Tight focusing of radially and azimuthally polarized vortex beams through a uniaxial birefringent crystal. 
Under the approximation of small birefringence, the properties of radially and azimuthally polarized vortex beams tightly focused through a uniaxial birefringent crystal are investigated.  The contour plots of intensity distribution near the focus and in the real focal plane are illustrated by performing numerical calculations.  The dependence of the focal shift on numerical aperture and birefringence are analyzed.  Moreover, the Strehl ratio in the real focal plane as a function of birefringence is also analyzed.  It is revealed that the variation of birefringence has no influence on the focal shift and the Strehl ratio of azimuthally polarized vortex beams.