An approximate analytical expression is calculated for the transmission of thin twisted nematic layers situated between a polarizer/analyzer pair. The approximation assumes that the twist angle of the nematic liquid crystal is smaller than the maximum retardation of the cell. The direction of the incident light is assumed to be parallel to the normal of the electrode. This configuration is analyzed for a general arrangement of polarizer and analyzer; the general result is evaluated for the case of the polarizer parallel and analyzer perpendicular to the liquid-crystal optical axis on the input and output electrodes, respectively. The results show that in the case of a thin twisted nematic layer the transmission depends on the thickness of the layer, on the birefringence of the liquid crystal, and on the wavelength of the light. This is a departure from the well-known independence of the transmission on these parameters for a thick twisted nematic layer. The analysis also shows that the transmission through thin layers can be minimized by tuning the layer thickness to particular values that depend on wavelength and on liquid-crystal birefringence. In this way, high image contrast can be obtained even for thin liquid-crystal layers.
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