Abstract-Illumination optics in emerging naked-eye 3D display, especially in time-spatial multiplexing, or directional backlight naked-eye 3D display system, is systematically examined. Key issues in directional backlight system include: 1) Directional transmission of the left-and right-eye images to the corresponding viewing zone with small crosstalk; 2) The luminance on the screen should be homogeneous even for the viewers moving around. In this paper, we propose an adaptive optimization solution based on root mean square (RMS) for the design of illumination optics of the naked-eye 3D system. Based on the designed free-form backlight illumination, the overall design schemes for both single-user and multi-user naked-eye 3D display are proposed and demonstrated. By utilizing the novel dynamic synchronized backlight technique, the temporal crosstalk is effectively brought into control. The display defects such as the dark bands appearing at the joints of the lens array or at the middle of the Fresnel lens are simulated numerically and tested experimentally, hence providing effective design guidelines for the optical components as well as their fabrication error tolerance. Additionally, we propose a continuous backlight technique to improve the luminance homogeneity. Furthermore, a quantitative evaluation mechanism for the moiré pattern based on the Fourier analysis method, by introducing the contrast sensitivity function (CSF), is presented. A novel arrangement of a quasirandom RGB sub-pixel array is proposed to reduce the visibility of moiré pattern. As a result, full HD glassless 3D display suitable for glassless virtual and augmented realities is demonstrated with an unprecedented display quality.