Convolution between the Tip Shape

and the Shape of a 3D Object Imaged by Near-Field Microscopy

Figure 1 (top) represents a line scanned by the tip of the microscope as it passes over a particle with fcc structure in (111) epitaxy, displaying lateral (111) and (100)  facets. The projections of two of these facets (perpendicular to the plane of the figure) form straight lines at angles of 70.53◦ and 54.74◦ to the horizontal. The tip profile, assumed parabolic, is also illustrated. The line imaged is the locus of points of contact between the tip and the surface of the particle. It is clear that the height is correctly determined by the measurement, but the edges are rounded off and the size of the particle is increased. The convolution effect (not a convolution in the mathematical sense) increases as the radius of curvature of the tip increases and as the slopes of the facets increase. If the shape of the tip is known, the images can be corrected, as shown in the lower part of Fig. 1.

Fig. 1. Distortion of the image of a 3D particle due to the shape of the tip in near-field microscopy. 

On the corrected profile, the mid-height size of the particles is now correct, but information has been lost at the base of the particle, up to a height equal to the radius of curvature of the tip.