Interlopers speak out: studying the dark universe using small-scale lensing anisotropies

Strongly lensed systems are powerful probes of the distribution of dark matter on small scales. In this paper, we show that line-of-sight haloes between the source and the observers give rise to a distinct anisotropic signature in the two-point function of the effective lensing deflection field. We show in particular that the non-linear coupling between line-of-sight haloes and the main lens plane imprints a characteristic quadrupole moment on this two-point function whose amplitude reflects the abundance of such haloes within the strongly lensed field. We discuss how, by taking ratios of different multipole moments, such observables could be made robust under the mass-sheet transform. We also demonstrate that future extremely large telescopes have the ability to detect the quadrupole moment due to this unique anisotropic signature under ideal conditions. Our approach opens the door to statistically distinguish the effect of line-of-sight haloes from that of the main-lens substructure on lensed images, hence allowing one to probe dark matter physics in a new way.