Reconstructing the melting channel shape in electron-beam welding from the parameters of penetrating X-ray radiation. Part I. Posing inverse geometrical problem

Abstract

Direct and inverse problems of reconstructing the shape of melting channel from the parameters of secondary penetrating bremsstrahlung X-ray radiation are posed. The inverse problem is shown to be reducible to solving an integral convolution-type equation and, in general case, Hadamard well-posed in the entire range of electron-beam welding (EBW) modes. The shape of melting channel is reconstructed based on the known theorem on the Fourier image of convolution.