We report a different mechanism for rotation sensing by analyzing the polarization of light exiting from a Sagnac loop. Unlike in an interferometric fiber optic gyroscope (I-FOG), here the counter-propagating waves in the Sagnac loop are orthogonally polarized at the loop exit and, consequently, cannot directly interfere with each other when recombined at the exit. We show that the Stokes parameters s2 and s3 of the combined waves are simply the cosine and sine functions of the phase difference between the counter propagation waves, which is linearly proportional to the rotation rate, allowing precise determination of the rotation rate by polarization analysis. We build such a proof-of-concept polarimetry FOG and achieved key performance parameters comparable to those of a high-end tactical-grade gyroscope. In particular, the device shows a bias instability of 0.09°/h and an angular random walk of 0.0015°/, with an unlimited dynamic range, demonstrating its potential use for rotation sensing. This new approach eliminates the need for phase modulation required in I-FOGs, and promotes easy photonics integration, enabling the development of low-cost FOGs for price-sensitive applications, such as autonomous and robotic vehicles.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Gyroscopes are essential for fully autonomous vehicle control. Since their first demonstration by Vali and Shorthill more than 42 years ago , fiber optic gyroscopes (FOGs) have proven useful in various military and civilian applications [2–4], such as precision rotation rate and angle detection for navigation systems in land, air, and sea vehicles, to become the most widely used fiber optic sensors in the world. Multiple commercial studies [5,6] have shown that FOG based inertial measurement units (IMU) perform better than those based on microelectromechanical systems (MEMS), especially in off-road tests involving severe jolts, sharp turns, and wheel spinning. However, their high price has prevented their mass deployment in cost-sensitive autonomous driving applications, especially level 4 and level 5 autonomous vehicles [7,8]. Great efforts toward the development of several low-cost chip-level optical gyroscopes [9–12] have provided devices with orders of magnitude lower performance than necessary for autonomous vehicle navigation applications.
Several FOG configurations have been proposed [13–21] to use resonant rings to reduce the size of the FOG, some of which [16,19–21] may have great potential to be integrated on photonic chips. However, one of the complications is to tightly lock the laser frequency with the resonant frequency of the resonant ring. As of today, the interferometric fiber optic gyroscope (I-FOG, Fig. 1(a)) , which exploits a Sagnac interferometer, is the only one that has been adopted for real-world applications due to its superior performance. Sagnac interferometers typically operate at a minimum sensitivity point, with the interference signal having a cosine relationship with the rotation-induced phase difference between the two counter-propagating optical waves , which makes slow rotations difficult to detect. In addition, the nonlinear nature of the signal around this minimum sensitivity point leads to inaccurate measurements. Therefore, the I-FOG requires active biasing of the Sagnac interferometer at the most sensitive operation point (the quadrature point). Measures to mitigate these effects rely on phase modulation as a general biasing method and closed-loop techniques that enhance the dynamic range and detection sensitivity of I-FOGs [2,22,23]. A 3 × 3 coupler-based Sagnac interferometer has also been proposed to solve the bias problem without phase modulation [24,25] but its inherent nonreciprocity causes bias errors [25–27], which has stalled its commercialization. Attempts at enhancing the performance of I-FOGs include work on the key gyroscope components, such as refinements to fiber coils [28,29] and the improvement of a LiNbO3-based integrated optical circuit (IOC) incorporating a 1 × 2 coupler and a phase modulator [12,22]. Despite these advances, I-FOG systems remain too expensive, which limits their economic viability in cost-sensitive commercial applications, such as robotics and autonomous vehicles.
In this paper, we present a novel approach that can acquire rotation information from a Sagnac loop at cost-effective levels for autonomous or robotic vehicle applications. This approach relies on the polarization analysis of the counter-propagating optical waves exiting from the Sagnac loop to detect rotation induced polarization variations, and therefore the resulting device is called a polarimetry fiber optic gyroscope (P-FOG). Specifically, the counter-propagating optical waves entering the Sagnac loop are orthogonally polarized to each other using a polarizing beam splitter (PBS) and subsequently recombined using the same PBS at the exit of the Sagnac loop without producing an interference signal. The resulting beam is analyzed by polarimetry. We show that the Stokes parameters s2 and s3 are simply the cosine and sine functions of the phase difference, which is proportional to the rotation rate of the Sagnac loop, while the parameter s1 is always equal to 0. Therefore, the phase difference and the corresponding rotation rate can be precisely obtained over an unlimited dynamic range by applying sine and cosine interpretation algorithms commonly used in sine–cosine encoders for motion control applications [30,31]. Interestingly, a different system using an orthogonal polarization Sagnac loop has been proposed for rotation detection 25 years ago [32,33]. Unfortunately, this orthogonal polarization fiber optic gyroscope (OP-FOG) has only provided a signal associated with the sine function of the phase difference, limiting its detection range to slow rotations and, consequently, thwarting its commercialization. In contrast, our P-FOG approach performs a full polarization analysis involving all the Stokes parameters to give both the sine and cosine functions of the phase difference. This enables phase unwrapping and hence rotation rate detection over an unlimited range, which represents a highly desirable feat that has only been attainable using a closed-loop I-FOG incorporating an expensive IOC and related high-speed electronics [22,23].
