  Quantum fluctuations in spacetime can, in some cases, lead to distortion in
astronomical images of faraway objects. In particular, a stochastic model of
quantum gravity predicts an accumulated fluctuation in the path length $\Delta
L$ with variance $\langle \Delta L^2\rangle\sim l_pL$ over a distance $L$,
similar to a random walk, and assuming no spatial correlation above length
$l_p$; it has been argued that such an effect is ruled out by observation of
sharp images from distant stars. However, in other theories, such as the
pixellon (modeled on the Verlinde-Zurek (VZ) effect), quantum fluctuations can
still accumulate as in the random walk model while simultaneously having large
distance correlations in the fluctuations. Using renormalization by analytic
continuation, we derive the correlation transverse to the light propagation,
and show that image distortion effects in the pixellon model are strongly
suppressed in comparison to the random walk model, thus evading all existing
and future constraints. We also find that the diffraction of light rays does
not lead to qualitative changes in the blurring effect.
