation artefacts. Conventional high-speed non-synchronous demodulators are shown to be incompatible with MF-AFM, due to the lack of robustness against unwanted frequency components in the input signal. In contrast, synchronous demodulators are shown to provide accurate estimates in the presence of other frequency components. The results show that the conventional lock-in amplifier, coherent demodulator, Kalman filter, Lyapunov filter and direct design method are suitable for MF-AFM. The comparison concludes with demodulator recommendations for a number of common AFM applications. To alleviate the complexity scaling issue of the multifrequency Kalman filter, the simpler Lyapunov filter is extended to track multiple frequencies. Investigations into tracking bandwidth, off-mode rejection and cross-coupling show promising MF-AFM capabilities. A proof of concept is verified through higher harmonic AFM amplitude and phase imaging on both a stiff and compliant sample with a five-channel Lyapunov filter. A limitation, common to both the Kalman and Lyapunov filters, is found to be a fixed first-order response. This motivates the extension of the direct design method to multiple frequencies, which is achieved by individually designing demodulators and operating them in parallel. Each MF-AFM demodulation technique is assessed with respect to sensitivity to unwanted frequency components, as well as implementation complexity on an FPGA. At high tracking bandwidths, model-based demodulation techniques are shown to benefit from having the ability to precisely zero other modeled frequency components. This is verified in AFM imaging experiments which show a large reduction in demodulation artefacts. The comparison concludes with demodulator recommendations for common MF-AFM imaging modes and applications.