Recasting radiographic image data for accurate Abel inversion

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One the primary goal of quantitative X-ray radiography is to compute the densities of objects in the scene being imaged. The most common approach to doing this is to use radiation transport modeling to simulate a forward radiograph that best matches the measured image. When the object being imaged is cylindrically symmetric, it is possible to instead infer object densities directly from the measured data, viewing the image as a single tomographic projection of the object. This is a two-stage process, as the intensity data must be converted to areal density, then the areal density is mapped to volumetric density by the inverse Abel transform. Abel inversion is an ill-posed problem, which means that it is sensitive both to noise in the measured intensity image and to errors in the conversion from intensity to areal density. In this work we develop a novel approach to computing areal density from intensity and show how the improved areal density calculations result in significantly improved volumetric density estimates. We further show correlation between the recasting model parameters and presumed source spectrum shape and compare results with experimental observations.