  We study the optical properties of the solar gravitational lens (SGL) while
treating the Sun as an extended, axisymmetric and rotating body. The
gravitational field of the Sun is represented using a set of zonal harmonics.
We develop an analytical description of the intensity of light that is observed
in the image plane in the strong interference region of a realistic SGL. This
formalism makes it possible to model not only the point-spread function of
point sources, but also actual observables, images that form in the focal plane
of an imaging telescope positioned in the image plane. Perturbations of the
monopole gravitational field of the Sun are dominated by the solar quadrupole
moment, which results in forming an astroid caustic on the image plane.
Consequently, an imaging telescope placed inside the astroid caustic observes
four bright spots, forming the well-known pattern of an Einstein cross. The
relative intensities and positions of these spots change as the telescope is
moved in the image plane, with spots merging into bright arcs when the
telescope approaches the caustic boundary. Outside the astroid caustic, only
two spots remain and the observed pattern eventually becomes indistinguishable
from the imaging pattern of a monopole lens at greater distances from the
optical axis. We present results from extensive numerical simulations, forming
the basis of our ongoing study of prospective exoplanet imaging with the SGL.
These results are also applicable to describe a large class of gravitational
lensing scenarios involving axisymmetric lenses that can be represented using
zonal harmonics.
