  The Zeeman effect is of limited utility for probing the magnetism of the
quiet solar chromosphere. The Hanle effect in some spectral lines is sensitive
to such magnetism, but the interpretation of the scattering polarization
signals requires taking into account that the chromospheric plasma is highly
inhomogeneous and dynamic (i.e., that the magnetic field is not the only cause
of symmetry breaking). Here we investigate the reliability of a well-known
formula for mapping the azimuth of chromospheric magnetic fields directly from
the scattering polarization observed in the \ion{Ca}{2}~8542~\AA\, line, which
is typically in the saturation regime of the Hanle effect. To this end, we use
the Stokes profiles of the \ion{Ca}{2}~8542~\AA\, line computed with the PORTA
radiative transfer code in a three-dimensional (3D) model of the solar
chromosphere, degrading them to mimic spectropolarimetric observations for a
range of telescope apertures and noise levels. The simulated observations are
used to obtain the magnetic field azimuth at each point of the field of view,
which we compare with the actual values within the 3D model. We show that,
apart from intrinsic ambiguities, the method provides solid results. Their
accuracy depends more on the noise level than on the telescope diameter.
Large-aperture solar telescopes, like DKIST and EST, are needed to achieve the
required noise-to-signal ratios using reasonable exposure times.
