A systematic and straightforward image processing method to extract quantitative phase and refractive index data from weak phase objects is presented, obtained using differential interference contrast (DIC) microscopy. The method is demonstrated on DIC images of optical fibers where a directional integration routine is applied to the DIC images to extract phase and refractive index information using the data obtained across the whole DIC image. By applying the inverse Abel transform to the resultant phase images, an accurate refractive index profile is obtained. The method presented here is compared to the refracted near-field technique, typically used to obtain the refractive index profile of optical fibers, and shows excellent agreement. It is concluded that through careful image processing procedures, DIC microscopy can be successfully implemented to obtain quantitative phase and refractive index information of optical fibers.