A brightness enhancing structure for a reflective display. A plurality of transparent hemi-beads form a film substantially covering and protruding inwardly from the structure's inward surface. A corresponding plurality of microstructured toroidal lenses are provided on the structure's outward side. Each lens is optically coupled to an adjacent one of the hemi-beads to redirect incident light rays toward the adjacent hemi-bead, such that the redirected light is totally internally reflected by the hemi-bead and reflected back in a direction approximately opposite that of the incident rays. This substantially reduces undesirable dark, non-reflective circular regions of each hemi-bead which would otherwise exist in the absence of this invention.