We present a new technique for determining the refractive index profiles of axially symmetric optical fibers based on imaging phase gradients introduced into a transmitted optical field by a fiber sample. An image of the phase gradients within the field is obtained using a new non-interferometric technique based on bright field microscopy. This provides sufficient information to reconstruct the refractive index profile using the inverse Abel transform. The technique is robust, rapid and possesses high spatial resolution and we demonstrate its application to the reconstruction of the refractive index profiles of a single-mode and a multimode optical fiber.