Amplitude modulation was one of the original modes of operation introduced by Binnig and Quate in their seminal 1986 AFM paper, in this mode the sensor is excited just off resonance. By exciting the sensor just above its resonant frequency, it is possible to detect forces which change the resonant frequency by monitoring the amplitude of oscillation. An attractive force on the probe causes a decrease in the sensors resonant frequency, thus the driving frequency is further from resonance and the amplitude decreases, the opposite is true for a repulsive force. The microscopes control electronics can then use amplitude as the SPM reference channel, either in feedback mode, or it can be recorded directly in constant height mode.
Amplitude modulation can fail if the non-conservative forces (damping) change during the experiment, as this changes the amplitude of the resonance peak itself, which will be interpreted as a change in resonant frequency. Another potential problem with amplitude modulation is that a sudden change to a more repulsive (less attractive) force can shift the resonance past the drive frequency causing it to decrease again. In constant height mode this will just lead to an image artefact, but in feedback mode the feedback will read this as a stronger attractive force, causing positive feedback until the feedback saturates.
An advantage of amplitude modulation is that there is only one feedback loop (the topography feedback loop) compared to three in frequency modulation (the phase/frequency loop, the amplitude loop, and the topography loop), making both operation and implementation much easier. Amplitude modulation, however, is rarely used in vacuum as the Q of the sensor is usually so high that the sensor oscillates many times before the amplitude settles to its new value, thus slowing down operation.