In materials science, FFT is a useful tool for us to extract patterns from complex structures. In this example, its application to studying the material concentration profile resulted from spinodal decomposition is demonstrated. This tool is implemented in Matlab, with a capability of performing 2D FFT on the data and identifying the characteristic length of the patterns.
The Matlab script and data files can be downloaded from: https://jbox.sjtu.edu.cn/l/z1XJP7 (SJTU VPN required).
In the below figure, the top subfigure is the original figure showing the concentration variation due to the spinodal decomposition, and the bottom one is the figure after a 2D FFT with shifting the zero frequency to the center of the image.
Assuming that the patterns exhibit an isotropic manner. A radial average is performed, from which a peak can be identified. The characteristic length of the patterns in the real space is just the inverse of up.