Title: Imaging dark matter at the smallest scales with $z\approx1$ lensed stars

Abstract: Observations of caustic-crossing galaxies at redshift $0.7<z<1$ show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicted such events should be common near the critical curves (CCs) of galaxy clusters, but some are found relatively far away from these CCs. We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal. We study the combined magnification from the macrolens, millilenses, and microlenses (3M-lensing). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead we find a that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of mcirolensing events found near and far from the CC. By measuring $\beta$ (the exponent of the LF), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive imaging regime where $\beta>2$ and the number density of events is greater around substructureand the number density of events is greater around substructures, and (ii) negative imaging regime where $\beta<2$. We study the particular case of seven microlensing events found by HST in the Dragon arc (at z=0.725). We find that a population of supergiant stars with a steep LF with $\beta=2.55$ fits the distribution of these events. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of $\sim 1.3 \times 10^8\,\Msun$ (within its Einstein radius).