A antiglare layer 12 having a fine uneven surface is formed directly or through other layer(s) on a transparent substrate film 11, and a layer 13 having a low refractive index, which is lower than the refractive index of the antiglare layer 12, is formed thereon. The refractive index of the antiglare layer 12 is higher than the refractive index of a layer in contact with said antiglare layer 12 on its surface remote from the layer 13 having a low refractive index. An SiOx film may be used as the layer 13 having a low refractive index. The SiOx film per se has excellent gas barrier property and antifouling property as an optical functional membrane and is an optical functional material characterized by having excellent moistureproofness, scratch resistance, adhesion to a substrate, transparency, low refractive index, dye deterioration preventive property, and other properties.