Abstract: An incident coordinate system was set up on the basis of the incident direction and normal direction on crystal surface. Using the inverse surface equation of wave normals and the boundary condition about the continuity of electromagnetic field tangential component at the surface of crystal, expressions about wave normal direction, ray direction, wave normal refractive index and ray refractive index were obtained. Based on the ray direction and refractive index of extraordinary light, an expression of optical path difference between ordinary and extraordinary lights was derived, when a ray of light with arbitrary incident direction passed through uniaxial crystal with arbitrary crystal axis direction. The transmissivity and field of view of a Lyot filter were analyzed. The tuning of Lyot f