  Recently, several new characteristics have been introduced to describe null
geodesic structure of strong gravitational field, such as photon regions,
transversely trapping surfaces and some generalizations. They give an
alternative and concise way to describe lensing and shadow features of compact
objects with strong gravitational field without recurring to complete
integration of the geodesic equations. Here we test this construction in the
case of the Weyl metrics when geodesic equations are non-separable, and thus
can not be integrated analytically, while the above characteristic surfaces and
regions can be described in a closed form. We develop further our formalism for
a class of static axially symmetric spacetimes introducing more detailed
specification of transversely trapping surfaces in terms of their principal
curvatures. Surprisingly, we find in the static case without spherical symmetry
certain features, such as photon regions, previously known in the Kerr space.
These photon regions can be regarded as photon spheres, "thickened" due to
oblateness of the metric.