We have fabricated a proof-of-concept P-FOG in the laboratory and evaluated the feasibility of the new approach for rotation sensing at 25°C and under variable temperature conditions. Using a 585 m-long fiber coil, we measured rotation rates up to 1000°/s, a bias instability of 0.09°/h over a 100 s average at 25°C, an angular random walk of 0.0015°/ for an integration time of 1s, and a subdegree/h rate measurement sensitivity with a data update rate of 200 points/s. The observed high rotation rate induces a phase difference exceeding 4.55π, which is many times larger than the maximum value that the earlier OP-FOG can handle [32,33]. A commercial closed-loop I-FOG modified by incorporating the same fiber coil as in the P-FOG showed a bias instability of 0.037°/h over a 100s average and an angular random walk of 0.0069°/ for an integration time of 1s at 25°C. Finally, Measurements on P-FOG conducted in a chamber at temperatures ranging from −40 to + 80°C with heating/cooling rates of 1°C/min gave average and peak-to-peak bias instabilities of 0.323°/h and 0.85°/h, respectively, over a 100s average. These results demonstrate that the P-FOG achieves a comparable performance level to high-end tactical-grade gyroscopes, according to the classifications shown in Table 1 , and is sufficient for autonomous vehicle applications .
We believe that our new approach can reduce the cost of FOG systems at least tenfold relative to that of I-FOG-based equivalents. Because no phase modulation is required, the entire P-FOG system can be readily incorporated in silicon optical benches [35–37] or photonic integrated circuits (PICs) [38–40] for low-cost production. Eliminating phase modulation also 1) rules out the need for a high-speed electronic drive circuit, 2) dramatically reduces the required speed of the digital data acquisition and processing circuit, and 3) substantially lowers power consumption, further reducing costs.
Figure 1(b) illustrates an implementation of the P-FOG discussed above. As shown in Fig. 1(b), linearly polarized light emitted by the light source first passes through a non-polarizing beam splitter (NPBS) to produce the input beam, which is split into two orthogonally polarized components of equal power using a Wollaston PBS. These two components are subsequently coupled into both ends of a polarization-maintaining optical fiber (PM fiber) and are aligned with the slow axis (or fast axis) of the fiber. Next, they travel in opposite directions along the PM fiber, forming a closed loop, before recombining at the PBS. As in a Sagnac interferometer, the counter-propagating waves experience a relative delay or phase difference when the system is under rotation. This relative delay is simply a differential group delay (DGD) between two orthogonally polarized components. Unlike in an I-FOG, the two orthogonally polarized counter-propagating waves cannot interfere either at the PBS or at the NPBS. It is important to point out that the Sagnac loop of the P-FOG (Fig. 1(b)) displays a fully reciprocal optical path and therefore is absence of nonreciprocal bias, which is critical for gyroscope applications [23–25]. Note that although the two counter propagating waves inside the fiber coil are co-polarized along the slow (or fast) axis of the PM fiber, they always remain orthogonal when entering and exiting the PM fiber coil at the Wollaston PBS, and consequently cannot directly interfere at the exit port (or the Wollaston PBS) of the Sagnac loop. However, as will be described next, the polarization analysis will involve interferences of different polarization components of the combined beam from the exit of the Sagnac loop for extracting the phase difference between the counter propagating waves induced by rotation.
The electric field of the optical input beam entering the PBS (Fig. 1(b)) can be written as:Eq. (2), we assume that PBS and NPBS do not induce any differential phase shift between the two orthogonally polarized beams so that the polarization rotation of the output light depends solely on the gyroscope rotation.
The recombination of the polarized components at the PBS is expected to alter the output state of polarization (SOP) when the fiber loop is rotated. Such a SOP change can be measured using a polarization analyzer or polarimeter (such as that of Fig. 2(a)). In particular, the SOP is expected to outline a circle that passes through both poles (right- and left-hand circular polarizations) of the Poincaré sphere as the phase difference increases (Fig. 2(b) and (c)), as will be described next.
