  In quantum mechanics, each conserved quantity (e.g., energy, position, linear
momentum and angular momentum) is associated with a Hermitian operator. Its
expected value can then be determined by performing a measurement on the
wavefunction. In modern electron microscopy, one can select the initial and
final states of the electron and the measurement basis by performing
measurements of scattering processes. For example, the orbital angular momentum
(OAM) of an electron can be used to reveal the n-fold symmetry of a
wavefunction scattered by a sample. Here, we introduce a new composite planar
chirality operator that can be used to measure a spiral-like feature in a
sample. This concept develops the concept of chirality to highlight a specific
roto-scale symmetry. We show that planar chirality can be characterized using
an electron OAM sorter to uncover the atomic structures of biomolecules in cryo
electron microscopy, either in a stand-alone analysis for fast identification
of protein structures or in the context of conventional cryo electron
microscopy to produce faster and more detailed 3D reconstructions by solving
upside-down orientation ambiguities.
