  Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic
force microscopy that probes the nonlinear tip-surface force by measurement of
the mixing of multiple tones in a frequency comb. A high $Q$ cantilever
resonance and a suitable drive comb will result in tip motion described by a
narrow-band frequency comb. We show by a separation of time scales, that such
motion is equivalent to rapid oscillations at the cantilever resonance with a
slow amplitude and phase or frequency modulation. With this time domain
perspective we analyze single oscillation cycles in ImAFM to extract the
Fourier components of the tip-surface force that are in-phase with tip motion
($F_I$) and quadrature to the motion ($F_Q$). Traditionally, these force
components have been considered as a function of the static probe height only.
Here we show that $F_I$ and $F_Q$ actually depend on both static probe height
and oscillation amplitude. We demonstrate on simulated data how to reconstruct
the amplitude dependence of $F_I$ and $F_Q$ from a single ImAFM measurement.
Furthermore, we introduce ImAFM approach measurements with which we reconstruct
the full amplitude and probe height dependence of the force components $F_I$
and $F_Q$, providing deeper insight into the tip-surface interaction. We
demonstrate the capabilities of ImAFM approach measurements on a polystyrene
polymer surface.
