  The holographic mask technique is used to create freely moving electrons with
quantized angular momentum. With electron optical elements they can be focused
to vortices with diameters below the nanometer range. The understanding of
these vortex beams is important for many applications. Here we present a theory
of focused free electron vortices. The agreement with experimental data is
excellent. As an immediate application, fundamental experimental parameters
like spherical aberration and partial coherence are determined.
