Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem, and most of the theory has been known for at least fifty years. Although the subject appears frequently in the literature, wave propagation through inhomogeneous anisotropic media is rarely addressed. The rapid advances in liquid-crystal lenses call for a good overview of the theory on wave propagation via anisotropic media. Therefore, we present a novel polarized ray-tracing method, which can be applied to anisotropic optical systems that contain inhomogeneous liquid crystals. We describe the propagation of rays in the bulk material of inhomogeneous anisotropic media in three dimensions. In addition, we discuss ray refraction, ray reflection, and energy transfer at, in general, curved anisotropic interfaces with arbitrary orientation and/or arbitrary anisotropic properties. The method presented is a clear outline of how to assess the optical properties of uniaxially anisotropic media.

Abstract— An attractive concept for 3‐D displays is the one based on LCDs equipped with lenticular lenses. This enables autostereoscopic multiview 3‐D displays without a loss in brightness. A general issue in multiview 3‐D displays is their relatively low spatial resolution because the pixels are divided among the different views. To overcome this problem, we have developed switchable displays, using liquid‐crystal (LC) filled switchable lenticulars. In this way, it is possible to have a high‐brightness 3‐D display capable of fully exploiting the native 2‐D resolution of the underlying LCD. The feasibility of LC‐filled switchable lenticulars was shown in several applications. For applications in which it is advantageous to be able to display 3‐D and 2‐D content simultaneously, a 42‐in. locally switchable prototype having a matrix electrode structure was developed. These displays were realized using cylindrically shaped lenticular lenses in contact with LC. An alternative for these are lenticulars based on gradient‐index (GRIN) LC lenses. Preliminary results for such switchable GRIN lenses are presented as well.

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For the first time, to our knowledge, we report ray-tracing simulations of an advanced liquid-crystal gradientindex lens structure for application in switchable two-dimensional/three-dimensional (3D) autostereoscopic displays. We present ray-tracing simulations of the angular-dependent lens action. From the results we conclude that the lens action of the advanced optical design corresponds to the desired performance for small viewing angles. For oblique viewing angles of approximately 30°and higher, the lens action becomes significantly weaker compromising the 3D performance of an autostereoscopic display. The general approach and the advanced ray-optics analysis procedures presented form a useful tool in the search for improvements for high viewing angles and enable a better understanding of the liquid-crystal technology discussed.