1. The damaging effect of the electron beam limits the amount of electrons
available for image formation. As a consequence, electron tomograms tend to
exhibit very high noise levels and low contrast.
2. The noise in electron tomographic reconstructions is the result of a complex
combination of different sources including signal-dependent shot noise due to
the quantum nature of the electrons, digitization noise of the detection device,
and additional structured noise due to the presence of support and embedding
media [6]. The noise is highly correlated in space, and is corrupted by the
contrast transfer function [7] and the missing wedge. Thus, it is hard to define
adequate noise models to take advantage of algorithms that explicitly take noise
characteristics into account.
3. The geometry of the electron tomography sample holders does not allow tilting
of the sample by more then 60°–70°. This restriction severely affects the
completeness of the projection data necessary for three-dimensional reconstruction, which is best visualized as a “missing wedge” in Fourier space. This
issue can be alleviated experimentally by taking a second data set after rotation
of the sample by 90° around the optical axis [8–10], but some of the data space
remains inaccessible and some missing data artifacts will still remain.
4. Aberrations of the optics of the electron microscope give rise to a point-spread
function best described in Fourier space by its Fourier transform, the contrast
transfer function. This function depends primarily on the amount of defocus
used for imaging and modifies both amplitudes and phases of the signal. The
contrast transfer function of the microscope is not very well defined in an
electron tomography setting, especially for thick specimens where there tends to
be a significant variance in focus. In addition, the tilting introduces a focus
gradient, further obstructing the underlying signal.
Cryo preservation allows imaging of biological samples with the electron
microscope in their native environment without any staining, chemical fixation, or
drying [11]. The quality of cryo-tomographic reconstructions can be correlated with
the electron dose. A total dose of 50–300 e
− /Å
2 tends to be a good compromise
with a sweet spot around 120 e
− /Å
2 [12]. This dose needs to be spread over the
whole data set. For a ±60° double tilt series with a 2° increment, the dose available
for a single image is thus only 1 e
− /Å
2 , which gives rise to extremely high noise
levels in the individual images. The signal in the resulting three-dimensional
reconstructions is improved by the dose fractionation effect [13] and can be further
enhanced by using new technologies such as direct electron detectors [14] or Volta
phase plates [15], but the signal-to-noise ratio for these tomograms is still well
below 1 (often only 0.1 or less). Owing to the technical difficulties of cryo-sample
sectioning [16] or cryo-milling approaches [17], conventional electron tomography,
which involves staining and plastic embedding, is often preferred in practice for
samples that require sectioning [18]. While the signal-to-noise ratio is improved in
these samples as compared to cryo-samples, the resulting images and reconstructions still tend to be quite noisy with signal-to-noise ratios usually well below five.
Furthermore, these types of samples can suffer additional problems such as uneven
302
N. Volkmann
available for image formation. As a consequence, electron tomograms tend to
exhibit very high noise levels and low contrast.
2. The noise in electron tomographic reconstructions is the result of a complex
combination of different sources including signal-dependent shot noise due to
the quantum nature of the electrons, digitization noise of the detection device,
and additional structured noise due to the presence of support and embedding
media [6]. The noise is highly correlated in space, and is corrupted by the
contrast transfer function [7] and the missing wedge. Thus, it is hard to define
adequate noise models to take advantage of algorithms that explicitly take noise
characteristics into account.
3. The geometry of the electron tomography sample holders does not allow tilting
of the sample by more then 60°–70°. This restriction severely affects the
completeness of the projection data necessary for three-dimensional reconstruction, which is best visualized as a “missing wedge” in Fourier space. This
issue can be alleviated experimentally by taking a second data set after rotation
of the sample by 90° around the optical axis [8–10], but some of the data space
remains inaccessible and some missing data artifacts will still remain.
4. Aberrations of the optics of the electron microscope give rise to a point-spread
function best described in Fourier space by its Fourier transform, the contrast
transfer function. This function depends primarily on the amount of defocus
used for imaging and modifies both amplitudes and phases of the signal. The
contrast transfer function of the microscope is not very well defined in an
electron tomography setting, especially for thick specimens where there tends to
be a significant variance in focus. In addition, the tilting introduces a focus
gradient, further obstructing the underlying signal.
Cryo preservation allows imaging of biological samples with the electron
microscope in their native environment without any staining, chemical fixation, or
drying [11]. The quality of cryo-tomographic reconstructions can be correlated with
the electron dose. A total dose of 50–300 e
− /Å
2 tends to be a good compromise
with a sweet spot around 120 e
− /Å
2 [12]. This dose needs to be spread over the
whole data set. For a ±60° double tilt series with a 2° increment, the dose available
for a single image is thus only 1 e
− /Å
2 , which gives rise to extremely high noise
levels in the individual images. The signal in the resulting three-dimensional
reconstructions is improved by the dose fractionation effect [13] and can be further
enhanced by using new technologies such as direct electron detectors [14] or Volta
phase plates [15], but the signal-to-noise ratio for these tomograms is still well
below 1 (often only 0.1 or less). Owing to the technical difficulties of cryo-sample
sectioning [16] or cryo-milling approaches [17], conventional electron tomography,
which involves staining and plastic embedding, is often preferred in practice for
samples that require sectioning [18]. While the signal-to-noise ratio is improved in
these samples as compared to cryo-samples, the resulting images and reconstructions still tend to be quite noisy with signal-to-noise ratios usually well below five.
Furthermore, these types of samples can suffer additional problems such as uneven
302
N. Volkmann