  We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to
simulate Au + Au collisions at beam energy $E_{beam}$ = 1.23$A$ GeV, which
corresponds to center of mass energy $\sqrt{s_{NN}} = 2.4$ GeV. Firstly, we
obtained reasonable rapidity and transverse mass spectra of $\pi^-$ and $\pi^+$
as well as "apparent" temperature parameters in comparison with the HADES data.
Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of
same charged pion-pairs, we obtained the square difference of outward radius
and sideward radius, i.e. $R_{out}^{2}-R_{side}^{2}$, as well as the freeze-out
volume ($V_{fo}$), which were basically consistent with the trend of HADES
experimental results. The azimuthal dependence of the HBT radii was also
calculated by a matrix method, and corrected by the rotation matrix. In
addition, the eccentricities of the $xy$- and $zy$- planes of pion-pair
emissions were also extracted for different pair transverse momentum and
collision centrality, which show that the $xy$-eccentricity increases with pair
transverse momentum as well as centrality but not for $zy$-eccentricity,
indicating a more asymmetric transverse emission of particle-pairs with higher
transverse momentum in off-central collisions.
