An optical shape sensing system employing an elongated device, an optical fiber embedded within the elongated device with the optical fiber, an optical interrogation console and a 3D shape reconstructor. In operation, the optical interrogation console generates reflection spectrum data indicative of a measurement of both an amplitude and a phase of a reflection for each core of the optical fiber as a function of wavelength. The 3D shape reconstructor executes a generation of local strain data for a plurality of positions along the optical fiber responsive to the reflection spectrum data, a generation of local curvature and torsion angle data as a function of each local strain along the fiber, and a reconstruction of the 3D shape of the optical fiber as a function of each local curvature and torsion angle along the optical fiber.