| Electron Tomagraphy (ET): |
Overview of Tomography
(Warning: under construction)
The fundamental concept behind tomographic reconstruction of all sorts is that it is possible to construct a three-dimensional (3d) representation of a 3d object by combining two-dimensional (2d) projection 
images of the 3d object. It will be useful for the rest of this discussion to present some of the history of this field, both to clear up certain misconceptions about tomography and also because the field uses several different terminologies and formalisms when dealing with the relationship between a 3d object and its 2d projections. The "N-dimensional" mathematical proof behind the relationship between objects and projections and the "Radon transform" itself were introduced by the Austrian mathematician Johann Radon in a hard-to-locate article published in 1917. For various reasons, Radon's treatment of the problem had very little practical impact at that time but was of enormous interest to people working in areas of pure mathematics such as integral geometry and partial differential equations. Even today, although many people make reference to Radon and Radon transforms when talking about tomography, Radon's approach to the problem is seldom actually used.
In the 1950's, the physicist Alan Cormack developed the theoretical underpinnings that lead to the field of X-ray computed tomography (CT) used in medial imaging. 
CT was a practical demonstration of the relationship between a 3d object and 2d projections (X-ray images, in this case). Cormack's early work was done without any knowledge of Radon's mathematical treatment: he notes in his 1979 Nobel lecture that he only learned about Radon's work (and the work of various other people in the area we now call tomography) in the early 1970's when returning to CT-scanning problems. Cormack not only developed the mathematics for dealing with the problem of generating a volume based on a set of X-ray images collected at various angles relative to the original 3d object, but he also produced a practical demonstration of the theory using an X-ray source and physical "phantom object" that mimicked the properties of the human body. In addition, Cormack described how noise in the X-ray images propagates into reconstructed volumes and developed practical ways of dealing with these effects. Cormack and the electrical engineer Godfrey Hounsfield (who built the first practical CT scanner) received the 1979 Nobel Prize in Physiology or Medicine "for the development of computer assisted tomography."
Another formalism that describes the relationship between 3d objects and 2d projections was developed by David DeRosier and Aaron Klug in the mid-1960's at the Medical Research Center's Laboratory for Molecular Biology in Cambridge, England. This work was done independently of both Radon's mathematics and Cormack's more practical work. The DeRosier and Klug description of the relationship between a 3d object and its 2d projections is familiar to everyone in the field of cryoTEM and is known either as the "projection theorem" or the "central section theorem" (which more closely ties the name to the concepts behind it). In essence, the central section theorem states that the Fourier transform of a 2d projection of a 3d object is a central section (i.e., passing through the origin of the transform) of the Fourier transform of the 3d object.
Details of Electron Tomography
Practical Tomography at IU
We have installed the tomography data collection program serialEM from the Boulder Laboratory for 3-D Electron Microscopy of Cells on the JEOL JEM 3200FS and are in constant communication both with David Mastronarde (the developer of this program) and Jacob Brink (JEOL USA's tomography guru) with regard to improvements in the program and its implimentation on the 3200FS.
serialEM controls most aspects of the operation of the 3200FS and allows for automated collection of tomographic tilt series. Tilt range limits are determined by both the specimen holder used and by the properties of the grid being examined (i.e., the space between grid bars, overall grid thickness, etc.). We currently have three holders (the JEOL high tilt holder , the Fischione dual axis tomography holder and the Gatan 914 cryo-tomography holder) with tilt ranges of ±70°. The 914 cryo-holder should only be used for cryo samples while the other two holders can be used interchangably. The Fischione holder is designed to make it extremely simple to collect dual tilt-axis data sets (see below), while the JEOL high tilt holder is much easier to use when loading and unloading a grid.
As noted above, in addition to the tilt range of a given holder, factors such as the spacing between grid bars and the actual grid thickness also strongly influence the "working tilt range" that can be acheived with any given sample. The best grids to use for tomography are slot or hole grids which have very large openings that are completly covered by a support film. Since there are no grid bars in these grids, the only regions that become occluded by the grid when highly tilted are immediately adjacent to the edge of the hole through the grid. Such grids are made by a variety of companies and are available from any vendor of TEM supplies. Although many commercially available slot/hole grids are made from nickle, we do not recommend using nickle grids in the 3200FS due to the paramagnetic properties of the metal. Also bear in mind that the material in each of the high tilt holders will block the electron beam some of the time for some areas that can be viewed when the holder is not tilted.
It is possible to use normal mesh EM grids for tomography. However, the finer the mesh, the less useful area exits as the grid is tilted to higher and higher angles:
serialEM can record a finely sampled tilt series using the full size of the UltraScan CCD in considerably less than 1 hour for well-behaved samples. It has the ability to use the in-column energy filter to record zero-loss images, plasmon images and/or energy filtered images of defined energy loss (EFTEM). The program also has built-in low dose capabilities which can be coupled to the energy filter for cryo electron tomography (cryoET) .
People who want to use the 3200FS for tomography should contact the director to discuss a particular project and will in most cases need to dedicate additional time for sample preparation and for training in the use of serialEM.
We do not yet have the ability to record tomographic tilt series routinely in STEM mode. If you are interested in this sort of tomography, please contact the director for further information and to discuss the options available to someone wishing to collect STEM tomography data.
Advanced Concepts and Techniques
Advantages of Dual Tilt Axis Tomography
