The Effect of the Spatial Extent of Double Tips on Crystallographic Image Processing for Scanning Tunneling Microscopes

One may glean information from scanning probe microscopy images that have been obscured by signals from multiple probe tips by utilizing crystallographic image processing techniques. We build on prior work that showed how a pair of delta function tips interacting with idealized p4mm wave functions would give image obscurations at tip-separations where the quantum signal (the current reflecting interference between the two tips) and the classical signal (the remaining terms) destructively interfere in scanning tunneling microscopy. The present paper extends that result to tips that have finite spatial extent to determine the consequences of that extent. Using a bonding H₂ tip wave function does not affect the classical result in any observable way. However, the interplay of the plane wave representing the component of the k-parallel wave vector in the direction of the line between the two tips, q₁, and the finite bonding H₂ tip extent in that same direction causes the tip separation at which total suppression occurs to shift somewhat away from the multiples of π/2, values at which the delta function model yielded the greatest interference between tips. As in previous work, our analysis finds that except for a very small range of tip separations close to where total suppression occurs—within roughly 0.05 radians relative to the p4mm Bloch surface functions having a period of 2π radians—crystallographic image processing and crystallographic averaging works well in removing the effects of a double scanning probe microscopy tip.