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In this paper, we studied the optics of transmissive bistable nematic liquid crystal displays by using the Poincare sphere approach. We derived analytical solutions of the polarization state of the outcoming light for the two bistable states. We have found the optimum modes of film compensated bistable twisted nematic liquid crystal displays. Our results show that the number of optimized modes at a fixed wavelength of film-compensated bistable twisted nematic (BTN) is infinite. We identified the optimized modes for displays operated in the whole visible light wavelength region. We calculated the transmission spectra of the two bistable states of the optimized modes.