Recovering the mass distribution of an extended gravitational lens

We investigate the possibility of determining mass distribution a gravitational lens via lensing observations. consider an extended, compact lens, representing its static external potential infinite set symmetric trace free (STF) multipole moments. Within wave-optical treatment, we evaluate caustics formed in lens's point spread function (PSF). study only quantity that is available astronomical observations: image PSF by imaging telescope. This observable may be used to recover some physical characteristics including shape, orientation and composition. Illustrating this, exotic lenses several well-known solids with uniform density. show when moments beyond quadrupole are observed, symmetry properties can recovered. The presence octupole moment implies breaking "north-south" lens. rotated hexadecapole axial symmetry. As such, if observations lensed images allow reconstruction these moments, important information about dynamics obtained. help choosing most appropriate profile characterize astrophysical lenses, such as dark matter halos presumed contain galaxies clusters galaxies. Our results novel offer new insight into realistic systems.