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We have experimentally demonstrated the strong coupling between single atoms and the higher-order Hermite-Gaussian transverse modes in a high-finesse optical microcavity. Compared to the usual low-order symmetric transverse modes, multiple lobes and the asymmetric spatial pattern of the titled modes provide more information about the motion of single atoms in the cavity. The motional information can be extracted from the measured transmission spectra, which includes the velocities and the positions of the atoms in vertical and off-axis directions. The scheme has great potential in time-resolved atom-cavity microscopy and in tracking the three-dimensional single atom trajectory in real time. [ABSTRACT FROM AUTHOR]