Etendue index of light in uniaxial crystals

An etendue index is introduced to calculate the etendue of a ray in an anisotropic medium based on Hamiltonian optics. As an example, the etendue index of an extraordinary ray in a uniaxial crystal is given. In addition, the general formula for the etendue index of a ray refracted from a vacuum into an extraordinary ray in a uniaxial crystal is given as a function of the angle of incidence and the orientation of the optic axis. As an application of the etendue index, the solid angle magnification of the refracted extraordinary ray in LiNbO 3 crystal is discussed.