Method and system for absolute three-dimensional measurements using a twist-insensitive shape sensor

An apparatus comprising:

• a reference fixture including a joint with at least one degree of freedom, the reference fixture adapted to be fixed in a world reference frame, wherein the reference fixture includes a hollow rod extending through the joint;
• a flexible and torsionally stiff tether having a proximal end, a distal end, and defining a first lumen extending therethrough, wherein the proximal end of the tether is coupled to the hollow rod so that the tether and the hollow rod rotate together, and wherein the distal end of the tether is coupled to a surgical instrument and limits movement of the surgical instrument relative to the reference fixture;
• the surgical instrument having a component that defines a second lumen, wherein the second lumen is not coaxially aligned with the first lumen;
• and
• a shape-sensing optic fiber continuously extending through the hollow rod, through the first lumen of the tether, and through a portion of the second lumen defined by the component of the surgical instrument, wherein the shape-sensing optic fiber comprises an optic fiber core surrounded by a cladding layer, the tether rotatable with the hollow rod relative to the shape-sensing optic fiber.