Circuits in the visual cortex integrate the information derived from separate ON (light-responsive) and OFF (dark-responsive) pathways to construct orderly columnar representations of stimulus orientation and visual space(1-7). How this transformation is achieved to meet the specific topographic constraints of each representation remains unclear. Here we report several novel features of ON-OFF convergence visualized by mapping the receptive fields of layer 2/3 neurons in the tree shrew (Tupaia belangeri) visual cortex using two-photon imaging of GCaMP6 calcium signals. We show that the spatially separate ON and OFF subfields of simple cells in layer 2/3 exhibit topologically distinct relationships with the maps of visual space and orientation preference. The centres of OFF subfields for neurons in a given region of cortex are confined to a compact region of visual space and display a smooth visuotopic progression. By contrast, the centres of the ON subfields are distributed over a wider region of visual space, display substantial visuotopic scatter, and have an orientation-specific displacement consistent with orientation preference map structure. As a result, cortical columns exhibit an invariant aggregate receptive field structure: an OFF-dominated central region flanked by ON-dominated subfields. This distinct arrangement of ON and OFF inputs enables continuity in the mapping of both orientation and visual space and the generation of a columnar map of absolute spatial phase.