Electron tomography : theory and applications, geometries and distortion removal

Electron tomography (ET) consists of recording at the electron microscope one or more series of projection images of an unique sample and of reconstructing its three dimensional structure. The sample is portrayed at the microscope for many times, tilting the holder properly in order to collect a suitable data set. The reconstruction can be performed by use of different algorithms, such as weighted back projection, algebraic techniques or direct Fourier methods. Most applications are in the field of biological sciences, where ET is used to reconstruct tissue sections, either embedded in epon or vitrified, and isolated organelles. The resolution is approaching 3 nm and is bridging the gap existing between light microscopy and single particle electron microscopy or X-ray crystallography. Principal problems of ET are sample deterioration and missing information due to the geometrical limits imposed by the experimental apparatus. Actually, biological samples suffer multiple exposures to the electron beam; they loose mass and shrink because of sublimation. Further, there are limits to the possible tilts of the holder, that can never produce a 180o viewing set, because of the sample thickness. Sample deterioration is controlled by reducing the electron dose, though it has the consequence of increasing the noise level. Geometrical limits give raise to an improper set of data, missing information in Fourier space and anisotropic resolution in direct space. Different schemes of data collection, such as dual axis or conical geometry, have been proposed to reduce this problem. Finally, a difficult task in ET is the alignment of the projections, which must be done a posteriori. Alignment means finding not only shift parameters but also the exact orientation of each projection, that never corresponds to the indication of the microscope. Alignment makes often use of reference gold particles and subsequent refinement by correlation techniques. In the case of sample deformation during data collection, a global alignment is not enough for a good reconstruction, and local corrections must be performed