similar as possible and all building blocks of the array possess the same crystallographic orientation with respect to a cartesian coordinate system that is fixed to the microscope. (The microscope's optical axis typically serves as the z-axis.) Unbending is often necessary when the 2D array of membrane proteins is paracrystalline rather than genuinely crystalline. It was estimated that unbending approximately doubles the spatial resolution with which the shape of molecules can be determined Inorganic crystals are much stiffer than 2D periodic protein membrane arrays so that there is no need for the unbending of images that were taken from suitably thinned parts of these crystals. Consequently, the CRISP program does not possess the unbending image processing feature but offers superior performance in the so-called phase origin refinement. The latter feature is particularly important for electron crystallographers as their samples may possess any space group out of the 230 possible groups types that exist in three dimensions. The regular arrays of membrane forming proteins that structural biologists deal with are, on the other hand, restricted to possess one out of only 17 (two-sided/black-white) layer group types (of which there are 46 in total and which are periodic only in 2D) due to the chiral nature of all (naturally occurring) proteins. Different crystallographic settings of four of these layer group types increase the number of possible layer group symmetries of regular arrays of membrane forming proteins to just 21. All 3D space groups and their subperiodic 2D periodic layer groups (including the above-mentioned 46 two-sided groups) project to just 17 plane space group types, which are genuinely 2D periodic and are sometimes referred to as the wallpaper groups. (Although quite popular, this is a misnomer because wallpapers are not restricted to possess these symmetries by nature.) All individual transmission electron microscopy images are projections from the three-dimensional space of the samples into two dimensions (so that spatial distribution information along the projection direction is unavoidably lost). Projections along prominent (i.e. certain low-index) zone axes of 3D crystals or along the layer normal of a membrane forming protein sample ensure the projection of 3D symmetry into 2D. (Along arbitrary high-index zone axes and inclined to the layer normal of membrane forming proteins, there will be no useful projected symmetry in transmission images.) The recovery of 3D structures and their symmetries relies on electron tomography techniques, which use sets of transmission electron microscopy images.