A tunable liquid crystal lenticular lens array is proposed to compose an auto-stereoscopic 3D display. The focusing can be achieved based on non-uniform phase retardation across the width of the LC lenticular lens, mimicking the effects of gradient index (GRIN) lens. The viewing distance and zones of this display can be adjusted in an on-line fashion to track the viewer position relative to the display. The proposed scheme can present the lenticular lens and the LC GRIN lens simultaneously, so that the simulation results can express the low value of crosstalk of 9% by the lenticular lens array and the LC GRIN lens array. IntroductionThe three-dimensional (3D) displays draw a great deal of interests recently for the next generation displays. In addition, the mobile phones equipped with a 3D display have initiated a niche market. Following the 3D phone of Sharp, several cell phone makers have developed 2-view 3D mobile phones and started manufacturing, in order to elevate the initial 3D market. Using lenticular lens array, the light emitting from each pixel can be seen only from the viewing zone for the corresponding perspective view [1-3]. Since the profiles of the lenticular lens array are fixed after the manufacturing, the viewing distance and corresponding view zones are then fixed. In this way, viewers have to adjust their viewing position relative to the display, in order to experience 3D images. In this study, a tunable liquid crystal (LC) [4] lenticular lens array is designed to replace the conventional lenticular lens array to display 3D images. By designing two special rectangular electrodes for the LC lenticular lens, the focusing can be achieved based on non-uniform phase retardation across the width of the LC lenticular lens, mimicking the effects of gradient index (GRIN) lens. Furthermore, by applying distinct driving voltages to the two electrodes of the LC lens, the viewing distance and zones can be adjusted in an on-line fashion to track the viewer position relative to the display. Note that the present study is different from existing studies of the 3D displays using liquid crystal lens[5-6], where the dispersion property of the liquid crystals are utilized to switch between 2D and 3D modes. Conventional Lenticular Lens ArrayThe 3D display performance delivered by the conventional lenticular lens array is first analyzed in this section as the baseline design, which is followed by the analysis on the tunable LC GRIN lenticular lens array.It is known that the function of the lenticular lens is to direct the diffuse light from a pixel such that it can be seen in a limited angle in front of the display. Then the different pixels can be directed to either the left or right viewing windows. In other words, right eye can receive the right views by the mechanism, and vice versa. For this reason, each lenticular lens should cover one pair pixels which display images corresponding to different viewing angle for separated left and right eyes in two-view auto-stereoscopic display [7] as shown in Fig. 1. As th...