Co-located angularly offset fiber Bragg grating pair for temperature-compensated unambiguous 3D shape sensing.

A 10 mm-long three-dimensional shape sensor in a single-mode fiber is described and demonstrated experimentally. The sensor is based on a pair of fiber Bragg gratings inscribed at the same location along the fiber axis but offset along different radial directions away from the fiber center. Each offset grating generates cladding mode resonances over a ${\sim}{20}\;{\rm{nm}}$-wide spectral bandwidth, and the two gratings are also offset in period so that their transmission spectra are separated by 40 nm, and thus non-overlapping and fully distinguishable. Directional bending sensitivity results from the differential amplitude response of the cladding mode resonances from the two gratings, depending on the relative orientation of the bend with the azimuthal direction of the grating offsets. It is further demonstrated that both axial deformation and temperature have no influence on the shape measurement as they both only cause a global wavelength shift of the spectra without amplitude change. The experimental results demonstrate that the shape orientation of an object can be unambiguously determined for bend directions covering the full 360° range around the fiber axis with sensitivities of the order of ${{1}}\;{\rm{dB/}}{{\rm{m}}^{- 1}}$ and small curvatures between 0 and ${{1}}\;{{\rm{m}}^{- 1}}$.