For an introduction to the theory of electron diffraction, see part 2 of Williams and Carter's Transmission Electron Microscopy text
While it is clear that precession reduces many of the dynamical diffraction effects that plague other forms of electron diffraction, the resulting patterns cannot be considered purely kinematical in general. There are models that attempt to introduce corrections to convert measured PED patterns into true kinematical patterns that can be used for more accurate direct methods calculations, with varying degrees of success. Here, the most basic corrections are discussed. In purely kinematical diffraction, the intensities of various  reflections, , are related to the square of the amplitude of the structure factor,  by the equation:
where g is the reciprocal space magnitude of the reflection in question and R is the radius of the Laue circle, usually taken to be equal to φ. While this correction accounts for the integration over the excitation error, it takes no account for the dynamical effects that are ever-present in electron diffraction. This has been accounted for using a two-beam correction following the form of the Blackman correction originally developed for powder x-ray diffraction. Combining this with the aforementioned Lorentz correction yields:
where ,  is the sample thickness, and  is the wave-vector of the electron beam.  is the Bessel function of zeroeth order.
This form seeks to correct for both geometric and dynamical effects, but is still only an approximation that often fails to significantly improve the kinematic quality of the diffraction pattern (sometimes even worsening it). More complete and accurate treatments of these theoretical correction factors have been shown to adjust measured intensities into better agreement with kinematical patterns. For details, see Chapter 4 of reference.
Only by considering the full dynamical model through multislice calculations can the diffraction patterns generated by PED be simulated. However, this requires the crystal potential to be known, and thus is most valuable in refining the crystal potentials suggested through direct methods approaches. The theory of precession electron diffraction is still an active area of research, and efforts to improve on the ability to correct measured intensities without a priori knowledge are ongoing.