  Optical aberrations have been studied for centuries, placing fundamental
limits on the achievable resolution in focusing and imaging. In the context of
structured light, the spatial pattern is distorted in amplitude and phase,
often arising from optical imperfections, element misalignment, or even from
dynamic processes due to propagation through perturbing media such as living
tissue, free-space, underwater and optical fibre. Here we show that the
polarisation inhomogeneity that defines vectorial structured light is immune to
all such perturbations, provided they are unitary. By way of example, we study
the robustness of vector vortex beams to tilted lenses and atmospheric
turbulence, both highly asymmetric aberrations, demonstrating that the
inhomogeneous nature of the polarisation remains unaltered from the near-field
to far-field, even as the structure itself changes. The unitary nature of the
channel allows us to undo this change through a simple lossless operation,
tailoring light that appears robust in all its spatial structure regardless of
the medium. Our insight highlights the overlooked role of measurement in
describing classical vectorial light fields, in doing so resolving prior
contradictory reports on the robustness of vector beams in complex media. This
paves the way to the versatile application of vectorial structured light, even
through non-ideal optical systems, crucial in applications such as imaging deep
into tissue and optical communication across noisy channels.
