The phase unwrapping of under-sampled interferograms using radial basis function neural networks

Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$ and $\pi$ while it is the absolute phase that is required to get a true measurement. There is a long history of methods designed to recover accurately this phase from the phase "wrapped" inside $]-\pi,\pi]$. However, noise and under-sampling limit the effectiveness of most techniques and require highly sophisticated algorithms that can process imperfect measurements. Ultimately, analysing successfully an interferogram amounts to pattern recognition, a task where radial basis function neural networks truly excel at. The proposed neural network is designed to unwrap the phase from two-dimensional interferograms, where aliasing, stemming from under-resolved regions, and noise levels are significant. The neural network can be trained in parallel and in three stages, using gradient-based supervised learning. Parallelism allows to handle relatively large data sets, but requires a supplemental step to synchronized the fully unwrapped phase across the different networks.