A touch-sensitive apparatus operates by light frustration (FTIR) and comprises a light transmissive panel (1) with a front surface and a rear surface. Light emitters (2) and light detectors (3) optically face the rear surface along a perimeter of a touch-sensitive region (4) on the panel (1). At least one diffusively reflecting element (40) is arranged on the front surface (5) along the perimeter of the touch-sensitive region (4). The light emitters (2) are arranged to emit a respective beam of light onto the diffusively reflecting element (40), so as to generate propagating light that propagates by total internal reflection inside the panel (1) across the touch-sensitive region (4), and the light detectors (3) are arranged to receive detection light generated as the propagating light impinges on the diffusively reflecting element (40), so as to define a grid of propagation paths (D) across the touch-sensitive region (4) between pairs of light emitters (2) and light detectors (3).