We describe a touch sensing system projecting light defining a touch sheet above a surface and a camera to capture a touch image of light scattered by a pen intersecting the touch sheet. A signal processor identifies a lateral location of the pen. The pen includes a light source to provide a light signal, and the system also includes two photodiodes to detect the signal from the pen. The touch detection is augmented by modelling the signals received at the photodiodes, dependent on the distance and angle of a pen, and using this to derive a probability of the observed received signals given the pen location determined from the touch sheet. This information can be used, for example, to allocate identities to the pens.