An optical system includes a lightguide having opposing top and bottom major surfaces. A round through opening extends between the two surfaces of the lightguide. An elongated channel is formed in one of the surfaces and at least partially surrounds and is substantially concentric with the opening. The channel has a depth (d) that varies along its length. Light extractors extract light that would otherwise propagate within and along the lightguide. The features of the lightguide can be varied to optimize performance of the lightguide for various purposes.