Neural network assisted software engineered refractive fringe diagnostic of spherical shocks.

Abstract

A shock is essentially a propagating variation in the pressure or density of a medium. If the medium is transparent, such as air, and the shock radially symmetric, the refractive fringe diagnostic can be used to examine its general features. A laser beam probes the shock, the central part of the beam, refracted to different degrees by the different density features within the shock, interferes with itself and with the outer unrefracted part creating a series of coarse and fine fringes. By examining this interference pattern one can gain insight into the density profile underlying the shock. A series of such experiments was conducted by the Plasma Physics Research Institute at the University of Natal in 1990. To model the situation computationally, they developed a ray-tracer which produced interference patterns for modified theoretical density profiles based on those predicted by Sedov. After numerous trials, an intensity pattern was produced which agreed approximately with experimental observations. Thus encouraged, the institute then sought to determine density profiles directly from the interference patterns, but a true mathematical deconvolution proved non-trivial and is still awaited. The work presented in this thesis reconstructs the ray-tracer using software engineering techniques and achieves the desired deconvolution by training a neural network of the back-propagation type to behave as an inverse ray-tracer. The ray-tracer is first used to generate numerous density profile - interference pattern pairs. The neural network is trained with this theoretical data to provide a density profile when presented with an interference pattern. The trained network is then tested with experimental interference patterns extracted from captured images. The density profiles predicted by the neural network are then fed back to the ray-tracer and the resultant theoretically determined interference patterns compared to those obtained experimentally. The shock is examined at various times after the initial explosion allowing its propagation to be tracked by its evolving density profile and interference pattern. The results obtained prove superior to those first published by the institute and confirm the neural network's promise as a research tool. Instead of lengthy trial and error sessions with the unaided ray-tracer, experimental interference patterns can be fed directly to an appropriately trained neural network to yield an initial density profile. The network, not the researcher, does the pattern association.