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, pp. 316-317   | 1 | 2 |

Section 2.5.6.2. Orthoaxial projection

B. K. Vainshteinc‡

2.5.6.2. Orthoaxial projection

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In practice, an important case is where all the projection directions are orthogonal to a certain straight line: [{\boldtau} \perp z] (Fig. 2.5.6.3[link]). Here the axis of rotation or the axis of symmetry of an object is perpendicular to an electron beam. Then the three-dimensional problem is reduced to the two-dimensional one, since each cross section [\varphi_{2i} ({\bf x}, z = \hbox{constant})] is represented by its one-dimensional projections. The direction of vector τ is defined by the rotational angle ψ of a specimen: [\varphi_{1} (x_{\psi_{i}}) \equiv L^{i} (\psi_{i}) = {\textstyle\int} \varphi_{2} ({\bf x}) \ \hbox{d} \tau_{\psi}\hbox{; } x_{i} \perp {\boldtau}_{\psi}. \eqno(2.5.6.8)] In this case, the reconstruction is carried out separately for each level [z_{l}]: [\hbox{set } \varphi_{1, \, z_{l}} (x_{\psi}) \equiv \hbox{ set } L_{z_{l}}^{i} \rightarrow \varphi_{2i} (xyz_{l}) \eqno(2.5.6.9)] and the three-dimensional structure is obtained by superposition of layers [\varphi_{2z_{l}} (xy) \Delta z] (Vainshtein et al., 1968[link]; Vainshtein, 1978[link]).

[Figure 2.5.6.3]

Figure 2.5.6.3| top | pdf |

Orthoaxial projection.

References

First citation Vainshtein, B. K. (1978). Electron microscopical analysis of the three-dimensional 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
 First citation Vainshtein, B. K., Barynin, V. V. & Gurskaya, G. V. (1968). The hexagonal crystalline structure of catalase and its molecular structure. Sov. Phys. Dokl. 13, 838–841.Google Scholar








































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