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. 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.