An optical shape sensing system employing an elongated device (20), an optical fiber (10) embedded within the elongated device (20) with the optical fiber (10) including one or more cores, an optical interrogation console (30) and a 3D shape reconstructor (40). In operation, the optical interrogation console (30) 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 (10) as a function of wavelength and the 3D shape reconstructor (40) reconstructs a 3D shape of the optical fiber (10). The 3D shape reconstructor (40) executes a generation of local strain data for a plurality of positions along the optical fiber (10) 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 (10) as a function of each local curvature and torsion angle along the optical fiber (10).
