Luminaire having improved uniformity of output

A luminaire, comprising:

• a housing including a compartment having a reflective inner surface and an optical element comprising:
• a light entry surface arrangement facing the compartment and including a central transmissive surface portion separated from a peripheral transmissive surface portion by a tapered surface portion having opposing reflective surfaces and tapering outwardly towards a light exit surface arrangement including a central stepped profile stepping toward the compartment, the central stepped profile including a transmissive roof section facing the central transmissive surface portion and one or more tapered total internal reflection sidewall sections each facing a reflective surface of the tapered surface portion, the transmissive roof section having a smaller cross-section than the central transmissive surface portion;
• and
• a light source arrangement in the compartment arranged to emit a first fraction of light onto the central transmissive surface portion and a second fraction of light onto at least one of the reflective inner surface, the tapered surface portion and the peripheral transmissive surface portion.