MORPHOLOGICAL ESTIMATION OF TIP GEOMETRY FOR SCANNED PROBE MICROSCOPY

Morphological constraints inherent in the imaging process limit the possible shapes of the tip with which any given tunneling microscope or atomic force microscope image could have been taken. Broad tips do not produce narrow image protrusions. Therefore, feature sizes within the image may be used to place an upper bound on the size of the tip. In this paper, mathematical morphology is used to derive, for each point on an image, a corresponding bounding surface for the tip. The actual tip must be equal to or smaller than the largest tip which satisfies all of the constraints. Example calculations are performed, demonstrating that if the imaged specimen contains sharp features and high relief, the tip shape deduced by this method will be a good estimate of the actual one. Once known, the tip geometry can be ''deconvoluted'' from images to recover parts of the actual surface which were accessible to the tip.