Studying defects in periodic structures with fourier maps

Abstract

Periodic structures play important roles in wide areas of science and technology; however, there are no existing methods to identify and quantify defects in periodic structures. Microscopy examination is costly both in terM.S. of instrumentation and time, and suffer from small field of view. In this study, a method is proposed based on measurable image contrast between periodic lines and the defects within; this is a quantitative Fourier transformation method. A periodic structure under examination is taken as a high resolution image which is then divided into square or rectangular cells. The data within each cell is Fourier transformed and the Fourier intensities of the zeroth and the First order peaks are noted. After applying these procedures to all cells, Fourier maps are produced for the entire image area. The variations in the intensities in the maps (color variables) indicate quantitatively how defective is the image in the cell. Initially, Fourier intensities are compared for various kinds of computer generated defects in periodic pattern as a standardisation procedure. The method is then demonstrated experimentally to quantify defects. Beads spread on a scanner bed served as defects for initial studies. The method was then applied to quantify defects on large area transparent grating electrode as well as on a grating structure produced on graphite (HOPG). The method is extended to periodic biological structures, soldiers in a parade, structural pattern formed of flying birds, oliographic clouds and walking footprints. Once automated, the method can serve analysis of large body of data.