Analysis of the Pattern Evolution Based on Spatial Correlation and Fourier Spectra Technique

Images of patterns are processed with some image processing technology, such as binary image processing, space correlation function and Fourier transformation, thus some important intrinsic elements of active plasma and pattern formation can be presented more clearly. Images of random filaments, hexagonal, hexagonal superlattice pattern, and chaos state are obtained in dielectric barrier discharge system with increasing voltage. Using spatial correlation function, it is found that the average distance decreases with voltage increasing, and most hexagonal cells in both hexagonal and hexagonal superlattice pattern are relative perfect. For further investigation, these images are transformed to frequency domain and Fourier spectra are studied. It is found that the mode changes with voltage increasing. Both random filaments and chaos have single wavelength with all directions. The hexagonal pattern is formed with single-wavelength three-wave resonance, while hexagonal superlattice pattern is governed by three-wave resonance of two sets of modes.