Calculating distributed twist of a multi-fiber 3D shape sensor bundle (MFB) using optical frequency domain reflectometry (OFDR) phase interrogation data

A method for calculating MFB twist distribution data along a multi-fiber shape sensor bundle (MFB) using optical frequency domain reflectometry (OFDR) phase interrogation data, the method comprising:

• acquiring OFDR interferometric interrogation data from an MFB having at least three single core radially offset fibers helically wrapped about and rigidly adhered to a central single core fiber, wherein the at least three single core fibers and the central single core fiber include fiber Bragg gratings (FBGs);
• extracting current phase signal data from the OFDR interferometric interrogation data for each of the at least three radially offset fibers and the central fiber;
• calculating a change in phase between the current phase signal data and previously acquired reference phase signal data from the OFDR interferometric interrogation data for each of the at least three radially offset fibers and the central fiber;
• unwrapping the change in phase for each of the at least three radially offset fibers and the central fiber;
• accounting for FBG gap-induced unwrapping discontinuities in the change in phase for each of the at least three radially offset fibers and the central fiber to create FBG gap-mitigated phase differences for each of the at least three radially offset fibers and the central fiber;
• averaging the radially offset gap-mitigated phase differences of each of the at least three radially offset fibers and subtracting the center fiber gap-mitigated phase difference from the average to yield a twist-phase difference that is indicative of a distributed twist of the multi-fiber bundle;
• removing bending-induced changes from the twist-phase difference to create bend-compensated twist-phase difference distribution;
• and
• converting the bend-compensated twist-phase difference distribution from units of the OFDR interferometric interrogation data to units of twist to calculate MFB twist distribution data along the MFB.