dynamical scattering
When we first learn how a crystal diffracts, we tell a simple story: a wave comes in, each atom scatters a little of it, the scattered wavelets add up, and the brightness of a reflection is just the squared strength of the structure factor (proportional to |F|^2). That simple story is called kinematic scattering, and it assumes the beam is scattered at most once as it passes through. It is a good approximation for X-rays through a small crystal, because X-rays interact only weakly with matter. Electrons are a completely different animal: they feel the electric field of every nucleus and electron directly, so they scatter roughly ten thousand times more strongly.
Because electrons scatter so strongly, a single pass through even a thin foil is not one scattering event but many. Energy sloshes back and forth between the straight-through beam and the diffracted beams, over and over, like water rocking between two connected tanks. This repeated, coherent re-scattering is dynamical scattering. In the simplest 'two-beam' case (only the transmitted beam and one diffracted beam matter), the intensity in the diffracted beam does not just grow with thickness — it oscillates sinusoidally, rising and falling as the foil gets thicker, with a characteristic period called the extinction distance (often a few tens of nanometres). These oscillations show up in images as thickness fringes and bend contours, the everyday fingerprints of dynamical behaviour.
The practical upshot is a warning and an opportunity. The warning: you cannot naively read electron diffraction intensities as |F|^2 to solve a structure, because the intensities are scrambled by multiple scattering; reflections that are forbidden by symmetry can even appear, borrowed from allowed ones by 'double diffraction'. The opportunity: dynamical scattering breaks Friedel's law, which is precisely why convergent-beam patterns can detect the absence of an inversion centre and fix the space group. Making electron diffraction quantitative therefore means either keeping the sample extremely thin (to approach the kinematic limit), using tricks like precession to average out the worst effects, or embracing the physics with full dynamical simulation.
In a bright-field TEM image of a wedge-shaped foil, you see a set of parallel light-and-dark fringes running along the wedge. Each fringe marks one more extinction distance of thickness — the intensity oscillating between transmitted and diffracted beams. Count the fringes and you have measured the local thickness, purely from dynamical scattering.
Thickness fringes are dynamical scattering made visible: intensity oscillating between beams as the foil thickens.
The common misconception is that electron diffraction spot intensities equal |F|^2 the way X-ray intensities roughly do. They do not — multiple scattering can brighten weak reflections, create symmetry-forbidden spots by double diffraction, and generally scramble the intensities unless the crystal is very thin.