A Modified Fourier Method of Shape and Surface Texture Analysis of Planar Sections of Particles

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Abstract
A mathematical model based on a Fourier series expansion has been used to represent the roughness of planar sections of particles, that is, the combined effect of shape and surface texture. A new coefficient T is introduced which more precisely expresses the total roughness of the projected two-dimensional profile. It also gives a measure of shape and texture contribution factors separately. The value of the total roughness coefficient depends on the Fourier amplitude coefficients Cn, the length of the perimeter of the profile, and the difference between the maximum and minimum radii. Therefore the value of the total roughness coefficient T is a better representation of grain morphology than is a coefficient derived only from Fourier terms to which shape makes a dominant contribution. This value is the sum of the shape contribution factor Pc and the texture contribution factor Tc.