What does this equation mean?

A subtlety worth making explicit: the word “resolution” is not measuring the same thing in each of the four techniques above, which is precisely why a naive numerical ranking across them is misleading. In TEM and SEM, resolution describes the smallest separation between two point-like features the optics can distinguish, fundamentally set by the electron wavelength and the lens aberrations of the column. In AFM, the relevant limit is a convolution of the true surface topography with the physical geometry of the cantilever tip itself — a blunter tip broadens every feature it scans regardless of the piezo scanner’s positional precision, so AFM’s headline sub-nanometre figures assume a tip sharp enough that this convolution effect is negligible, an assumption that degrades as tips wear during use [ 8 ] . In X-ray crystallography, “resolution” refers to the highest-angle diffraction spots still measurably above background, expressed in Angstroms of d -spacing under Bragg’s law, and it is a property of how well-ordered the crystal is — how few molecules in it are misaligned relative to their neighbors — at least as much as it is a property of the X-ray source or detector [ 9 ] . Comparing a TEM’s “0.1 nanometre” to a crystal structure’s “1.5 Angstrom resolution” as though they were entries on the same scale conflates an optical resolving-power limit with a statement about crystalline order; both are real and both are useful, but they answer different underlying questions and neither displaces the value of the other.