## 1 Introduction  
Liquid crystal displays (LCDs) have played a leading role in the display market by virtue of their long service life, low power consumption, and low price. However, the viewing angles are restricted because of refractive index anisotropy. To improve the viewing angles in LCDs, in-plane switching (IPS) and fringe-field switching (FFS) have been used to control the liquid-crystal (LC) molecular behavior in the plane [1, 2]. Furthermore, multiple domains have been used to symmetrically arrange LC molecules to reduce the difference in phase retardation according to the direction [3, 4].  
Another method that ensures a wide viewing angle involves adding a phase retardation film to the outer part of the LC panel, which can compensate for the difference of phase retardation between the normal direction and oblique directions. A lens array has also been used as a diffuser for LCDs with quasi-collimated backlights (QCBLs) [5, 6]. However, a wide viewing angle may be a drawback for personal devices. Therefore, a technique is required to switch the viewing angles of an LCD in different usage environments. Several types of the LCDs for controllable viewing angles have been reported: Dividing the pixels according to the viewing angles [7, 8, 9], additional viewing angle control systems [10, 11], switchable viewing angle backlight systems [12, 13]. However, these methods reduce the resolution and brightness compared to the conventional LCDs, or use unique liquid crystals such as the blue phase and discotic phase, thereby causing problems in temperature reliability and fabrication process. Some of the methods with the viewing angle control system increase the weight and volume of the display due to the additional complex systems. As another method for adjusting the viewing angle, a technique of controlling the focal length or diffusing the light by electrically controlling the wavefront using the LC-polymer composite has been proposed [14; 15; 16]. However, the LC-polymer composite has a vulnerability to the light, low thermal stability, and electro-optical hysteresis due to the characteristics of a polymer compared to the nematic liquid crystal. In particular, the hysteresis of the LC-polymer composite, caused by the differences in LC molecular behavior with an applied voltage, results in image distortion or change in transmittance [17].  
In this paper, a new method is proposed to electrically control the viewing angle of LCDs in various usage environments by using an electric-field-driven liquid crystal (ELC) lens [18] as a diffuser in front of the LCD. The ELC diffuser disperses or transmits light depending on whether a voltage is applied, so light distribution can be realized with a wide or narrow viewing angle. The retardation distribution affects the optical characteristics of the ELC diffuser and is obtained by numerically calculating the behavior of the liquid crystal through de [PERSON] order tensor theory and Ericksen-Leslie equation [19]. [PERSON]'s design of experiments method was used to optimize the design factors of the ELC diffuser [20]. Finally, an LCD system was equipped with the ELC diffuser, and the light distribution was calculated by ray tracing, and the viewing angles could be switched by the voltages applied to the diffuser.