strain responses, each 120o out of phase with the others. By comparing the amplitude and phase of these three
strain curves, one can determine the applied bend radius and its direction relative to the fiber’s coordinate
system.
Under twist, all of the three outer cores experience a common-mode strain. If the fiber is twisted in the
direction of the helix, a tensile strain is applied to the triad of outer cores. A twist in the opposite direction
places the outer cores in compression. By observing the magnitude of the common-mode strain signal, one can
determine the distributed state of twist along the length of the sensing fiber. Strain measurements in the
center core are used as a reference to compensate for tensile strain and temperature changes in the shape
sensing fiber. This twist measurement is then used to convert the 3D curvature measurement from the fiber’s
local coordinate system to a fixed “master” 3D grid, defined by the position and vector direction of the fixed
launch point at the start of the shape sensing fiber.