  We study Rabi rotations arising in intensity-dependent photon echoes from an
ensemble of self-assembled InGaAs quantum dots. To achieve a uniform
distribution of intensities within the excited ensemble, we introduce flattop
intensity profiles of picosecond laser pulses. This allows us to overcome the
damping of Rabi rotations imposed by the spatial inhomogeneity of Rabi
frequencies by a Gaussian laser profile. Using photon echo polarimetry, we
distinguish between the coherent optical responses from exciton and trion
ensembles. Here, we demonstrate that a photo-induced charging of the quantum
dots leads to a significant reduction of the number of neutral quantum dots
under resonant excitation with intensive optical pulses with areas exceeding
$\frac{\pi}{2}$. The trion ensemble shows robust Rabi rotations when the area
of the refocussing pulse is increased up to 5.5$\pi$. We analyze the remaining
attenuation of Rabi rotations by theoretical modeling of excitation induced
dephasing, inhomogeneity of dipole moments, and coupling to acoustic phonons.
The latter is identified as the dominating mechanism resulting in a loss of
optical coherence during the action of the involved optical pulses.
