Author:

Abstract:

In nature (e.g. a bee honeycomb, muscle structure, crystals) or in engineering (e.g. micro lens arrays, nano pore/pillar arrays, solar cells) two-dimensional highly regular arrays are produced. Hexagonal, square or triangular grids are most common. Perfect symmetry of the grids does not exist in practical situations. Given the image of some array, one may analyse the properties of each of the individual nodes of the grid and compute parameters like their size, the location of their centers, perhaps their orientation, etc. These parameters could be combined to define some number indicating the deviation from the ideal grid. We have tried to compute some order parameter from the Fourier transform of the image. For example a perfect hexagonal array has a Fourier spectrum that consists of a central peak, surrounded by six smaller peaks and their harmonics. This is a sparse exponential representation. The more the nodes in the image are dislocated from the perfect grid, the more noise will show up in the spectrum. Thus the amount of noise in the Fourier domain can be used as a measure for the disorder of the original grid. Unfortunately, images may depend on many parameters (number of nodes, size of the nodes, shape of the nodes, orientation of the image,...) so that the Fourier technique only works in a rather restrictive number of situations and it is probably not useful in practical situations.