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The orbital angular momentum (OAM) of light and matter waves is a parameterthat is getting increasingly more attention over the past couple of years.Beams with a well defined OAM, the so-called vortex beams, are applied alreadyin e.g. telecommunication, astrophysics, nanomanipulation and chiralmeasurements in optics and electron microscopy. Also the OAM of a wave inducedby the interaction with a sample, shows great potential of interest. In allthese experiments it is crucial to measure the exact (local) OAM content of thewave, whether it is an incoming vortex beam or an exit wave after interactingwith a sample. In this work we investigate the use of spiral phase plates as analternative to the programmable phase plates used in optics to measure OAM. Wederive analytically how these can be used to study the local OAM components ofany wave function. By means of numerical simulations we illustrate how the OAMof a pure vortex beam can be measured. We also look at a sum of misalignedvortex beams and show how using SPPs the position and the OAM of eachindividual beam can be detected. Finally we look at the OAM induced by amagnetic dipole on a free electron wave and show how the SPP can be used tolocalize the magnetic poles and measure their "magnetic charge".  Although our findings can be applied to study the OAM of any wave function,they are of particular interest for electron microscopy where versatileprogrammable phase plates do not yet exist.

Local orbital angular momentum revealed by spiral phase plate imaging in transmission electron microscopy