Method and Device for Image Display and Eye Tracking through a Catadioptric Lens

In one implementation, an apparatus includes: a display to emit light in a first wavelength range; one or more light sources to emit light in a second wavelength range; a camera to detect the light in the second wavelength range; and an eyepiece to reflect and refract the light in the first wavelength range while passing, without substantial distortion, the light in the second wavelength range, wherein the eyepiece includes two lens halves separated by a retarder that changes light in the first wavelength range from a first polarization to a second polarization different from the first polarization.