Recently transflective liquid crystal displays (LCD) received a lot of attention. A transflective display has a transmissive mode and a reflective mode. It combines the high contrast, high brightness of the transmissive mode with energy-saving of reflective mode and has good performance in various illumination conditions. However, state-of-the-art transflective displays have problems such as different electro-optical properties, difficulty in compatibility and optimization of both modes, low efficiency of light utilization, and complexity in structure.; This dissertation focuses on finding new designs of transflective displays that address those problems. One way to do this is to study film compensation of LCD. We first studied film compensation of bistable twisted nematic (BTN) LCD. Starting form the reduced (3x3) Mueller matrices, we derived and simplified the conditions that film compensated BTN can be optimized. Based on these relations, electro-optical properties of some particular configurations, and designs of transflective BTN with high brightness and contrast were given.; To confirm and get a better understanding of the results, we use the Poincare sphere to analyze film compensated BTN. The key to this approach is the existence of "fixed points". Compared with the matrix approach, this approach is more simple, elegant, and efficient.; We then generalized the Poincare sphere approach to a universal approach of LCD. We applied the universal approach to film compensation of ECB and IPS, and the design of achromatic birefringent filters.; We also give two more new designs of transflective displays. In the first design, a dichroic mirror is used to split the visible spectrum into two parts used in transmissive and reflective modes, respectively. Both modes can be optimized. It has a simple structure and good light utilization. A design for a full-color transflective display with good performance is also given.; In the second design, each pixel is divided into two sub-pixels, a transmissive one and a reflective one. By using polymer stabilization, the birefringence of the transmissive sub-pixels is twice that of the reflective ones. The display has single cell gap, low driving voltage, fast response, high contrast and brightness, and the transmissive and reflective modes are synchronized.
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