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In this work we present an alternative way to look at electron diffraction ina transmission electron microscope. In stead of writing the scatteringamplitude in Fourier space as a set of plane waves, we use the cylindricalFourier transform to describe the scattering amplitude in a basis of orbitalangular momentum (OAM) eigenstates. We show how working in this framework canbe very convenient when investigating e.g. rotation and screw axis symmetries.For the latter we find selection rules on the OAM-coefficients thatunambiguously reveal the handedness of the screw axis. Detecting theOAM-coefficients of the scattering amplitude thus offers the possibility todetect the handedness of crystals without the need for dynamical simulations,the thickness of the sample nor the exact crystal structure. We propose anexperimental setup to measure the OAM-components where an image of the crystalis taken after inserting a spiral phase plate in the diffraction plane andperform mulsti-slice simulations on $\alpha$-quartz to demonstrate how themethod indeed reveals the chirality. Experimental feasibility of the techniqueis discussed together with its main advantages with respect to chiralitydetermination of screw axes. The method shows how the use of a spiral phaseplate can be extended from a simple phase imaging technique to a tool tomeasure the local OAM-decomposition of an electron wave, widening the field ofinterest well beyond chiral space group determination.

Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries