多维温度场对光纤环Shupe效应误差影响的理论分析

Shupe effect of fiber sensing coils in multidimensional thermal field

光纤环作为干涉型光纤陀螺的核心敏感元件,易受时变温度环境引起的Shupe非互易性相移的影响,进而严重降低对于惯性空间转动的测量精度.本文推导了目前广泛应用的四极绕法光纤环的温度效应误差模型,分析了沿光纤环径向、轴向与圆周方向多维温度场对于零偏漂移的影响机理并进行了仿真验证.研究结果表明,径向与轴向的瞬态温场引起的零偏误差正比于光纤环各层外内壁温变速率之差的加权和,并且随着接近光纤进出的顶层,其所占份额将线性增大.圆周方向的零偏误差则取决于光纤进出端与长度中点连线两侧温变速率空间分布的对称性,并且当不均匀的温度场分布远离进出端时,其影响将减小.以上发现可为复杂温度环境下工作的陀螺仪表与惯性导航系统的热结构设计提供理论指导与工程参考.

Optical fibers have a wide range of applications and constitute the core of fiber-optic gyroscope which is revolutionizing the ancient inertial rotation detection. However, fiber coils in these instruments are susceptible to surrounding physical quantities, which can seriously deteriorate their accuracy. And the thermally induced parasitic effect is one of the most critical factors leading to the bias drift. This drift error is due to the nonreciprocity phase shift in the counterpropagating optical loops when a thermal gradient passes through the fiber coil as described by Shupe. The quadrupole winding patterns along with other coiling schemes have been proposed to reduce the Shupe effect by maintaining fiber parts at equal distances from the coil center beside each other. Many researchers have investigated the thermal effect on this drift on the assumption that the temperature transient propagates only radially along the fiber coil, while little attention has been paid to the case of the multidimensional thermal field. This can hardly satisfy completeness of the theory, and be applied to certain complicated working conditions. In this paper, we develop theoretical models that describe drift signals caused by radially, axially and circumferentially transmitted thermal effects on the quadrupole winding fiber coil. The obtained findings indicate that the bias error excited by the thermal flow in radial and axial directions is proportional to the weighted sum of the difference in temperature changing rate between outer and inner sides of the fiber ring. And the share of the sum linearly grows when approaching to the top surface near the input and output end（I/O end） of the fiber. Thus, it is suggested that it should be avoided to place heat sources in the neighboring area. For the circumferentially distributed temperature field, the drift depends on the symmetry of the thermal gradients on both sides of the centerline connecting the fiber midpoint and the I/O end. This circumferential thermal effect can be dominant, since it tends to cover a larger spatial scale than its counterparts in radial and axial directions. And besides making a good symmetrical design of the temperature distribution with respect to the centerline, it can be suppressed by arranging the nonuniformity of the thermal field in the opposite direction of the fiber coil to the I/O end, which is also beneficial to reducing its sensitivity to the angular change. Our results can help better understand the mechanisms for the thermal error formation and guide us in optimizing and facilitating the thermo-structure design of both fiber gyroscopes and navigation systems.