  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.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies