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Figure 5.12 Principle of the random-conical data collection: (a) untilted; (b) tilted field with molecule attached to the support in a preferred orientation; (c) equivalent projection geometry. From Radermacher et al. (1987b), reproduced with permission of Blackwell Science Ltd.

Figure 5.13 Coverage of 3D Fourier space achieved by regular conical tilting. Shown is the relationship between inclined Fourier plane (on the right), representing a single projection, and the 3D Fourier transform (on the left). For random-conical data collection, the spacings between successive planes are irregular. Adapted from Lanzavecchia et al. (1993).

Figure 5.13 Coverage of 3D Fourier space achieved by regular conical tilting. Shown is the relationship between inclined Fourier plane (on the right), representing a single projection, and the 3D Fourier transform (on the left). For random-conical data collection, the spacings between successive planes are irregular. Adapted from Lanzavecchia et al. (1993).

within a square-shaped domain. The body formed by rotating an inclined square around its center resembles a yo-yo with a central cone spared out. Since the resolution of each projection is limited to a circular domain (unless anisotropic resolution-limiting effects such as axial astigmatism intervene, see section 3.2 in chapter 2), the coverage of the 3D Fourier transform by useful information is confined to a sphere contained within the perimeter of the yo-yo (not shown in figure 5.13).

We will come back to the procedural details of the random-conical data collection and reconstruction after giving a general overview over the different reconstruction algorithms.

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