ENVELOPE RECONSTRUCTION OF PROBE MICROSCOPE IMAGES

Scanning probe microscope images often contain distortions caused by the finite size and imperfect shape of probe tips. Previous reports show that if the shape of the probe tip is known, these distortions can be accounted for, and an undistorted image of the sample can be reconstructed. Existing reconstruction methods are formally complete and correct, but in practice they rely on numerical derivatives of the image data and are sensitive to noise. In the present work a new method (''envelope image analysis'') is developed, in which a reconstructed image is synthesized from the original, distorted image as the envelope of a set of tip surface functions. The new method is essentially equivalent to the existing methods, but does not require numerical derivatives and is insensitive to noise. Variants of the new approach can also be used to create artificial probe microscope images from models, or to reconstruct the shape of the probe tip from an image of a known sample. As examples, the new envelope methods are applied to two specific problems: (1) the reconstruction and interpretation of scanning force microscope images of actin filaments, and (2) determining the shape of the probe tip from an image of a known grating structure.