Two-dimensional wave-number spectral analysis techniques for phase contrast imaging turbulence imaging data on large helical device

An analysis method for unfolding the spatially resolved wave-number spectrum and phase velocity from the 2D CO₂ laser phase contrast imaging system on the large helical device is described. This is based on the magnetic shear technique which identifies propagation direction from 2D spatial Fourier analysis of images detected by a 6 × 8 detector array. Because the strongest modes have wave-number at the lower end of the instrumental k range, high resolution spectral techniques are necessary to clearly resolve the propagation direction and hence the spatial distribution of fluctuations along the probing laser beam. Multiple-spatial point cross-correlation averaging is applied before calculating the spatial power spectrum. Different methods are compared, and it is found that the maximum entropy method (MEM) gives best results. The possible generation of artifacts from the over-narrowing of spectra are investigated and found not to be a significant problem. The spatial resolution Δρ (normalized radius) around the peak wave-number, for conventional Fourier analysis, is ∼0.5, making physical interpretation difficult, while for MEM, Δρ ∼ 0.1.