I'm trying to gain a better understanding of Atomic Force Microscopy, specifically the relationship between its lateral and depth resolution. I've seen a variety of metrics on the two, but in general, the depth resolution appears to be about two orders of magnitude more accurate than the lateral resolution. See the page Fundamental Theory of Atomic Force Microscopy for an example.
My question is, does the lower lateral resolution limit the usefulness of the higher depth resolution? In my current mental model, it seems like the height of a sample could vary significantly between points that aren't laterally resolvable. If that's the case, would the generated "height map" contain large discontinuities?
In the papers I've seen, the "height maps" are rather smooth, so I wonder if I'm missing something.