Development of reconstruction algorithms of three-dimensional crystal lattice from projection images

We developed two reconstruction algorithms of crystal lattices from their two-dimensional projection images. Algorithms are modifications of the back-projection algorithm of computed tomography. The first algorithm is based on a straight line discretization. The second algorithm is based on minimizing the distance to the line projected onto a plane. A method for modeling three-dimensional sites structure of an ideal crystal lattice developed. The study on a set of crystal lattices was conducted. The results of research of oriented at projections lattices showed that the first algorithm restores a lattice in the 89% rightly and the second - in 98%. The problem of minimizing a distance is solved without approximations therefore the second algorithm restores a crystal lattice better than the first one.