Given an arbitrarily cut uniaxial crystal wedge, a procedure is described using reflection perpendicular-incidence ellipsometry (PIE) for (1) locating the optic axis, and (2) determining the ordinary (No) and extraordinary (Ne) complex refractive indices. The optic axis is located by finding the principal directions of the two wedge faces and subsequently solving three spherical triangles. No and Ne are determined by two complex ratios of principal reflection coefficients (of light normally incident on and linearly polarized along the principal directions of each face) as measured by PIE. The solution for No and Ne is explicit but requires finding the roots of a sixth-degree algebraic equation in No.
R. M. A. Azzam, "Determination of the optic axis and optical properties of absorbing uniaxial crystals by reflection perpendicularincidence ellipsometry on wedge samples," Appl. Opt. 19, 3092-3095 (1980) http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-19-18-3092