Use of topographic coordinate data obtained by a mechano-optical system to determine the actual areas of macroscopic surfaces

摘要

Abstract: This paper describes a method for determining the actual area of a region of a macroscopic surface. The method entails determining a statistical distribution of a surface's limiting inclinations, and then computing from these data the incremental surface area that is due solely to its highest frequency oscillations. The area so determined is added to the incremental area that is due solely to the next group of lower frequency oscillations. The sum of these terms is equated to the actual relative area of the region. The procedure consists of determining the surface coordinates of a region of a surface at successively different distances between its coordinate points in the reference plane. The data is acquired by a mechano-optical system, that was developed in our laboratory, that is described elsewhere. Inclination angle distribution are determined from these data by dividing the area into small triangular regions, and then calculating the angles made between the average planes of these triangular regions and the reference plane. These are found to vary as a function of the average areas of the regions or the distances between coordinates. However, when the fractions of each inclination angle are plotted against the distance between coordinates in the reference plane, two linear curves are obtained. The limiting distributions are determined from the intercept values obtained on extrapolating the curves for the more closely spaced data to 'zero' distance between points. The incremental areas due to the next group of lower frequency oscillations are computed from the coordinates spaced at the closest interval of the second linear region of the fraction versus distance curves. In addition to the area determinations, we also determined the average ratios of actual to nominal profile lengths, R$- L$/, for orthogonal directions on the respective v surface. The R$-L$/ values were found to depend on the direction of the traces. For one of the directions, the R$-L$/ values were found to correlate with the surface areas of the respective materials, determined at the same scale as that used to determine the R$-L$/ values. These values differed however, from the actual surface areas of the materials that were determined, as described above. !31