Double Two-Dimensional Discrete Fast Fourier Transform for Determining of Geometrical Parameters of Fibers and Textiles

Abstract

We have developed a computing method to determine the geometrical parameters of fibers and the textile periodical structure. This method combines two two-dimensional discrete fast Fourier transforms to calculate a diffraction pattern from a diffraction pattern image of material under consideration. The result is the same as that of observation of a diffraction pattern which is achieved by illuminating the diffraction pattern image of material by a beam of coherent monochromatic light. After the first transform we obtain the Fraunhofer diffraction picture with clearly visible elements of the periodical structure of material, but distances in this picture are reciprocally proportional to distances in the periodical structure of the source object so additional calculations are required. After the second transform we have a clear periodical structure of diffraction maximums where distances between them are equal to distances between repeating elements in the source material (fibers, knots, yarns, etc.).