A touch-sensitive apparatus operates by light frustration and comprises a light transmissive panel with a front surface and a rear surface. Light emitters and light detectors optically face the rear surface along a perimeter of a touch-sensitive region on the panel. At least one non-imaging, diffusively transmitting optical element is arranged on the rear surface along the perimeter of the touch-sensitive region. The light emitters are arranged to emit a respective beam of light onto the non-imaging optical element so as to generate, by diffuse transmission, propagating light that propagates by total internal reflection inside the panel across the touch-sensitive region, and the light detectors are arranged to receive detection light generated, by diffuse transmission, as the propagating light impinges on the non-imaging optical element, so as to define a grid of propagation paths across the touch-sensitive region between pairs of light emitters and light detectors.