One aspect of the quantum nature of spacetime is its foaminess at very small scales. Many models for spacetime foam are defined by the accumulation power $alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $alpha$ is defined by theexpression for the path-length fluctuations, $delta ell$, of a source at distance $ell$, wherein $delta ell simeq ell^{1 - alpha} ell_P^{alpha}$, with $ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {em Chandra} to set the constraint $alpha gtrsim 0.58$, which rules out the random walk model (with $alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $alpha gtrsim 0.67$ and $alpha gtrsim 0.72$, respectively. These limits on $alpha$ seem to rule out $alpha = 2/3$, the model of some physical interest.
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