Inversion of interferometric data from cylindrically symmetric, refraction less plasmas

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Abstract
This paper discusses the problem of uniqueness and the compromise between resolution and variance when determining plasma densities by inverting inaccurate interferometric data from cylindrically symmetric refractionless plasmas or other similar phase objects. Methods are given to show what unique information about plasma structure can be provided by a finite set of interferometric data, and how to determine the best possible resolution given that the variance of the estimate is to be less than a specific value. The problem of structural appraisal is also resolved by computing plasma densities which reproduce the data to within desired errors; the flattest model, and models produced through linear programming techniques are important in this respect. Linear programming techniques are discussed in detail because they can be used to generate models which are constrained to be non-negative, and also to provide numerical bounds on the smallest supremum of the plasma density or its gradient.

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