# Bearing ratio of a surface

The bearing ratio curve of a horizontal slice is clear. However, I wonder how the bearing ratio of a surface is calculated. For example, bearing ratio curve of an image of 512x512 pixels from SPM?

Hello Rocky,

The area material ratio or “bearing ratio” curve of a surface is a graph showing the fraction of the surface area above a particular height as compared to the total surface area as a function of the height. For 2D data (such as that acquired with SPM), the surface is typically defined on a grid of equal size “pixels” so for this case, the “bearing ratio” is a graph that shows the ratio of the number of pixels above a particular height divided by the total pixels in the 2D surface plotted as a function of the height.

The definition is the same for a slice only that instead of considering all the pixels within a 2D region, we consider only the pixels within the specified slice. The simplest case is for a horizontal slice (one row of pixels) or a vertical slice (one column of pixels).

You can find additional discussion of the Area Material Ratio Curve at the following link:
Areal Material Ratio

Other details can be obtained from the ISO standards that define the areal material ratio of the scale-limited surface (ISO 25178-2:2012(E) 4.4.2)

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Thank you very much for your information.