International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B. ch. 2.5, p. 318

These methods have been derived for the twodimensional case; consequently, they can also be applied to threedimensional reconstruction in the case of orthoaxial projection.
Let us discretize by a net of points ; then we can construct the system of equations (2.5.6.10).
When h projections are available the condition of unambiguous solution of system (2.5.6.10) is: . At we can, in practice, obtain sufficiently good results (Vainshtein, 1978).
Methods of reconstruction by iteration have also been derived that cause some initial distribution to approach one satisfying the condition that its projection will resemble the set . Let us assign on a discrete net as a zeroorder approximation the uniform distribution of mean values (2.5.6.7) The projection of the qth approximation at the angle (used to account for discreteness) is .
The next approximation for each point jk is given in the method of `summation' by the formula where is the number of points in a strip of the projection . One cycle of iterations involves running around all of the angles (Gordon et al., 1970).
When carrying out iterations, we may take into account the contribution not only of the given projection, but also of all others. In this method the process of convergence improves. Some other iteration methods have been elaborated (Gordon & Herman, 1971; Gilbert, 1972b; Crowther & Klug, 1974; Gordon, 1974).
References
Crowther, R. A. & Klug, A. (1974). Three dimensional image reconstruction on an extended field – a fast, stable algorithm. Nature (London), 251, 490–492.Google ScholarGilbert, P. F. C. (1972b). Iterative methods for the threedimensional reconstruction of an object from projections. J. Theor. Biol. 36, 105–117.Google Scholar
Gordon, R. (1974). A tutorial on ART (algebraic reconstruction techniques). IEEE Trans. Nucl. Sci. NS21, 78–93.Google Scholar
Gordon, R. & Herman, G. T. (1971). Reconstruction of pictures from their projections. Commun. ACM, 14, 759–768.Google Scholar
Vainshtein, B. K. (1978). Electron microscopical analysis of the threedimensional structure of biological macromolecules. In Advances in optical and electron microscopy, Vol. 7, edited by V. E. Cosslett & R. Barer, pp. 281–377. London: Academic Press.Google Scholar