Quantitative phase microscopy with polarized light has been used to determine the change in refractive index introduced into an optical fiber when the fiber is bent through a constant radius of curvature. By obtaining phase images for two orthogonal directions of the polarization of the incident light, one can infer the induced axial strain profile within the fiber. Radii of curvature from 1 to 8 cm were considered, and in each case excellent agreement, within λ/100, was obtained between experimental results and theory.