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

#### Volume 5, Issue 4 (July 1977)

**ISSN:** 0090-3973

**CODEN:** JTEOAD

**Page Count:** 7

Czarnecka, ET

*Research associate, The University of Calgary, Calgary, Alberta*

Gillott, JE

*Professor, The University of Calgary, Calgary, Alberta*

**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 *P*_{c} and the texture contribution factor *T*_{c}.

**Paper ID:** JTE11666J

**DOI:** 10.1520/JTE11666J

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

Symposium , 0000-00-00

Committee D18