:Direct methods in crystallography are a collection of mathematical techniques that seek to determine crystal structure based on measurements of diffraction patterns and potentially other a priori knowledge (constraints). The central challenge of inverting measured diffraction intensities (i.e. applying an inverse Fourier Transform) to determine the original crystal potential is that phase information is lost in general since intensity is a measurement of the square of the modulus of the amplitude of any given diffracted beam. This is known as the phase problem of crystallography.
:If the diffraction can be considered kinematical, constraints may be used to probabilistically relate the phases of the reflections to their amplitudes, and the original structure can be solved via direct methods (see Sayre equation as an example). Kinematical diffraction is often the case in x-ray diffraction, and is one of the primary reasons that technique has been so successful at solving crystal structures. However, in electron diffraction, the probing wave interacts much more strongly with the electrostatic crystal potential, and complex dynamical diffraction effects can dominate the measured diffraction patterns. This makes application of direct methods much more challenging without a priori knowledge of the structure in question.