Analysis and simulation of a fiber optical gyroscope with Shupe error compensated optically

The fiber optic gyroscope (FOG)based on Sagnac effect has became to one of the most important sensors in developing due to light in quality, high accuracy, compact in dimension and long life and has played a very important role in both military and civil use. It is the most difficult problem that the FOG has an obvious bias drift caused by temperature change and temperature grade, so its application is limited to a great extent. Fiber coil is one of the most critical components in FOG. Here, the characteristic of temperature error of the fiber optical coil was analyzed. At first, by studying the glass transition of coating adhesive in the fiber coil, the element model of the fiber coil with the glass transition of coating adhesive in FOG was built. Then the discrete mathematics model of SHUPE error with the glass transition of coating adhesive in FOG was built. Finally, based on the temperature models mentioned above, the effects caused by the glass transition of coating adhesive on temperature performance of fiber optic gyroscope were analyzed. Theoretical analysis and experimental results show that effect caused by the glass transition of coating adhesive had seriously affected the temperature performance of FOG. By optimizing the glass transition temperature of coating adhesive, the SHUPE error of fiber coils can be reduced. At the same time, the amplitude uniformity of the SHUPE error can be improved greatly to reduce the difficulty in temperature compensation.

Firstly, this paper determines that the main cause of the Shupe error is the temperature distribution gradient in the fiber coil that changes with time and space by studying the Shupe error mathematical model of fiber optic gyroscope (FOG). To solve this problem, according to the structural form and composition of the fiber coil, the equivalent physical property parameters of the fiber coil are analyzed and obtained, and the equivalent model of the fiber coil is established. Then, a variety of structural forms with different protective layers are designed for the optical fiber coil under the condition that space allows, such as thermal conduction layer and thermal insulation layer, and the finite element transient temperature field simulation analysis is performed for each structural form. The simulation results show that the optimal protective layer structure is that the inner layer is thermal conduction layer, and the outer layer is thermal insulation layer. Compared with the structure without protective layer outside the fiber coil, the temperature difference within the fiber coil is reduced from 9.32℃ to 0.5℃, and the average temperature rise of the fiber coil is reduced from33.34℃ to 4.26℃. Finally, a local heating experiment is performed on the FOG with such protective layer structure, and the results show that the zero bias stability of the FOG is improved from the original 0.0118°/h to 0.0055°/h, which is of great significance for improving the temperature performance of FOG.

With the possible exception of nonsilica glasses, each time a new fiber technology has emerged, someone has applied it to FOGs and reported beneficial results. The development of the FOG has essentially tracked that of commercial optical fibers for more than 40 years, running parallel since 1976, when Vali and Shorthill first demonstrated the concepts originally proposed by Pircher and Hepner in early 1967. The nine-year gap between first proposal and experimental demonstration was undoubtedly caused because, in 1967 practical, single-mode fibers simply did not exist, and even by 1976 they were in their infancy and confined to a handful of research laboratories around the globe. FOG technology received a further boost at the beginning of the 1980s when stress-birefringent polarization-maintaining (PM) fibers were developed almost simultaneously by multiple commercial and academic institutions, including NTT, Corning, Hitachi, Bell Laboratories, and the University of Southampton. It was the advent of PM fibers that paved the way for commercial FOG development by delivering practical immunity to environmental variations such as vibration and temperature. To this day, precisionwound coils of PM fiber dominate the FOG industry. Nevertheless, with FOG technology challenging the ring laser gyro (RLG) in navigation-grade sensors and even making in-roads into strategic levels of precision, virtually every new development in fiber technology has been investigated extensively to discover if theoretical performance advantages in FOGs may be realized.

The Shupe effect in a fiber optical gyroscope with polarization-maintaining photonic crystal fiber was studied. The thermal sensitivitise of the polarization-maintaining photonic crystal fiber and conventional polarization-maintaining fiber were simulated and measured. Then the Shupe error in the gyroscope was analyzed. The contrast results showed that the Shupe error of the gyroscope with the polarization-maintaining photonic crystal fiber is quantitatively comparable to that using the conventional polarization-maintaining fiber.

Dual-polarization interferometric fiber optic gyroscope (IFOG) is a novel scheme in which the polarization nonreciprocal (PN) phase error of the two orthogonal polarizations can be optically compensated. In this work, we investigate the effective of PN phase error compensation under varying temperature. It is proved that, the thermally induced strain deforms the fiber, and results in perturbations on the birefringence and polarization cross coupling which degrades the IFOG's stability. A wave propagation model and analytical expressions of PN phase error are derived by using coupled-wave equation and Jones matrix. We theoretically and experimentally verify that, although the single-mode (SM) and polarization-maintaining (PM) fiber coils behave different owing to their intrinsic properties of wave propagation, the thermal strain induced PN phase error can still be compensated under slow and adiabatic temperature variations. This could be a promising feature to overcome the temperature fragility of IFOG.

