Methods and apparatus for determining shape parameter(s) using a sensing fiber having a single core with multiple light propagating modes

A system for interrogating an optical sensing fiber comprising a multimode core, the system comprising:

• multiple reference branches and multiple measurement branches, the multiple measurement branches comprising an array of single-core, single-mode optical fibers, each optical fiber of the array of single-core, single-mode optical fibers having a different optical delay;
• a tunable laser configured to generate laser light over a range of wavelengths, the laser light configured to be coupled into the multiple reference branches and the multiple measurement branches for interferometrically probing the multimode core;
• and
• a micro lens array and collimator lens configured to optically couple the laser light from the array of single-core, single-mode optical fibers into the multimode core, and configured to image backward traveling multimode light from the multimode core onto the array of single-core, single-mode optical fibers, wherein light from each mode of the backward traveling multimode light is directed into a corresponding fiber of the single-core, single-mode optical fibers.