Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2021/paper-1/1/ii/solution

Reducing the feedback gain increases the distance traveled before the vertical actuator responds to a change in height. A simple illustrative response is
where is the accessible, tip-convolved profile and is the recorded actuator height. At scan speed , the characteristic spatial lag is .
On a left-to-right trace, descent into a pore is late: the tip initially remains too high and may lose contact. At the opposite rim it also rises late, increasing the contact force before the actuator catches up. The lower plateau may be shortened or not reached, making the depression appear too shallow. The whole response is displaced towards larger .
On the right-to-left retrace the same temporal lag produces the opposite displacement in laboratory coordinates. Descent is now delayed at the right-hand edge and ascent at the left-hand edge. imaging trace and retrace separate most strongly near height changes, with opposite spatial shifts and rounded transitions. The central low-gain curves in the figure show this behavior on common axes. Reduced gain alone does not require oscillatory ringing; the first-order lag already explains the principal difference.

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