We present optical systems suitable for focusing two substantially collimated beams or sheets of light propagating in different directions onto a common focal point. In some embodiments the optical systems comprise separate focusing elements for each beam or sheet of light, while in other embodiments the optical systems comprise a focusing element and a redirection element. The optical systems have particular application in the receive optics of infrared touch screens, where they enable the detection of additional light paths that assist in the determination of two or more simultaneous touch events.