  We report experimental measurements of the dynamical polarizability of
dysprosium, at a wavelength of 532 nm. We measure all three components (scalar,
vector, tensor) of the anisotropic polarizability for the ground and the
excited manifolds of the intercombination transition of Dy at 626 nm. The
apparatus on which the measurements are performed is first presented. We obtain
with this setup imaging of single Dy atoms with fidelity above 99 % and losses
below 2.5 % induced by imaging. We then describe the methods used to extract
the polarizability. In particular, we combine a measurement of trap frequency
and trap depth on single atoms in optical tweezers, allowing us to obtain a
measurement of the ground state polarizability free of errors in trap waist
calibration. The obtained values give a magic condition between two Zeeman
states in the ground and excited manifolds, which was used to image single
atoms in optical tweezer arrays. The scalar polarizability of the ground state
is in disagreement with theoretical expectations, calling for future
investigations to resolve the discrepancy.
