text: In transmission electron microscope, a thin crystalline sample is illuminated by parallel beam of electrons accelerated to  energy of hundreds of kiloelectron volts. At these energies samples are transparent for the electrons if the sample is thinned enough (typically less than 100 nm). Due to the wave–particle duality, the high-energetic electrons behave as matter waves with wavelength of a few thousandths of a nanometer. The  relativistic wavelength is given by
  where  is Planck's constant,  is the electron rest mass,  is the elementary charge,  is the speed of light and  is an electric potential accelerating the electrons (also called acceleration voltage). For instance the acceleration voltage of 200 kV results in a wavelength of 2.508 pm. 
  Since the  spacing between atoms in crystals is about a hundred times larger, the electrons are diffracted on the  crystal lattice, acting as a diffraction grating. Due to the diffraction, part of the electrons is  scattered at particular angles (diffracted beams), while others pass through the sample without changing their direction (transmitted beams). In order to determine the diffraction angles, the electron beam  normally incident to the atomic lattice can be seen as a planar wave, which is re-transmitted by each atom as a spherical wave. Due to the constructive interference, the spherical waves from number of diffracted beams under angles  given, approximately, by the Bragg condition
  where the integer  is an order of diffraction and  is the distance between atoms (if only one row of atoms is assumed as in the illustration aside) or a distance between atomic planes parallel to the beam (in a real 3D atomic structure). For finite samples this equation is only approximately correct. 
  After being deflected by the microscope's magnetic lens, each set of initially parallel beams intersect in the back focal plane forming the diffraction pattern. The transmitted beams intersect right in the optical axis. The diffracted beams intersect at certain distance from the optical axis (corresponding to interplanar distance of the planes diffracting the beams) and under certain azimuth (corresponding to the orientation of the planes diffracting the beams). This allows to form a pattern of bright spots typical for SAD.
  SAD is called "selected" because it allows the user to select the sample area from which the diffraction pattern will be acquired. For this purpose, there is a selected area aperture located below the sample holder. It is a metallic sheet with several differently sized holes which can be inserted into the beam. The user can select the aperture of appropriate size and position it so that it only allows to pass the portion of beam corresponding to the selected area. Therefore, the resulting diffraction pattern will only reflect the area selected by the aperture. This allows to study small objects such as crystallites in polycrystalline material with a broad parallel beam.
  Character of the resulting diffraction image depends on whether the beam is diffracted by one single crystal or by number of differently oriented crystallites for instance in a polycrystalline material. The single-crystalline diffractogram depicts a regular pattern of bright spots. This pattern can be seen as a two-dimensional projection of  reciprocal crystal lattice. If there are more contributing crystallites, the diffraction image becomes a superposition of individual crystals' diffraction patterns. Ultimately, this superposition contains diffraction spots of all possible crystallographic plane systems in all possible orientations. For two reasons, these conditions result in a diffractogram of concentric rings:
  # There are discrete spacings between various parallel crystallographic planes and therefore the beams satisfying the diffraction condition can only form diffraction spots in discrete distances from the transmitted beam.
  # There are all possible orientations of crystallographic planes and therefore the diffraction spots are formed around the transmitted beam in the whole 360-degree azimuthal range.