A MATHEMATICAL MORPHOLOGY APPROACH TO IMAGE-FORMATION AND IMAGE-RESTORATION IN SCANNING TUNNELING AND ATOMIC-FORCE MICROSCOPIES

In the nanometer resolution range, image formation in STM and AFM cannot be described by a convolution process but is essentially governed by the geometrical interaction between the specimen surface and the tip surface. This non-linear process can be simply described by a dilation of the surface profile by a three-dimensional structuring element which has the shape of the tip. Accordingly, the restoration procedure using these concepts consists in performing the erosion of the image by the same structuring element. A preliminary investigation of a possible blind restoration procedure (i.e. restoration without a very precise knowledge of the tip shape and without the need of using a known test object) is performed.