Colloidal particles offer huge potential to provide new insights into the behaviour of liquids, both because their positions can be directly measured, and because they can be manipulated with externally applied fields. Experimentally this is achieved by exposing the particles to interfering lasers.1,2 The fact that colloidal suspensions are “soft” means we can go beyond linear response by exposing the system to strong fields. Here, we capitalize on this opportunity by directly measuring the response of a liquid to a spatially periodic external field. By choosing colloidal particles that can be modelled as hard spheres, we are able to investigate the same phenomena with both theory and simulation. We extend linear response theory to predict both the linear and quadratic response of the density modulation induced by the applied field using correlations measured in the unperturbed liquid. We also observe a structural change perpendicular to the applied field modulations, which varies nonmonotonically with the field period. These results open new research directions; by imposing artificial density modulations it is possible to measure properties of the liquid’s structure which are inaccessible to scattering experiments.