text: The principal steps for solving a structure of an inorganic crystal from HREM images by CIP are as follows (for a detailed discussion see ).
  # Selecting the area of interest and calculation of the Fourier transform (= power spectrum consisting of a 2D periodic array of complex numbers)
  # Determining the defocus value and compensating for the contrast changes imposed by the objective lens (done in Fourier space)
  # Indexing and refining the lattice (done in Fourier space)
  # Extracting amplitudes and phase values at the refined lattice positions (done in Fourier space)
  # Determining the origin of the projected unit cell and determining the projected (plane group) symmetry
  # Imposing constrains of the most likely plane group symmetry on the amplitudes an phases. At this step the image phases are converted into the phases of the structure factors.
  # Calculating the pseudo-potential map by Fourier synthesis with corrected (structure factor) amplitudes and phases (done in real space)
  # Determining 2D (projected) atomic co-ordinates (done in real space)
  A few computer programs are available which assist to perform the necessary steps of processing. The most popular programs used by materials scientists (electron crystallographers) are CRISP, VEC, and the EDM package. There is also the recently developed crystallographic image processing program EMIA, but so far there do not seem to be reports by users of this program.
  Structural biologists achieve resolutions of a few ångströms (up from a to few nanometers in the past when samples used to be negatively stained) for membrane forming proteins in regular two-dimensional arrays, but prefer the usage of the programs 2dx, EMAN2, and IPLT. These programs are based on the Medical Research Council (MRC) image processing programs  and possess additional functionality such as the "unbending"  of the image. As the name suggests, unbending of the image is conceptually equivalent to "flattening out and relaxing to equilibrium positions" one building block thick samples so that all 2D periodic motifs are as 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.
  The origin refinement part of CIP relies on the definition of the plane symmetry group types as provided by the International Tables of Crystallography, where all symmetry equivalent positions in the unit cell and their respective site symmetries are listed along with systematic absences in reciprocal space. Besides plane symmetry groups p1, p3, p3m1 and p31m,  all other plane group symmetries are centrosymmetric so that the origin refinement simplifies to the determination of the correct signs of the amplitudes of the Fourier coefficients.
  When crystallographic image processing is utilized in scanning probe microscopy, the symmetry groups to be considered are just the 17 plane space group types in their possible 21 settings.