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Recent frequency-modulated atomic force microscopy (FM-AFM) can measurethree-dimensional force distribution between a probe and a sample surface inliquid. The force distribution is, in the present circumstances, assumed to besolvation structure on the sample surface, because the force distribution andsolvation structure have somewhat similar shape. However, the forcedistribution is exactly not the solvation structure. If we would like to obtainthe solvation structure by using the liquid AFM, a method for transforming theforce distribution into the solvation structure is necessary. Therefore, inthis letter, we present the transforming method in a brief style. We call thismethod as a solution for an inverse problem, because the solvation structure isobtained at first and the force distribution is obtained next in generalcalculation processes. The method is formulated (mainly) by statisticalmechanics of liquid.

A solution for an inverse problem in liquid AFM: calculation of three-dimensional solvation structure on a sample surface