Three-dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions instead of Fourier Transforms

摘要: Abstract A new technique is proposed for the mathematical process of reconstruction a three-dimensional object from its transmission shadowgraphs; it uses convolutions with functions defined in real space object, without using Fourier transforms. The rotated about an axis at right angles to direction parallel beam radiation, and sections normal are reconstructed data obtained by scanning corresponding linear strips shadowgraphs different angular settings. Since formulae convolution method involve only summations over one variable time, while two-dimensional transform requires double summations, much faster (typically factor 30); relative increase speed larger where greater resolution required. Tests computer-simulated show that also more accurate than method. It has good potentialities application electron microscopy x-radiography. A reconstructing helical structures this suggested.