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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 counter-propagating 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.
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Keywords:
- multidimentional thermal field /
- Shupe effect /
- fiber coil /
- quadrupole winding
[1] Vali V, Shorthill R W 1976 Appl. Opt. 15 1099
[2] Paturel Y, Honthaas J, Lefevre H, Napolitano F 2014 Gyroscopy and Navigation 5 1
[3] Webber M, Willig R, Raczkowski H, Dineen A 2012 J. Lightwave Technol. 30 2356
[4] Wen F, Wu B J, Li Z, Li S B 2013 Acta Phys. Sin. 62 130701(in Chinese) [文峰, 武保剑, 李智, 李述标 2013 62 130701]
[5] Jin J, Li Y, Zhang Z C, Wu C X, Song N F 2016 Chin. Phys.. 25 084213
[6] L X Q, Huang X Y, Gao F, Wang X F 2015 J. Chin. Inertial Technol. 23 399(in Chinese) [闾晓琴, 黄鑫岩, 高峰, 王学锋 2015 中国惯性技术学报 23 399]
[7] Shupe D M 1980 Appl. Opt. 19 654
[8] Frigo N J 1983 Proc. SPIE 412 268
[9] Dyott R B 1996 Electron. Lett. 32 2177
[10] Williams M R 2008 US Patent 2008/0130010
[11] Tirat O F J, Euverte J M 1996 Proc. SPIE 2837 230
[12] Zhang C X, Du S S, Jin J, Zhang Z G 2011 Optik 122 20
[13] Zhang Y G, Gao Z X, Wang G C, Gao W 2014 IEEE Photo.Tech. Lett. 26 18
[14] Ling W W, Li X Y, Xu Z L, Zhang Z Y, Wei Y H 2015 Opt. Commun. 356 290
[15] Mohr F 1996 J. Lightwave Technol. 14 27
[16] Li Z H, Meng Z, Liu T G, Yao X S 2013 Opt. Express 21 2521
[17] Sawyer J, Ruffin P B, Sung C C 1997 Opt. Eng. 36 29
[18] Lefevre H C 2014 The Fiber-Optic Gyroscope (2nd Ed.) (Boston, London: Artech House) pp98-99
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[1] Vali V, Shorthill R W 1976 Appl. Opt. 15 1099
[2] Paturel Y, Honthaas J, Lefevre H, Napolitano F 2014 Gyroscopy and Navigation 5 1
[3] Webber M, Willig R, Raczkowski H, Dineen A 2012 J. Lightwave Technol. 30 2356
[4] Wen F, Wu B J, Li Z, Li S B 2013 Acta Phys. Sin. 62 130701(in Chinese) [文峰, 武保剑, 李智, 李述标 2013 62 130701]
[5] Jin J, Li Y, Zhang Z C, Wu C X, Song N F 2016 Chin. Phys.. 25 084213
[6] L X Q, Huang X Y, Gao F, Wang X F 2015 J. Chin. Inertial Technol. 23 399(in Chinese) [闾晓琴, 黄鑫岩, 高峰, 王学锋 2015 中国惯性技术学报 23 399]
[7] Shupe D M 1980 Appl. Opt. 19 654
[8] Frigo N J 1983 Proc. SPIE 412 268
[9] Dyott R B 1996 Electron. Lett. 32 2177
[10] Williams M R 2008 US Patent 2008/0130010
[11] Tirat O F J, Euverte J M 1996 Proc. SPIE 2837 230
[12] Zhang C X, Du S S, Jin J, Zhang Z G 2011 Optik 122 20
[13] Zhang Y G, Gao Z X, Wang G C, Gao W 2014 IEEE Photo.Tech. Lett. 26 18
[14] Ling W W, Li X Y, Xu Z L, Zhang Z Y, Wei Y H 2015 Opt. Commun. 356 290
[15] Mohr F 1996 J. Lightwave Technol. 14 27
[16] Li Z H, Meng Z, Liu T G, Yao X S 2013 Opt. Express 21 2521
[17] Sawyer J, Ruffin P B, Sung C C 1997 Opt. Eng. 36 29
[18] Lefevre H C 2014 The Fiber-Optic Gyroscope (2nd Ed.) (Boston, London: Artech House) pp98-99
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