The invention relates to a lighting system (LSI) which comprises a plurality of light engines (LEa1,1, LEa2,1, LEa3,1) and a system-exit window (OS). Each light engine comprising a first predetermined number of light emitting diodes, a second pre-determined number of dichroÊc beam splitters, and an engine-output window. The light engine superposes light emitted by the light emitting diodes via at least one dichroÊc beam splitter on the engine-output window. The lighting system further comprises a plurality of light guides (LGa1,1, LGa2,1, LGa3,1) for guiding light emitted by the light engines towards the system-exit window. The light guides comprise a light-guide-output window (OGa1,1, OGa2,1, OGa3,1) The plurality of light-guide-output windows is arranged in an array constituting the system-exit window. The light guides enable the light engines to be located remotely from the system-exit window. This enables an effective cooling of the light emitting diodes of the light engines while allowing the light-guide-output windows to be stacked adjacent in the system-exit window.