In this work, the fiber optic gyroscope (FOG) with an elliptic fiber coil (EFC) is applied to the inertial measurement of petroleum well trajectory for the special condition of the borehole diameter limitation in the inclinometer while drilling (IWD). The three-dimensional (3D) Shupe error mathematical model and finite element model of the EFC are established by the quadrupole symmetrical technique, which is based on the Shupe effect of fiber coil. Then, the simulation experiments and the temperature experiments of the EFC are carried out to verify the correctness of the mathematical model. Under this prerequisite, the influence of the structure parameters of the EFC on the Shupe error is analyzed. In order to compare the rotation rate error between the EFC and the circular fiber coil (CFC), the temperature experiments of the EFC and the CFC are carried out with the same temperature excitation when the fiber length, the layers of fiber coil, and the radius of fiber coil of the EFC are the same as those of the CFC. The results show that the bias stability of the EFC is 35% to 39% smaller than that of the CFC before the temperature compensation, and after the temperature compensation, the bias stability of the EFC is 49% to 70% smaller than that of the CFC.

Research on the performance of polarization-maintaining fiber (PMF) for fiber coils is significant for the precision improvement of an interferometric fiber optic gyroscope (IFOG) working in harsh environments. In this paper, we firstly report analytical models of the fiber polarization theory and present two types of hybrid PMF structures by a collaboration of geometry and stress effects: a Panda-type horizontal-elliptical core PMF (Panda-type HE-PMF) based on a superposition of geometry and stress, and a Panda-type longitudinal-elliptical core PMF (Panda-type LE-PMF) with geometry offset stress effect, achieving enhanced and suppressed modal performance by adjusting geometric anisotropy of elliptical-core in different directions. Then, the influence mechanisms of the geometric birefringence on the modal performance of both PMFs as the variation of fiber structural parameters are investigated via numerical simulations to determine the target fiber designs. The other significant attribute, including effective mode area (Aeff), nonlinear coefficient (γ), and chromatic dispersion (D), and their tolerance to PMF parameter fluctuations are also evaluated. Finally, both target PMFs with structural optimization are practically fabricated and wound into four fiber coils with quadrupolar (QAD) and 16-polar symmetrical winding patterns, respectively. The polarization ability and thermal performance are further demonstrated by experiments conducted on both PMFs, wound fiber coils, and built IFOGs under static and dynamic environments (over a wide temperature range of -40 °C to 70 °C), and compared with a conventional PMF. The testing results suggest that designed HE-PMF coils both achieve high birefringence, static extinction ratio (ER) values of up to 30.80 dB and 31.93 dB, respectively, corresponding to an almost one-fold increase over conventional coils. Remarkably, the ER property of the HE-PMF coil by combining this HE-PMF design and a 16-polar winding pattern consistently remains above 29.5 dB with a minimal fluctuation in ER of only 3.0 dB across the entire variable temperature conditions. The bias stability of the IFOG assembled with this coil is strongly enhanced to 0.0019 °/h and 0.082 °/h under static and dynamic conditions, respectively, which is a significant improvement over conventional coils of 0.136 °/h. Also, the static angle random walk performance of the improved IFOG is reduced to 0.000624 °/√h. In contrast, the LE-PMF as a comparison is shown to limited polarization characteristics with a low birefringence and ER due to the suppression effect of the geometric birefringence, and the applied IFOG output also exhibits larger drift, indicating a poor thermal ability. Experimental results show great agreement with theoretical analysis and numerical simulations, confirming the validity of design principles. The advances in both designs are instructive for the engineering applications of PMFs for IFOGs and for improving the accuracy of fiber sensors.

Acoustic wave coupling in dual-wavelength orthogonal polarized Brillouin random fiber laser (BRFL) based on polarization-maintaining (PM) fiber is characterized experimentally for the first time. Dual-wavelength BRFL is generated when the pump light is injected to the Brillouin gain PM fiber at 45 degrees from the slow axis. The dynamics of intensity and frequency of dual-wavelength and single-wavelength BRFLs are investigated. The spectrum of Pearson’s correlation coefficient between different frequencies of the dual-wavelength BRFL shows several correlation peaks due to gain competition of two spatially overlapped coupled modes induced by acoustic wave coupling. The dual-wavelength BRFL presents a lower laser frequency drift with a standard deviation of 2.55 MHz and a larger relative intensity fluctuation with a standard deviation of 0.54 compared with that of single-wavelength BRFL (3.68 MHz and 0.32), which is attributed by increased photon-phonon coupling over the Brillouin gain fiber resulting from the coupling of acoustic waves in fast and slow axis due to 45 degrees pumping. In addition, replica symmetry breaking (RSB) is observed in dual-wavelength BRFL due to the increased gain competition of more random modes from acoustic wave coupling, which leads to correlated intensity fluctuations from trace to trace. The exploration of the internal spectral correlation, intensity fluctuation, RSB and frequency drift exposes the acoustic wave coupling in the dual-wavelength Brillouin random lasing process.

