= Solution
\b[The controlled quantity is the maximum repulsive <force> in each tapping cycle.] In <PeakForce quantitative nanomechanical mapping>, a vertical modulation below the <cantilever> resonance produces a force-distance cycle at each pixel. The optical lever measures deflection; the calibrated <cantilever> stiffness converts this to <force>. Subtract the measured peak <force> from the setpoint and use <proportional-integral control> to adjust the mean vertical scanner position. Excessive peak <force> makes the controller withdraw the sample or tip; insufficient <force> makes it approach. The scanner position required to maintain the setpoint supplies the topography signal. This controls the top of the repulsive branch in the preceding curve, rather than the oscillation amplitude used in conventional tapping mode.<PeakForce QNM by Bruker>[Peak normal-force control and simultaneous mechanical-property channels]{ref}
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-1-afm-feedback.png]
{title=Peak-force feedback with an independent vertical modulation}
{source=paper-1-afm-feedback.py}
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