  High-statistics $\pi^-\pi^-$ and $\pi^+\pi^+$ femtoscopy data are presented
for Au+Au collisions at $\sqrt{s_\mathrm{NN}}=2.4$ GeV, measured with HADES at
SIS18/GSI. The experimental correlation functions allow the determination of
the space-time extent of the corresponding emission sources via a comparison to
models. The emission source, parametrized as three-dimensional Gaussian
distribution, is studied in dependence on pair transverse momentum, azimuthal
emission angle with respect to the reaction plane, collision centrality and
beam energy. For all centralities and transverse momenta, a geometrical
distribution of ellipsoidal shape is found in the plane perpendicular to the
beam direction with the larger extension perpendicular to the reaction plane.
For large transverse momenta, the corresponding eccentricity approaches the
initial eccentricity. The eccentricity is smallest for most central collisions,
where the shape is almost circular. The magnitude of the tilt angle of the
emission ellipsoid in the reaction plane decreases with increasing centrality
and increasing transverse momentum. All source radii increase with centrality,
largely exhibiting a linear rise with the number of participants, irrespective
of transverse momentum. A substantial charge-sign difference of the source
radii is found, appearing most pronounced at low transverse momentum. The
extracted source parameters are consistent with the extrapolation of their
energy dependence down from higher energies.
