An apparatus for use in tracking an eye that is illuminated by infrared light, the apparatus comprising: a waveguide that is transparent and includes an input-coupler and an output-coupler; and an infrared illumination source configured to produce infrared light that can be used to illuminate the eye while the input-coupler is axially aligned with the eye, resulting in infrared light beams reflected from the eye being incident on the input-coupler of the waveguide; characterized in that the input-coupler comprises a plurality of curved grating lines that are configured to diffract light beams reflected from the eye and incident on the input-coupler into the waveguide, the light beams propagating by way of total internal reflections through the waveguide towards a common region at which is located the output-coupler and exiting the waveguide through the output-coupler; wherein the plurality of curved grating lines of the input-coupler have a radially varying pitch that decreases with increases in distances between the curved grating lines and the output-coupler, wherein the plurality of curved grating lines of the input-coupler each have a point of convergence that is located within the region of the waveguide at which is located the output-coupler, and wherein the radially varying pitch causes different infrared light beams reflected from the eye that are incident on different horizontal and vertical positions of the input-coupler to propagate through the waveguide at respective different angles of reflection and exit the waveguide at respective different angles of incidence relative to a surface of the waveguide through which the infrared light beams exit, thereby causing the infrared light beams traveling through the waveguide and exiting the waveguide to be angularly encoded. a waveguide that is transparent and includes an input-coupler and an output-coupler; and an infrared illumination source configured to produce infrared light that can be used to illuminate the eye while the input-coupler is axially aligned with the eye, resulting in infrared light beams reflected from the eye being incident on the input-coupler of the waveguide; characterized in that the input-coupler comprises a plurality of curved grating lines that are configured to diffract light beams reflected from the eye and incident on the input-coupler into the waveguide, the light beams propagating by way of total internal reflections through the waveguide towards a common region at which is located the output-coupler and exiting the waveguide through the output-coupler; wherein the plurality of curved grating lines of the input-coupler have a radially varying pitch that decreases with increases in distances between the curved grating lines and the output-coupler, wherein the plurality of curved grating lines of the input-coupler each have a point of convergence that is located within the region of the waveguide at which is located the output-coupler, and wherein the radially varying pitch causes different infrared light beams reflected from the eye that are incident on different horizontal and vertical positions of the input-coupler to propagate through the waveguide at respective different angles of reflection and exit the waveguide at respective different angles of incidence relative to a surface of the waveguide through which the infrared light beams exit, thereby causing the infrared light beams traveling through the waveguide and exiting the waveguide to be angularly encoded.