Gravitational lensing is a potentially powerful tool for elucidating the origin of gamma-ray emission from distant sources. Cosmic lenses magnify the emission from distance sources and produce time delays between mirage images. Gravitationally-induce
d time delays depend on the position of the emitting regions in the source plane. The Fermi/LAT satellite continuously monitors the entire sky and detects gamma-ray flares, including those from gravitationally-lensed blazars. Therefore, temporal resolution at gamma-ray energies can be used to measure these time delays, which, in turn, can be used to resolve the origin of the gamma-ray flares spatially. We provide a guide to the application and Monte Carlo simulation of three techniques for analyzing these unresolved light curves: the Autocorrelation Function, the Double Power Spectrum, and the Maximum Peak Method. We apply these methods to derive time delays from the gamma-ray light curve of the gravitationally-lensed blazar PKS 1830-211. The result of temporal analysis combined with the properties of the lens from radio observations yield an improvement in spatial resolution at gamma-ray energies by a factor of 10000. We analyze four active periods. For two of these periods, the emission is consistent with origination from the core and for the other two, the data suggest that the emission region is displaced from the core by more that ~1.5 kpc. For the core emission, the gamma-ray time delays, $23pm0.5$ days and $19.7pm1.2$ days, are consistent with the radio time delay $26^{+4}_{-5}$ days.
We investigate potential $gamma-gamma$ absorption of gamma-ray emission from blazars arising from inhomogeneities along the line of sight, beyond the diffuse Extragalactic Background Light (EBL). As plausible sources of excess $gamma-gamma$ opacity,
we consider (1) foreground galaxies, including cases in which this configuration leads to strong gravitational lensing, (2) individual stars within these foreground galaxies, and (3) individual stars within our own galaxy, which may act as lenses for microlensing events. We found that intervening galaxies close to the line-of-sight are unlikely to lead to significant excess $gamma-gamma$ absorption. This opens up the prospect of detecting lensed gamma-ray blazars at energies above 10 GeV with their gamma-ray spectra effectively only affected by the EBL. The most luminous stars located either in intervening galaxy or in our galaxy provides an environment in which these gamma-rays could, in principle, be significantly absorbed. However, despite a large microlensing probability due to stars located in intervening galaxies, gamma-rays avoid absorption by being deflected by the gravitational potentials of such intervening stars to projected distances (impact parameters) where the resulting $gamma-gamma$ opacities are negligible. Thus, neither of the intervening excess photon fields considered here, provide a substantial source of excess $gamma-gamma$ opacity beyond the EBL, even in the case of very close alignments between the background blazar and a foreground star or galaxy.
