  The Universe opacity to gamma rays is still an open question, in particular
anomalies may have been observed. Assuming that such anomalies find their
origin in conventional physics like intrinsic source spectra or the density of
the extragalactic background light, they would be evenly distributed over the
sky. If they exist, axion-like particles (ALPs) would have a potential effect
on the opacity of the Universe to gamma rays, possibly related to the anomalies
in the spectral indices of distant gamma-ray sources. In the scenario where
ALPs from distant sources convert back to photons in the Galactic magnetic
field, their effect on the opacity is expected to depend on the position of the
sources. In that case the anomaly is expected to exhibit peculiar correlations
on the sky. We propose a method to test the origin of the opacity anomaly,
based on angular correlations of spectral softening anomalies. Such a diagnosis
requires a wide-field survey of high-energy gamma-ray sources over a broad
range of energy. The future Cherenkov Telescope Array (CTA) is perfectly suited
to perform such a study. It is shown that while the current sample of sources
is not large enough to base conclusions on, with this method CTA will be
sensitive to ALP couplings to gamma rays of the order of 3e-11 GeV^-1 for ALP
masses below 1e-8 eV.
