Methods and apparatus to measure visual appearance of randomly arranged birefringent fibers are disclosed. One method comprises emitting light, creating Ni polarization states of the emitted light, illuminating the birefringent fibers with the emitted light so polarized, thereby generating IRi internal reflection components, ERi external reflection components, and Di diffusion components of the light in the birefringent fibers, observing the light from the illuminated birefringent fibers, creating Oi polarization states of the observed light, forming Xi images of the observed polarized light, each image comprising an information (Ni, Oi, IRi, ERi, Di), wherein i=1, 2, . . . n and n≧4, measuring the intensity Ii in each pixel in the X, images, and separating the i-th internal reflection component, the i-th external reflection component, and the i-th diffusion component from the i-th image for the Xi images.