Method for determining the optical axis and (n(e), n(o)) of a birefringent crystal

There is a phase difference between s and p polarizations when a circularly polarized heterodyne light beam is reflected from a birefringent crystal. It can be measured accurately with a common-path heterodyne interferometric technique. We have derived an equation that describes the relationship between the phase differences and n(e), n(o), and alpha. Two groups of solutions for (n(e), n(o)) can be obtained from this equation by the phase measurements performed at three incident angles under moderate conditions. Each group consists of three pairs of solutions for (ne), n(o)). Finally, by justifying with physical conditions, we obtained the correct solution for (n(e), n(o)). Azimuth angle alpha of the birefringent crystal optical axis can also be determined. And the feasibility of this method is demonstrated.