Muon pair production by photons in atmosphere: is any room left for high-energy muon astronomy?

Production of muon pairs by high-energy photons in electromagnetic and hadronic showers in atmosphere has been calculated. The effect of muon pair production in hadronic extensive air showers (EAS) is unlikely to be seen by next generation detectors. Applications of muon pair production process in electromagnetic showers to the very high energy gamma-ray astronomy are discussed. It is shown that, although this process dominates over conventional pion and kaon decay above a few TeV in photon-initiated showers and provides a distinctive signature of photon-induced event (muon pair), it is practically impossible to discriminate such events statistically from the background of muon pairs produced in the hadronic EAS. The rate of events is very low and requires detectors of a huge size.