Mathematical Behavior of Optical Density of γ-Ray Radiography Images of Steel Pipes

Abstract

The purpose of this article is to determine the mathematical function of the optical behavior of radiographic films/images produced by gamma-ray radiography of the steel pipes. In order to achieve this goal, we used realistic films for welding tests on the oil and gas pipelines in the operational areas. Eight films were selected in each, three sections including the base metal, weld line, and defects were carefully examined. First, the best film was selected and more than 40 probability functions were fitted on its data. Among the fitted probability functions, 13 functions were selected from a condition of R-sq ≥ 0.95. Eventually, these 13 functions were applied to the data of all available films for a better comparison. Furthermore, a new function was proposed by the authors, which showed that the fitting was based on the results. The new proposed function, fulfilled not only the best R-sq, but also the most flexibility in the case of scattered data.