Is the Electron Microscope the best Instrument for Playing Bach?

It is now common to claim the fabrication of heterointerfaces, which are atomically flat over distances in the micron range. However, when chemical lattice imaging and digital pattern recognition are combined to examine quantitatively individual semiconductor heterointerfaces of the highest quality, substantial atomic scale roughness is observed. In this paper, I review the application of chemical imaging and pattern recognition techniques to the characterization of heterointerfaces at near-atomic resolution and discuss the possible ways the results can be combined with optical measurements to give an overall picture of interfacial roughness.