Compact head-up display

A method of providing pupil expansion for a diffracted light field comprising diverging ray bundles, wherein the diffracted light field is spatially-modulated in accordance with a hologram displayed on a spatial light modulator and comprises an expanding light cone such that the light field size increases with propagation distance within the first waveguide pupil expander and has a light field size defined in a direction substantially orthogonal to a propagation direction of the light field, and wherein the method comprises:

• directing the diffracted light field into a first waveguide pupil expander, wherein the first waveguide pupil expander comprises an input port, output port, a first pair of parallel surfaces and a second pair of parallel surfaces, wherein the first pair of parallel surfaces are orthogonal to the second pair of parallel surfaces;
• guiding the diffracted light field from the input port to the output port by internal reflection between the first pair of parallel surfaces;
• wherein a first surface of the first pair of parallel surfaces is partially transmissive-reflective such that the light field is divided at each internal reflection and a plurality of replicas of the light field are transmitted through a region of the first surface that forms the output port;
• and
• wherein the second pair of parallel surfaces are also arranged to light guide the light field from the input port to the output port by at least one total internal reflection, wherein the light field size is substantially equal to or greater than a second spacing size, defined between first and second surfaces of the second pair of parallel surfaces during internal reflection of the light field within the first waveguide pupil expander, and wherein the second pair of parallel surfaces retain the diffracted light field within the first waveguide pupil expander and ensure that the diffracted light field only leaves the first waveguide pupil expander via the output port.