AFM tip-convolution artefact

A distortion caused by the finite shape or multiple contact points of a scanning tip. For a single-valued sample height $h$ and a tip profile $t$ measured upward from its apex, nonpenetration requires the indicated apex height to satisfy $z(x)\ge h(u)-t(u-x)$ for every $u$. The ideal accessible envelope is consequently $z(x)={\max }_u[h(u)-t(u-x)]$. This geometric operation is distinct from an ordinary linear convolution and from feedback lag.

Duplicated or distorted surface features arising when more than one effective apex contributes to the measured envelope. Attachment or loss of a particle can change the image abruptly without changing the sample.