Limits on a bent waveguide for a wedge display

Wedge displays seem immune to slight bends even though they are likely to be introduced by the physical limits of the tools used for wedge manufacture. We show how the maximum angular error which can be introduced by a bend of constant curvature is determined by its thickness, radius of curvature, and the angle of the ray before entry into the bend. The maximum change in angle therefore depends on the number of bounces through the bend, not on how the ray enters. For a 500 lines VGA image of 20 mm thick curved part, the minimum acceptable radius of curvature is about 51.6 m. That Wedge panels seem able to tolerate more than this is probably because through a real bend, the radius of curvature varies.