Patent ID: 7813599

Claim:
A method of determining the shape of a fiber optic cable having an optical fiber and a protective sleeve, wherein the optical fiber is fully circumscribed by the protective sleeve and is unbound along the entirety of an interface with the protective sleeve to thereby allow the optical fiber to freely twist and untwist within the protective sleeve only in accordance with its own elasticity, the method comprising: securing the fiber optic cable to a stationary member at a first end of the fiber optic cable to provide a calibrated end position, wherein said securing prevents the cable from bending or twisting at the first end; collecting strain data at a plurality of different positions along a length of the optical fiber and forming a data set thereof; calculating a set of curvature data and a set of bending direction data of the optical fiber using said set of strain data; deriving an explicitly-defined curvature function for said set of curvature data and an explicitly-defined bending direction function for said set of bending direction data by applying a curve-fitting operation to a respective one of said set of curvature data and said bending direction data; deriving an explicitly-defined torsion function resultant of the natural elasticity of the optical fiber using said bending direction function; determining an initial condition of a normal vector of the first end of the fiber optic cable as a function of the calibrated location of said first end; and determining the shape and a position of a second end of the fiber optic cable using each of said initial condition of said normal vector, said bending direction function, said curvature function, and said torsion function.