Focus cues play a significant role in three-dimensional (3-D) depth perception. Conventional stereoscopic displays, however, lack the ability to correctly render these cues, because they present a pair of stereoscopic images on a fixed image plane while forcing the eyes to converge at different distances to view objects at different depths. Using a fast liquid-lens device, we present the design and implementation of a timemultiplexed dual-focal plane display that is capable of rendering correct or near-correct focus cues as well as other depth cues, such as occlusion and shading for a 3-D scene. The focus range of the dual focal planes can vary from infinity to as close as 8 diopters. Two driving mechanisms are proposed to render near-correct focus cues and their effects on image sharpness, flicker, and brightness are compared. © 2009 Optical Society of America OCIS codes: 120.2040, 120.2820, 120.4570, 220.1080, 330.1400 Focus cues (accommodation and retinal blur) of a 3-D scene play a significant role in 3-D depth perception [1] . Conventional stereoscopic displays, however, lack the ability to correctly render these cues, as they present a pair of stereoscopic images on a fixed image plane while forcing the eyes to converge at different distances to perceive depth. These displays thus force an unnatural decoupling of the accommodation and convergence cues and induce incorrect retinal blurs that do not vary with the rendered depth of a virtual scene. Many researchers have carried out studies to investigate the adverse effects of such unnatural viewing conditions [1] [2] [3] [4] . Their results suggest that unfaithful focus cues are associated with a variety of visual artifacts, such as the underestimation of the rendered depth of a 3-D scene and visual fatigue after a prolonged exposure to stereoscopic environments. There have been emerging research interests in developing 3-D displays with correct or near-correct focus cues. Classified as one of the true 3-D displays, a volumetric display can render correct focus cues by portraying millions of voxels within a physical volume [5, 6] . The practical development of such technology, however, faces many technical challenges, such as low computational efficiency, limited rendering volume, and difficulty of correctly rendering viewdependent lighting effects such as occlusion, specular reflection, and shading. Multifocal plane displays render near-correct focus cues for virtual objects in different depths by presenting perspective images on multiple discrete focal planes. Each of the focal planes is responsible for rendering 3-D objects with a depth range centered around it, and these discrete focal planes together render a volume of 3-D objects with near-correct focus cues specific to a given viewpoint. Rolland et al. presented a theoretical framework of a spatially multiplexed multifocal plane head-mounted display (HMD) by using a stack of 14 planar displays as the image source [7] , and Akeley et al. recently demonstrated a three-focal plane display prototype by optically splitting a large liquidcrystal display panel into three zones located at different depths [8] . An alternative to the spatially multiplexed scheme is the time-multiplexed approach by the usage of active optical elements, in which 3-D objects of different depths are rendered sequentially on a single 2-D focal plane whose focal distance is adjusted in synchronization with the depth of the objects being rendered. If a high enough rate can be achieved, all objects would appear to have near-correct focus cues without visible flicker. Schowengerdt and Seibel [9] demonstrated a dual-focal plane retinal scanning display using a deformable membrane mirror (DMM) device. In this design, a 2-D image is generated on a pixel-by-pixel basis by raster scanning a laser beam across the visual field, and the focus cues of each pixel are rendered by defocusing the laser beam through the DMM. Our approach to a time-multiplexed multi-focalplane display is achieved by modulating the focal distance of a 2-D display time-sequentially with a liquid lens [10] . It requires no moving parts for rendering focus cues and uses conventional microdisplay and graphics hardware. Mainly owing to the low speed of the liquid-lens device, the preliminary results in a dual-focal plane prototype failed to demonstrate faithful focus cues at a frame rate higher than 5 Hz [10] . We have now adopted a faster liquid lens (Arctic 314, Varioptic, Inc.), with a response speed of about 9 ms, to increase the frame rate of a dual-focal plane display to up to 37.5 Hz. We have also explored an alternative rendering mechanism that reduces artifacts and improves depth cue accuracy. Moreover, in order to compensate the reduced clear aperture from 3 mm (Arctic 320) to 2.5 mm (Arctic 314), we have made modifications to the original design [10] . As shown in Fig. 1(a) , the liquid lens is offset from the center of the radius curvature O of the spherical mirror by ⌬; thus the exit pupil of the HMD is magnified by m p = R / ͑R +2⌬͒ to the size of the clear aperture of the liquid lens. The focal distance is specified by the
REF have shown a liquid lens based solution to change the plane of focus inside a head mounted display (HMD).
Time-multiplexed dual-focal plane head-mounted display with a liquid lens
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