Atomic force microscope (AFM) enabled us to observe the surface in the atomic scale, also to know the roughness information quantitatively. However, the incline information of the sample has not been treated statistically although the incline distribution gives us important information to investigate the surface analysis.
In the most of cases, the height of the top of any corrugation is obtained by drawing the cross section of the sample, and it is also be able to quantify of the surface roughness by getting the height histogram. Using such method, it is not able to know how much the surface corrugations incline against the horizontal plane since all data are transformed to such the height histogram only, though the quantitative information about incline is also necessary for surface analysis in practical. In this report, the new algorithm, named "incline histogram", for obtaining the surface incline histogram is proposed.
For expression about incline, two parameters θ (polar angle) and φ (azimuth angle) are necessary in general. However, in the several cases, only θ is mainly used for the contact angle analysis. Thus, the algorithm of this report has been developed for obtaining the distribution of only θ against the normal vector of the horizontal plane and for displaying as a histogram. One of the merits of this algorithm is easy to reduce the influence of spike noises which AFM data are unavoidable.
The well-used expression of any topographic data is stored in two-dimensional N×M matrix. Taking from the 2×2 data matrix from the original data array, element is defined as plane spanned by this small matrix. The angle θ, between the normal vector of the element and that of the horizontal plane, can be calculated at the whole parts of the original data array.
Some examples of the application will also be presented. From the results of the examine of this algorithm, it can be concluded that this algorithm is the convenient for evaluating the real corrugation and shape with good angle accuracy < 0.2deg.
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