Neural Network Reconstruction of the Electron Density of High Energy Density Plasmas From Under-Resolved Interferograms

Interferometry can accurately measure the electron density of a high energy density plasma by comparing the phase shift between a laser beam passing through the plasma and a reference beam. While the actual phase shift is continuous, the measured shift has discontinuities, since its measurement is constrained between $-\pi $ and $\pi $ , an effect called “wrapping.” Although many methods have been developed to recover the original, “unwrapped” phase shift, noise and under-sampling often hinder their effectiveness, requiring advanced algorithms to handle imperfect data. Analyzing an interferogram is essentially a pattern recognition task, where radial basis function neural networks (RBFNNs) excel. This work proposes a network architecture designed to unwrap the phase interferograms, even in the presence of significant aliasing and noise. Key aspects of this approach include a three-stage learning process that sequentially eliminates phase discontinuities, the ability to learn directly from the data without requiring a large training set, the ability to mask regions with missing or corrupted data trivially, and a parallel Levenberg-Marquardt algorithm (LMA) that uses local network clustering and global synchronization to accelerate computations.