Retardation element, liquid crystal display device, and projection display device

A retardation element, comprising:

• a transparent substrate;
• a retardation imparting antireflection layer formed of an optical multilayer film, and configured to impart a retardation to an oblique incident light ray among incident light rays, and to prevent the incident light rays from being reflected;
• a first birefringent layer that comprises an optically anisotropic inorganic material, wherein an angle formed between a principal axis of refractive index anisotropy of the optically anisotropic inorganic material and a surface of the transparent substrate is not 90°;
• and
• a second birefringent layer that comprises an optically anisotropic inorganic material, wherein an angle formed between a principal axis of refractive index anisotropy of the optically anisotropic inorganic material and the surface of the transparent substrate is not 90°,
• wherein the second birefringent layer contacts the first birefringent layer such that an angle formed between a first line segment representing the principal axis of refractive index anisotropy of the first birefringent layer and a second line segment representing the principal axis of refractive index anisotropy of the second birefringent layer is neither 0° nor 180° when the first line segment and the second line segment are projected on the transparent substrate such that an end A of the first line segment at a side of the transparent substrate and an end B of the second line segment at a side of the transparent substrate coincide with each other, and
• wherein the second birefringent layer has an average thickness approximately equal to an average thickness of the first birefringent layer.