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Background radiation fields pervade the Universe, and above a certain energyany $\gamma$-ray flux emitted by an extragalactic source should be attenuateddue to $e^+e^-$ pair production. The opacity could be alleviated if photonsoscillated into hypothetical axion-like particles (ALPs) in ambient magneticfields, leading to a $\gamma$-ray excess especially at high optical depths thatcould be detected with imaging air Cherenkov telescopes (IACTs).  Here, we introduce a method to search for such a signal in $\gamma$-ray dataand to estimate sensitivities for future observations. Different magneticfields close to the $\gamma$-ray source are taken into account in which photonscan convert into ALPs that then propagate unimpeded over cosmological distancesuntil they re-convert in the magnetic field of the Milky Way. Specifically, weconsider the coherent field at parsec scales in a blazar jet as well as theturbulent field inside a galaxy cluster. For the latter, we explicitly derivethe transversal components of a magnetic field with gaussian turbulence whichare responsible for the photon-ALP mixing. To illustrate the method, we applyit to a mock IACT array with characteristics similar to the Cherenkov TelescopeArray and investigate the dependence of the sensitivity to detect a$\gamma$-ray excess on the magnetic-field parameters.

On detecting oscillations of gamma rays into axion-like particles in turbulent and coherent magnetic fields