# Displays Based on Dynamic Phase-Only Holography
## 3 Spatial Light Modulators (SLMs)  
The SLM is responsible for the shape of the wave front in the display system which, by free-space propagation, determines the resultant display. In order to achieve a fully complex wave front, which varies in amplitude and phase at each point on the wave front, it is currently necessary to cascade or superimpose two SLMs using beam splitters or a grating or combine two areas from a single SLM. The value of complex coding would be minimal computation and near perfect reconstruction. The sub-systems required for complex coding are currently being researched in a number of laboratories [2,10]. It has been possible to achieve initial holographic display systems at the full resolution of the SLM by using limited modulation devices in particular phase-only electrically addressed devices [11] and amplitude-only optically addressed [9] devices. The former are principally Liquid Crystal on Silicon (LCOS) SLMs and the latter are Liquid Crystal Light Valves (LCLVs) [12]. Due to the technical maturity of the LCOS SLMs, they are the focus of the present paper. LCOS devices are composed of a liquid crystal layer above a semiconductor backplane. The front substrate is a cover glass coated with a transparent conductor to act as a common electrical conductor. The lower substrate is a CMOS backplane with an additional outer aluminum layer that is used to create a pixelated mirror surface. These mirrors also act as the pixel electrodes. The LCOS devices have the advantage that the signal lines, the gate lines, and the transistors are below the mirrored surface, which results in a high fill factor (typically greater than 90%). Relatively conservative 0.18 and 0.35 micron processes with 5 V drive capability and high yield are used by the LCOS fabrication houses. Additionally, the small feature sizes enabled by CMOS processing allow for very small pixel sizes. The maximum diffraction angle of the spatial light modulator is inversely proportional to the pixel pitch. The perfect phase modulating spatial light modulator (PSLM) would ideally have characteristics similar to a holographic film including a continuous modulation surface (i.e., no pixels) and analogue phase modulation that is capable of greater than 2\(\pi\) phase delay in a large number of steps. Phase-only holograms have been created using liquid crystal TV screens [13]. They have been developed over the last decade so that there is now a reasonably sized supply [11]. All current multilevel phase-only modulating devices use 'Electrically Controlled Birefringence' (ECB), which is shown in Figure 4.  
ECB was the first electro-optic effect to be observed in liquid crystals [14]. It is the birefringence reduction in a planar aligned nematic liquid crystal (NLC) layer upon application of an electric field. The birefringence reduction allows the phase modulation of the reflected beam to be reduced by 2\(\pi\) when the polarization of the incident light is parallel to the alignment direction. The birefringence reduction is due to a tilted director where the angle of tilt is determined by two competing torques including the elastic torque within the material that tries to align the director parallel to the alignment direction and a field-induced torque that tends to align the director parallel to the field. When both torques exist, there is a competition between them and the director aligns to minimize the total energy. Figure 3: Fourier hologram with a physical lens and software lens. At the edge of the pixel, the electric field has a component parallel to the cell substrate surfaces, which is known as the lateral field, the non-uniform field [15], or the inhomogeneous field [16]. It is now more commonly referred to as a fringing field. In addition, there is a reverse tilt declination over the driven pixel due to the conflict between the pre-tilt and the director rotation because of the vertical electric field. There are two methods for matrix addressing the CMOS pixel array.