Abstract: A quadrupole winding for an optic sensing coil has fiber optic layers that are wound in pairs, with each layer pair beginning with fiber elements at equal distances from the coil center. Coils having a quadrupole winding pattern are less prone to errors caused by time-dependent physical changes in a section of the fiber. The coil is wound in a precision pattern, each turn lying in contact with the preceding and succeeding turn. Subsequent layers are wound with each turn lying in the groove formed by two underlying turns, with the overall winding pattern taking a hexagonally close packed configuration. Fabrication is facilitated by following every fourth-numbered layer, beginning with layer one with a two-turn pattern for passing between the subsequent two layers and a first adjacent flange, and by following every fourth-numbered layer, beginning at layer three with a two-turn pattern for passing between the subsequent two layers and a second adjacent flange.