Overview of Factors Affecting Lens Performance for 3D Displays Liwei Li*, Doug Bryant*, Tony Van Heugten**, Dwight Duston**, Philip J. Bos* *Liquid Crystal Institute, Kent State University, Kent, OH 44240, USA **eVision LLC. Roanoke, VA 24019, USA Abstract In response to the demand for high quality tunable lenses in 3-D display applications, we discuss the effects of different design factors on liquid crystal based electro-optic lens performance with LC modeling and lens modeling methods. In addition, a high quality LC lens is demonstrated, and measurement approaches are introduced to evaluate the performance in terms of particular metrics, and verify the modeling results. Keywords Liquid crystal device; LC tunable lens; electro-optic lens design; 3D displays 1. Introduction In 3-D display applications, high quality lenses, as important optical components, are in great need for input and output of the system. For example, lenticular lens array is used in autostereoscopic 2D 3D switchable displays [1]; Also, it has been demonstrated that using a corrective lens of tunable refractive power is able to effectively reduce this discrepancy between accommodation and convergence and weaken the visual fatigue it causes [2, 3]. Conventional glass or plastic lenses have been widely used not only in 3-D display systems, but also in almost all imaging systems. The tunable focal length is usually achieved by the relative movement of the lens components within a lens system, which requires space and complicated design. Electro-optic lenses based on Liquid crystals have been considered as potential candidates for replacing or simplifying bulky conventional optics, with the advantages of tunable power with electric field, small size and weight, low cost, low power consumption, and high speed switching. Unlike LC displays which use a change in the polarization state of transmitted light resulting from the refractive index modulation, LC lenses use the resultant phase of linearly polarized light exiting the surface. Generating the desired refractive index profile with external field becomes the key to the performance, and various electrode structures and addressing approaches have been introduced, such as: a set of discrete ring-patterned electrodes addressed individually with different voltages [4], the spatial distribution of electric field on a hole-patterned electrode plate to control the index profile [5], a spherically-shaped electrode which can be electrically addressed to tune the power continuously [6], a planar electrodes and a shaped dielectric layer for shaping the electric field [7], or a polymer-stabilized liquid crystal (PDLC) lens with variable focus [8]. While each one of these approaches can be used to vary the power of the lens, only the multiple ring approach can guarantee that the perfect parabolic lens profile is maintained for all powers. Therefore, we will focus on the ring- patterned approach for a more precise control of the phase profile. However, factors of LC lens design and their contributions to the final performance have not been made clear. In this paper, therefore, we start by introducing the LC simulations and lens modeling methods used, and introduce main electro-optic lens design factors, analytically and quantitatively analyze their effects on the lens performance in terms of particular metrics, followed by a demonstration of a high quality LC lens, and measurement approaches are introduced to evaluate the performance. Last, with both calculation and measurement results, a summary of effects of lens design factors will be given. 2. LC Lens evaluation metrics Metrics for evaluating the quality of the LC lens are needed to determine what to calculate with simulations and measure with experiments. Ideally, a collimated light beam parallel to the optical axis with plane wave is focused by a perfectly aspheric positive lens to form the airy disk patterns, containing most of the light intensity in the center lobe at the focal plane. Therefore, by comparing the intensity peak for LC lens to the ideal lens (same power) case (i.e. strehl ratio), its focusing ability can be determined, from which its imaging performance can be predicted as well. Thus, strehl ratio is the first primary metric to evaluate the quality of the LC lens. The second metric used in this paper is Modulation Transfer Function (MTF), which is one of the most important specs for lens evaluation. The MTF curve shows the spatial frequencies of the image, and their corresponding contrast ratio, intrinsically determined by the lens. For example, with low frequencies, images can be well resolved with high contrast, and beyond the cutoff frequency, the images are blurred. Generally speaking, therefore, MTF demonstrates the relationship of lens resolution and image contrast. 3. LC calculations and lens modeling The LC director field calculation takes the electrode pattern, applied voltages, cell thickness, and the liquid crystal properties as input, numerically calculates the 2D director profile throughout the cell. Then, the Optical Path Difference (OPD) or phase profile of the lens can be calculated by integrating the effective refractive index across the cell thickness for each point on the lens surface [3]. With a given lens OPD calculated or measured, lens modeling is used to calculate the light distribution at focal plane based on wave nature of the light. Taking light propagation simulation as the core, the approach focuses on the complex amplitude at different parallel planes in sequence in the light propagation space. Any components with a finite size added in the path like a lens (gradient in phase) or a stop (gradient in amplitude) is considered. According to the Huygen-Fresnel principle and fundamental scalar diffraction theory, the wavefront is consisting of infinite number of point sources, each of which generates a secondary spherical wave. After light passes through a lens, at the exit plane, lens OPD is applied as a phase term in the transmission function of the modeling. Therefore, the light distribution at any plane behind the lens can be calculated by coherently integrating the complex amplitude given by all point sources in the lens aperture area of the exit plane [9]. For the purpose of most accurate results, 29.1 / L. Li SID 2012 DIGEST • 379 ISSN 0097-966X/12/4301-0379-$1.00 © 2012 SID