We analyze the electro-optic polarization transmission characteristics of liquid crystal cells in the Poincare sphere representation. We determine fundamental conditions on maximizing of brightness and contrast ratio of liquid crystal display devices for polychromatic light by use of retardation films. For optimizing two colors, at least two properly designed retardation films are needed, and for three wavelengths, either it can be approximated to the two-color case or three retardation films are needed.