Methods and apparatus to determine the orientation 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 of the light in the birefringent fibers, observing the light from the illuminated birefringent fibers, creating Oi polarization states of the observed light, forming Ii images of the observed polarized light, each image comprising an information (Ni, Oi, IRi), wherein i=1, 2, . . . , n and n≧3, separating the i-th internal reflection component from the i-th image, and calculating an angle of a neutral axis of the birefringent fibers using the IRi internal reflection components.