Objective In response to the need for high-precision and engineering applications of resonant fiber optical gyroscopes (RFOGs), research is conducted on the relevant factors that affect polarization noises and thus the output error of gyroscopes in varying temperature environments. Polarization noise is one of the main optical noises that cause output errors in RFOGs. Since the core sensitive component of RFOGs, namely the fiber ring resonator (FRR), is mostly wound by polarization maintaining optical fiber, when the birefringence index of polarization maintaining optical fibers changes with temperature, it will cause the superposition and interference effects of the resonant light waves corresponding to the two intrinsic polarization states of the resonator, resulting in asymmetry in the resonance curve, polarization noises, and detection errors at the resonance frequency point and thereby causing gyro output errors. Therefore, suppressing polarization noise in varying temperature environments has profound significance. The measures taken by researchers to suppress polarization noise can be divided into two categories: stabilizing the phase difference between primary and secondary polarization and reducing the intensity of secondary polarization states. Researchers have successively adopted a single 90 degrees fusion joint scheme within the FRR, a twin 90 degrees fusion polarization maintaining transmission FRR scheme, and a secondary polarization axis rotation fusion polarization starting resonant cavity to stabilize the primary and secondary polarization phase difference. Researchers have reduced the intensity of secondary polarization states by inserting polarization controllers, online polarizers, etc. into the FRR or utilized a new fiber optic scheme to reduce the impact of polarization noises on the gyroscope. The above studies have achieved good results in noise suppression, but most studies have been conducted at room temperature or small-range temperature variations. When facing engineering applications, gyroscopes need to improve their environmental adaptability within the full temperature range. To meet the needs of both high-precision and engineering applications, we study the factors that affect polarization noises and thus the output error of gyroscopes in varying temperature environments. Methods Jones matrix is a relatively simple method to describe the polarization characteristics of optical devices. We establish a complete optical transmission model based on the Jones matrix method. By analyzing the clockwise and counterclockwise optical transmission in the resonant cavity, the difference between the coupling errors of the clockwise and counterclockwise polarization modes is used as the output error of the gyroscope, eliminating the common mode error, and the problem of using double the frequency deviation caused by polarization noise as the output error of the gyroscope in the past while ignoring the difference in forward and backward light transmission is solved. In the full temperature range of - 40 degrees C-80 degrees C, the factors that affect the polarization noise and lead to the gyro output error are simulated and calculated, including the angle alignment error of the coupler, the length difference of the optical fibers on both sides of the twin 90 degrees fusion point, and the uneven temperature distribution difference of a section of optical fibers on the FRR or each adjacent end of optical fibers when the system is locally heated, so as to obtain the gap between the actual structure of the system and the theoretical calculation and quantify the control accuracy of relevant parameters based on specific gyro error requirements in varying temperature environments. Results and Discussions First, based on the twin 90 degrees fusion point integrated online polarizer structure, the resonant cavity optical path is modeled, and its polarization characteristics are analyzed to obtain the resonance curves of the clockwise and counterclockwise light transmission in the cavity for one cycle (Fig. 2). In addition, the frequency difference between clockwise and counterclockwise is taken as the output error of the gyroscope caused by polarization noises, and the influence of polarization errors on the gyroscope output under varying temperature environments is studied. When the ambient temperature changes within the whole temperature range, the errors caused by the polarization of clockwise and counterclockwise light transmission are very close, both within +/- 3 (degrees)/h, and the overall difference is within +/- 0. 02 (degrees)/h, both showing periodic changes with temperatures ( Fig. 3). However, this result cannot support the development requirements of the navigation level gyroscope engineering prototypes, and parameter control is needed to reduce the polarization error output. The relationship between the angle alignment error of the coupler (Fig. 4), the fiber length difference on both sides of the twin 90 degrees fusion point (Fig. 5), and the output error of the gyroscope is simulated and calculated. Based on the control parameters obtained from this result and the gyro operating environment, active devices such as lasers or circuit components dissipate heat during normal operation, resulting in local temperature disturbance to the FRR close to them (Fig. 6), and the influence of the fiber ring temperature and its ambient temperature distribution difference on the gyro output error caused by polarization noise is analyzed, including the non-uniform temperature distribution difference on a section of optical fiber (Fig. 7) and the temperature distribution difference between two adjacent optical fibers (Fig. 8), which guides error distribution design due to polarization noise in varying temperature environments. Conclusions We establish a complete optical transmission model for FRR based on the Jones matrix. By analyzing the polarization noise of the clockwise and counterclockwise optical transmission and adopting the dual point 90 degrees fusion integrated online polarizer structure, the resonance curve in FRR is derived, and the gyroscope output caused by polarization error in varying temperature environments is obtained; due to the periodicity and regularity of the gyroscope output within the whole temperature range, the varying temperature range of - 40 degrees C -- 20 degrees C is used instead of the full temperature environment, and different influencing factors are analyzed separately. The results show that when the extinction ratio of the online polarizer is 30 dB, the alignment error of the coupler angle is less than 2. 78 degrees, and the output error of the gyroscope is less than 0. 01 (degrees)/h; as the coupler coefficient k gets larger, the fault tolerance value of the fiber length difference on both sides of the double 90 degrees fusion point becomes higher. When k is 0. 05, and Delta L is controlled within 0. 207 m, there is a gyroscope output error of less than 0. 01 (degrees)/ h. On this basis, when the temperature distribution on a section of optical fiber is uneven due to the internal temperature rise of the gyro prototype in engineering applications, the difference of the uneven temperature distribution should be less than 13. 2 degrees C; when there is a non-uniform temperature difference between every two adjacent fibers on the FRR, its value should be less than 3. 122 degrees C, and the output error of the gyroscope is less than 0. 01 (degrees)/h. The above analysis is based on the requirements of suppressing polarization noises in gyroscopes, which provides certain theoretical guidance for error allocation design in full-temperature environments.
