Figure 1

Schematic illustration depicting the setup of the AMFlex2-OLTor1-FMLat1-FMFlex3 mode. Topographical feedback is driven at the coupled resonance frequency of the second flexural and the first torsional eigenmode using the flexural component for amplitude modulation. The first-torsional-eigenmode amplitude and phase are recorded at the same frequency in an open-loop configuration. Optionally, the setup can be expanded by one or two phase-locked loops, tracking the phase at resonance of the first lateral and/or the third flexural eigenmode which allowed us to quantify forces in in-plane and/or out-of-plane direction from the respective frequency-shift data. Dissipative tip-sample interactions can be analyzed from the drive amplitudes (alat,1, aflex,3) and the respective phase shifts (Φflex,2, Φtor,1). The cantilever dimension was substantially reduced for simplicity.