A mathematical morphology approach to image formation and image restoration in scanning tunnelling 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