In this work we consider the problem of obtaining a capacitive image by scanning a "one-dimensional" surface of a closed conductor of arbitrary geometry. To solve our problem we propose a novel integral numerical method. The method is applied to different geometries by considering deterministic surfaces as complex as those with a fractal structure and random rough surfaces with Gaussian statistics. We find that the images obtained by simulating a prototype of a capacitive microscope, strongly depend on the interaction between the object and the probe. Despite this interaction, important information can be obtained regarding the statistical properties of the random roughness of the object surface.
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