distribution, and their order of collection will all impact the qualities of data in the
tomogram’s 3D Fourier space, and therefore of the tomogram itself.
Tilt range effectively dictates Z-axis resolution and resolution anisotropy.
Because the grid bars of the electron microscope are electron opaque, the specimen
cannot be tilted a full ±90°, resulting in incomplete data on the 3D structure of the
specimen, the so-called “missing wedge” of data in Fourier space. In practical terms
this effectively reduces resolution along the Z-axis, which must be considered
during interpretation of results. The missing wedge in Fourier space manifests in
real space tomograms as a ‘smearing’ of object parallel to the direction of the beam,
making spherical objects appear ellipsoidal, and planar structures such as cell
membranes becoming invisible when perpendicular to the beam [57]. The amount
of missing data depends on the tilt range parameter; the user’s choice of this
depends upon the desired resolution, stage stability at high tilt, desired speed of
acquisition, microscope voltage, and specimen thickness. In a 300 kV microscope it
may be possible to tilt to ±70° for thin samples, less so in lower-voltage microscopes, except with very thin samples. To reduce the amount of unsampled data in
Fourier space, dual-axis tilt series can be collected. Here, after collecting the first tilt
series the grid is turned 90° around the axis parallel to the beam, either manually, or
mechanically within the microscope [55]. With the grid rotated, a second,
orthogonal tilt series can be collected. The electron dose is split evenly between the
two tilt series and both tilt series used to calculate a single tomogram with
decreased anisotropy due to shrinking the missing wedge to a smaller “missing
pyramid”. For example, with a ±67° tilt range, a dual-axis dataset shrinks the
unsampled data from 26% to 10%. Some filamentous structures have been shown to
only become visible in dual-axis tomograms [58]. As the total dose tolerated by the
biological specimen remains constant, however, and the number of projection
images collected doubles, the electron dose per image is halved, leading to less
accurate tilt series alignment. The large amount of time needed to collect a dual-axis
tilt-series as well as the errors in alignment associated with it diminish the benefits,
and in practice dual-axis tomography is rarely performed. It is noteworthy that the
maximum achievable resolution remains unchanged but the data improves by
becoming more isotropic [59].
The resolution of a reconstructed tomogram is dependent upon the tilt increment
between successive projection images (i.e., the size of gaps in data in Fourier space)
[60]. The Crowther criterion states that d ’ pD/N, where d is the smallest
resolvable distance, D is the diameter of a cylindrical specimen, and N is the
number of projection images over a ±90° range. Theoretically, therefore, the finer
the tilt increment, the higher the achievable resolution. It is important to note that
the final signal-to-noise ratio of a tomogram is independent of the number of images
in the tilt series, given constant electron dose; higher tilt increments are therefore
used only to speed up the process and increase the signal-to-noise ratio of individual
tilt frames to facilitate accurate tilt series alignment. The tilt increment must
therefore be set to enable acquisition of spatial frequencies of interest, while
3 Electron Cryo-Tomography
75
tomogram’s 3D Fourier space, and therefore of the tomogram itself.
Tilt range effectively dictates Z-axis resolution and resolution anisotropy.
Because the grid bars of the electron microscope are electron opaque, the specimen
cannot be tilted a full ±90°, resulting in incomplete data on the 3D structure of the
specimen, the so-called “missing wedge” of data in Fourier space. In practical terms
this effectively reduces resolution along the Z-axis, which must be considered
during interpretation of results. The missing wedge in Fourier space manifests in
real space tomograms as a ‘smearing’ of object parallel to the direction of the beam,
making spherical objects appear ellipsoidal, and planar structures such as cell
membranes becoming invisible when perpendicular to the beam [57]. The amount
of missing data depends on the tilt range parameter; the user’s choice of this
depends upon the desired resolution, stage stability at high tilt, desired speed of
acquisition, microscope voltage, and specimen thickness. In a 300 kV microscope it
may be possible to tilt to ±70° for thin samples, less so in lower-voltage microscopes, except with very thin samples. To reduce the amount of unsampled data in
Fourier space, dual-axis tilt series can be collected. Here, after collecting the first tilt
series the grid is turned 90° around the axis parallel to the beam, either manually, or
mechanically within the microscope [55]. With the grid rotated, a second,
orthogonal tilt series can be collected. The electron dose is split evenly between the
two tilt series and both tilt series used to calculate a single tomogram with
decreased anisotropy due to shrinking the missing wedge to a smaller “missing
pyramid”. For example, with a ±67° tilt range, a dual-axis dataset shrinks the
unsampled data from 26% to 10%. Some filamentous structures have been shown to
only become visible in dual-axis tomograms [58]. As the total dose tolerated by the
biological specimen remains constant, however, and the number of projection
images collected doubles, the electron dose per image is halved, leading to less
accurate tilt series alignment. The large amount of time needed to collect a dual-axis
tilt-series as well as the errors in alignment associated with it diminish the benefits,
and in practice dual-axis tomography is rarely performed. It is noteworthy that the
maximum achievable resolution remains unchanged but the data improves by
becoming more isotropic [59].
The resolution of a reconstructed tomogram is dependent upon the tilt increment
between successive projection images (i.e., the size of gaps in data in Fourier space)
[60]. The Crowther criterion states that d ’ pD/N, where d is the smallest
resolvable distance, D is the diameter of a cylindrical specimen, and N is the
number of projection images over a ±90° range. Theoretically, therefore, the finer
the tilt increment, the higher the achievable resolution. It is important to note that
the final signal-to-noise ratio of a tomogram is independent of the number of images
in the tilt series, given constant electron dose; higher tilt increments are therefore
used only to speed up the process and increase the signal-to-noise ratio of individual
tilt frames to facilitate accurate tilt series alignment. The tilt increment must
therefore be set to enable acquisition of spatial frequencies of interest, while
3 Electron Cryo-Tomography
75