SAI, the Surface Area Index, is the surface area at the lateral resolution of the measured/filtered surface as compared to that of a perfectly flat/smooth surface. The calculation involves fitting triangular patches between the measured points and adding up the total area of all patches. A ratio is then formed of the total surface area measured and the nominal flat area of measurement. This analysis is a precursor to a complete fractal analysis of the surface.i Since SAI is a ratio, it is a unitless quantity.
Depiction of the calculation of the Surface Area Index (SAI). Demonstrating only a few triangular patches whereas the complete analysis involves fitting patches over the complete image.
The combination of different surface texture amplitudes and spacings are further manifested in the overall surface provided by the texture. The SAI parameter finds application for issues relating to surface wetting, fluid flow, coating adhesion, printing etc.
i C.A. Brown, P.D. Charles, W.A. Johnsen, S. Chester, fractal analysis of topographic data by the patchwork method, Wear 161 (1993) 61-67.