Moisture-Induced Mechanical Strain in Gyroscope Optical Fiber Coil

Abstract

Moisture in the sensing coil of fiber-optic gyroscope (FOG) gives rise to bias drift. To explain and predict this phenomenon, one needs to quantify the strain along the fiber induced by moisture. In this paper, a full theoretical approach to determine the strain field into the sensing coil induced by a moisture loading is proposed. The approach consists in solving an analytical Fickian diffusion model in a semi-infinite medium, to implement a semi-analytical mechanical model of the moisture diffusion effect. The computed strain along the fiber is then compared with the distributed strain along the fiber measured using Rayleigh optical frequency domain reflectometry (Rayleigh-OFDR). Agreement between predicted and measured data demonstrate the validity of the proposed approach. Finally, a step function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$60\%RH$</tex-math></inline-formula> (relative humidity) is shown to be equivalent to a thermal loading of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1 \ ^{\circ }C/min$</tex-math></inline-formula> on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta T = 15 \ ^{\circ }C$</tex-math></inline-formula> and these loadings may induce an estimated bias of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.1 \ ^{\circ }/h$</tex-math></inline-formula> .