With the progress of study on fiber optic gyroscope (FOG), the higher demand for performance of polarization maintaining fiber (PMF), and miniaturization is one of the important development direction. Compared to other stress-induced PMF, the birefringence of elliptical cladding type PMF has small effect when we make stress area smaller, and it can meet the requirements of fiber optic gyroscope. Therefore, 40 microns ultrafine diameter elliptical cladding type polarization maintaining fiber can be the preferred option of the FOG towards light, small, spiritual direction. In this paper, we use finite element method to analysis stress-induced birefringence of 40 microns ultrafine diameter elliptical cladding type PMF, get the stress contours on cross-section of PMF, and calculate the stress birefringence, the polarization mode field distribution and modal birefringence. Under the given simulation conditions, the magnitude of stress birefringence in core is about 10-4, and the magnitude of model birefringence is about 10-4. The results show that 40 microns ultrafine diameter elliptical cladding type PMF has a uniform stress field distribution and a large birefringence. It is conductive to achieve miniaturization of PMF.

Polarization maintaining (PM) fibers can be used for distributed force/pressure sensing in which the birefringence axis of the PM fiber should preferably be oriented 45° from the direction of the force/pressure for the maximum sensitivity. However, it is a challenge to achieve such 45° axis orientation for a long length of PM fiber in practice. In this paper, we report the development of what we believe the first equipment and process for making PM fiber based sensing tapes, capable of automatically adjusting the fiber axis orientation 45° with respect to the tape surface. In particular, we develop a machine vision system with the ability of continuously determining fiber axis orientation in real time as the fiber passes by and feeding back the orientation information to a fiber rotation apparatus to automatically adjust its orientation before fixing the fiber on a transparent PET tape with UV epoxy. We show the results of a successfully fabricated 70-m-long PM fiber sensing tape achieving an axis orientation accuracy of 45 ± 3° throughout the whole length of the tape, which is further validated with a distributed polarization crosstalk analyzer (DPXA). Finally, we demonstrate distributed transversal load sensing with 14 force applying weights randomly distributed along the sensing tape using the DPXA, with a polarization crosstalk measurement uniformity of 0.62 dB (standard deviation) using the same applied weight of 100 grams. The same sensing tape can also be used for pressure sensing with properly designed fixtures.

A recent JEOS-RP publication proposed Comments about Dispersion of Light Waves, and we present here complementary comments for birefringence dispersion in polarization-maintaining (PM) fibers, and for its measurement techniques based on channeled spectrum analysis. We start by a study of early seminal papers, and we propose additional explanations to get a simpler understanding of the subject. A geometrical construction is described to relate phase birefringence to group birefringence, and it is applied to the measurement of several kinds of PM fibers using stress-induced photo-elasticity, or shape birefringence. These measurements confirm clearly that the difference between group birefringence and phase birefringence is limited to 15–20% in stress-induced PM fibers (bow-tie, panda, or tiger-eye), but that it can get up to a 3-fold factor with an elliptical-core (E-core) fiber. There are also surprising results with solid-core micro-structured PM fibers, that are based on shape birefringence, as E-core fibers.

Femtosecond inscription of fiber gratings into polarization maintaining (PM) fibers and large mode area (LMA) fibers is studied. Transmission spectra for a Bragg grating written in a panda PM fiber is obtained where the polarization orientation with respect to the index modification of the grating is of particular interest. Transmission spectrum of a grating written in a LMA fiber with large core and cladding diameters is also obtained.

Endoscopes with small diameters are widely desired in medical and industrial fields. In this letter, we experimentally demonstrated single-pixel imaging (SPI) using a polarization-maintaining (PM) fiber array with few cores to achieve endoscope size reduction. We designed a PM fiber array with four fibers for the SPI system. The fiber array generated spatial patterns modulated using thermo-optic phase modulation. These patterns were then used to project objects, and the light intensities were detected. Using the pattern information and obtained intensities, we reconstructed the object information. This letter provides the first experimental demonstration of an SPI system incorporating a PM fiber array with four fibers. The results represent an advancement for realizing a compact endoscope based on SPI algorithms. The resolution of the reconstructions obtained using the SPI system can be improved. Thus, the results of this letter can be used as a reference for further developments.

In this study, a theoretical design of a simple fiber-optic gyroscope is proposed. This fiber-optic gyroscope not only realizes the full-dynamic-range of Sagnac-phase measurement, but also eliminates the excess phase affected by the elliptical birefringence of a single-mode fiber coil. Under the conditions that the fiber coil has 1100 turns and the fiber length is 242.9 m, the bias stability of this gyroscope is theoretically evaluated as 9.44 °/h. In this study, we also discuss the error signal that arises from the intensity stability, as well as the polarization nonreciprocity. We generate 1000 random values to simulate the possible distribution of a bias drift, and the result shows that the drift of the Sagnac phase is less than 10 $^{-3{\circ}}$ . In addition, we deduce the influence of the error signal induced by polarization nonreciprocity. The result indicates that the maximum error arises if the reciprocal phase of the SMF is $\varphi = 2m\pi $ ( $m = 0, \pm 1, \pm 2, \pm 3,\ldots$ ) and the optical rotation angle is $\theta = 45^{\circ}$ .

Compact, repetition rate locked all-PM fiber femtosecond laser system based on low noise figure-9 Er:fiber laser