  Orbital angular momentum (OAM) of photons is carried upon the wave front of
an optical vortex and is important in physics research due to its fundamental
degree of freedom. As for the interaction with materials, the optical OAM was
shown to be transferred to the valence electron based on modified selection
rules where a single ion is carefully aligned to the center of a vortex
[Schmiegelow et al.(2016)]. We here demonstrate an elaborate way of extracting
the distributed OAMs in the two-dimensional x-ray wave field at the exit-face
of the specimen by a vorticity-sensitive microscopy, which detects vorticity in
the reciprocal-space wave field downstream of the optical vortices. This method
enables us to measure the distributed topological charges and OAMs by a single
image with the wide field of view over 300 $\mu$m. Among various wavelength,
the research of x-ray OAM is especially interesting since it could be closely
related to the predicted OAM-induced x-ray dichroism [Veenendaal et al.(2007)].
