  The recently developed information-theoretic approach to crystallographic
symmetry classifications and quantifications in two dimensions (2D) from
digital transmission electron and scanning probe microscope images is adapted
for the analysis of an experimental electron diffraction spot pattern, for the
first time. Digital input data are considered in this approach to consist of
the pixel-wise sums of approximately Gaussian distributed noise and an unknown
underlying signal that is strictly 2D periodic. Structural defects within the
crystals or on the crystal surfaces, instrumental image recording noise, slight
deviations from zero-crystal-tilt conditions in transmission electron
microscopy, inhomogeneous staining in structural biology studies of intrinsic
membrane protein complexes in lipid bilayers, and small inaccuracies in the
algorithmic processing of the digital data all contribute to a single
generalized noise term. The plane symmetry group and projected Laue class(or 2D
Bravais lattice type) that is anchored to the least broken symmetries are
identified as genuine in the presence of generalized noise. More severely
broken symmetries that are not anchored to the least broken symmetries are
identified as pseudo-symmetries. Our point symmetry quantification study of an
electron diffraction spot pattern is highly topical because a new contrast
mechanism for 4D scanning transmission electron microscopy was recently
demonstrated by other authors. The usage of objective symmetry quantifications
is bound to become the preeminent condition of the establishment of that
contrast mode as an industry-wide standard.
