A head-mounted apparatus comprising: a waveguide comprising an input end, and first and second, opposed guide surfaces for guiding light along the waveguide, the first guide surface being arranged to guide light by total internal reflection and the second guide surface having a stepped shape comprising a plurality of facets extending in a lateral direction across the waveguide and oriented to reflect input light from the input end through the first guide surface as output light, and intermediate regions between the facets that are arranged to direct light through the waveguide without extracting it, the waveguide arranged to extend across at least one eye of the user when the head-mounted apparatus is worn; and an illumination system comprising a two-dimensional array of light sources that are selectively operable, wherein the array of light sources are distributed across the input end of the waveguide in the lateral direction to provide the input light directed from selectively different lateral positions distributed in the lateral direction, the input light output through the first guide surface being directed in output directions that are distributed with respect to a normal to the first guide surface in the lateral direction in dependence on the lateral position of the input light, and the array of light sources are further distributed in a direction perpendicular to the lateral direction and the illumination system further comprises a focusing optical element having positive optical power in a direction perpendicular to the lateral direction arranged between the array of light sources and the waveguide to provide the input light directed in selectively different input directions distributed perpendicular to the lateral direction, the input light output through the first guide surface being directed in output directions that are further distributed with respect to a normal to the first guide surface in a perpendicular direction to the lateral direction in dependence on the input direction of the input light. a waveguide comprising an input end, and first and second, opposed guide surfaces for guiding light along the waveguide, the first guide surface being arranged to guide light by total internal reflection and the second guide surface having a stepped shape comprising a plurality of facets extending in a lateral direction across the waveguide and oriented to reflect input light from the input end through the first guide surface as output light, and intermediate regions between the facets that are arranged to direct light through the waveguide without extracting it, the waveguide arranged to extend across at least one eye of the user when the head-mounted apparatus is worn; and an illumination system comprising a two-dimensional array of light sources that are selectively operable, wherein the array of light sources are distributed across the input end of the waveguide in the lateral direction to provide the input light directed from selectively different lateral positions distributed in the lateral direction, the input light output through the first guide surface being directed in output directions that are distributed with respect to a normal to the first guide surface in the lateral direction in dependence on the lateral position of the input light, and the array of light sources are further distributed in a direction perpendicular to the lateral direction and the illumination system further comprises a focusing optical element having positive optical power in a direction perpendicular to the lateral direction arranged between the array of light sources and the waveguide to provide the input light directed in selectively different input directions distributed perpendicular to the lateral direction, the input light output through the first guide surface being directed in output directions that are further distributed with respect to a normal to the first guide surface in a perpendicular direction to the lateral direction in dependence on the input direction of the input light.