Consider the two dimensional example shown on the left. It is an AFM profile of a single "bump" which is wider than it is high. What does this scan line tell us about the topography of the tip and sample?

From our understanding of the convolution process we know that the profile can be created by an infinite number of tip/sample combinations. At the one extreme, an very sharp tip can pass over a sample whose topography matches the profile, in which case there is almost no convolution or distortion. At the other extreme, the tip might be so blunt that its apex has the shape of the inverted profile. When imaging a very sharp sample feature, the tip shape is reflected in the obtained image.

In this way we can take any AFM scan and get a "worse case" scenario as to what the tip may have been.

Consider now the line scan having two bumps, one less wide than the other. Again we ask, what does this tell us about the shape of the tip? There are now two possibilities.

Case 1 : Tip with single apex

If we take the two profiles and overlap them at their apices, the smaller topography will better represent that of the tip. A line scan having many more features on it could further improve the possibilities for a tip and sample combination.
If the sample features are small enough, their contribution to the convoluted image is almost negligible. If we then extend this estimation procedure and apply it for several features on a sample we can get a good indication of the tip shape in all directions.

The niobium thin film is such a sample. The 500x500 nm image shown contains several posts, the thinest giving a good estimate of the true tip shape.

Case 2 : Double tip

The two maxima shown in the profile might also indicate that the tip used to obtain the scan line itself contained two maxima. As before, there are two extremes for the tip shape.