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Figure 2
Scheme for the Fourier-space reconstruction used in the program icr3d. (a) Three-dimensional reconstruction in Fourier space by the summation of central sections (two are shown, one in blue and one in red), which derive from the projection angles of the two-dimensional images (indicated by red and blue arrows). The depth of each central section depends on the reciprocal dimension of the reconstructed object (1/D) measured in the projection direction. (b) Contributions from the input Fourier components of two individual particle images (red and blue points) to the output Fourier components of the three-dimensional reconstruction (black points) are confined to the central section (red and blue dashed lines) as in (a). These are added to neighbouring three-dimensional Fourier components within ellipsoidal contributing envelopes (red and blue ellipses), the dimensions of which are reciprocally related to the maximum dimensions of the reconstructed object in the relevant directions. (c) Maximum dimensions of a reconstructed object expressed as fractions of the cubic reconstructed volume shown in the xy and xz planes. (d) Corresponding ellipsoidal Fourier-space contribution envelopes (red ellipses), which can be compared with the spherical contribution envelopes (black circles) that relate to a reconstructed object with maximum dimensions equal to the cubic reconstructed volume. (e) The fractional distance (dFrac) used to determine sinc-weighted contributions to the output Fourier components is calculated from the distances (B and B′) between the input Fourier components (red dots) and the output Fourier components (black dots) as a fraction of the distance to the edge of the ellipsoidal contributing envelope (A and A′).

Journal logoSTRUCTURAL
BIOLOGY
ISSN: 2059-7983
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