  Berry curvature that describes local geometrical properties of energy bands
can elucidate many fascinating phenomena in solid-state, photonic, and phononic
systems, given its connection to global topological invariants such as the
Chern number. Despite its significance, the observation of Berry curvature
poses a substantial challenging since wavefunctions are deeply embedded within
the system. Here, we theoretically propose a correspondence between the
geometry of far-field radiation and the underneath band topology of
non-Hermitian systems, thus providing a general method to fully capture the
Berry curvature without strongly disturbing the eigenstates. We further
experimentally observe the Berry curvature in a honeycomb photonic crystal slab
from polarimetry measurements and quantitatively obtain the non-trivial valley
Chern number. Our work reveals the feasibility of retrieving the bulk band
topology from escaping photons and paves the way to exploring intriguing
topological landscapes in non-Hermitian systems.