Polarization analysis can be implemented in a number of ways, including those based on rotating wave plates [41–43], rotating polarizer , and binary magneto-optic rotators [45,46]. However, these methods rely on taking multiple measurements sequentially to obtain the complete polarization information (i. e. Stokes parameters), which require the SOP of the optical beam to be relatively stable and therefore are not suitable for a P-FOG in which the SOP varies dynamically. For such an application, all measurements for obtaining the Stokes parameters must be taken simultaneously. Figure 2(a) shows such a polarization analyzer  capable of performing the simultaneous measurements to determine the SOP of an optical beam. In a P-FOG, the output beam from the NPBS (Fig. 1(b)) is expanded and passes through a four-faceted optical wedge to create four spatially divided subbeams. These subbeams propagate in four slightly different directions before being focused by a lens onto four photodetector (PD) chips placed at distinct spots on the focal plane of the lens, similar to a quadrant photodetector, as shown in Fig. 2(a). These PD chips detect the optical powers of the four subbeams and convert them into proportional photovoltages. Four additional polarizer chips can be placed on the wedge (Fig. 2(a)) or in front of the PD chips to analyze the SOP of the optical beam. The first subbeam passes through a polarizer aligned with the axis before entering the first PD to give the photovoltage V1 as , where the coefficient accounts for optical loss, PD quantum efficiency, and the electronic gain of each channel. The second subbeam passes through an orthogonal polarizer aligned with the axis before entering the second PD to yield the photovoltage V2 as: . The third subbeam passes through a polarizer with a 45° orientation with respect to the axis before entering the third photodetector to afford the photovoltage V3 as . Finally, the fourth subbeam passes through a circular polarizer before entering the fourth PD to provide the photovoltage V4 as . The circular polarizer consists of a quarter-wave plate whose birefringence axis is aligned with the (or ) axis combined with a polarizer whose axis forms a 45° angle with respect to the (or ) axis. Optical losses and detector efficiencies vary according to channels but the electronic gain can always be adjusted to ensure that is the same for all channels. Let , the Stokes parameters  of the recombined light beam can be calculated using , ,and as:
From Eqs. (5) and (6) one can see that , indicating that the SOP traces out a circle in the (s2, s3) plane on the Poincaré sphere (Fig. 2(c)) as Δϕ increases. In addition, the Stokes parameters s3 and s2 represent the sine and cosine, respectively, of the phase difference Δϕ, which is the polarization rotation angle in the (s2, s3) plane or the polar angle of the SOP on the Poincaré sphere. This situation is similar to the case where a sine–cosine rotary encoder (or an analog quadrature encoder) is used to obtain the rotation angle in a motor [30,31]. Consequently, Δϕ can be accurately evaluated over an unlimited range using the interpretation algorithms commonly used in sine–cosine rotary encoders [30,31]. Interestingly, the SOP trace is contained in the (s2, s3) plane, which eliminates the need to measure s1 and can further simplify the detection optics of P-FOG (Fig. 2). Compared with the prior OP-FOG [32,33], this scheme yields an additional cosΔϕ term, which is crucial because it enables the unwrapping of the phase difference, and consequently provides an unlimited dynamic range for rotation rate measurements. Note that although the Sagnac loop in the P-FOG displays a fully reciprocal optical path, the wave plate in the polarization analyzer may cause additional bias drift because wave plate’s retardation generally has temperature dependence. Fortunately, it is possible to make a temperature insensitive wave plate using two different birefringence materials with opposite signs of thermal coefficient to minimize such bias drift .
In principle, this new polarimetric configuration exhibits following five major advantages. 1) It does not require phase modulation to bias the gyroroscope system, resulting in significant cost savings. 2) The SOP rotation angle is linearly proportional to the system rotation rate, simplifying the extraction of both the amplitude and direction of the rotation rate from the SOP measurement. 3) The simplicity of the optical circuit facilitates its fabrication with a silicon optical bench or PIC. 4) The P-FOG benefits from simpler and less power-consuming electronics than an I-FOG because it does not need a dedicated signal to drive the phase modulator nor high-speed field-programmable gate array/digital signal processing for the digital closed-loop design. Only a low-power circuit is required to detect the polarization rotation information. 5) Subtraction and division operations substantially reduce relative intensity noise effects  from the light source and multipass interferences along the optical paths in the detection circuit during the Stokes parameter computations, which decrease the cost of light sources. It should be pointed out that a P-FOG requires 4 photodetectors to simultaneously detect 4 beams of light, while an I-FOG only requires a single photodetector, although the signal processing for extracting the rotation information is more straightforward and faster for the P-FOG.
To demonstrate the feasibility of the polarimetric design (Fig. 1(b)), we constructed a P-FOG device using a 585 m-long PM fiber coiled with a quadrupole winding pattern to minimize the Shupe effect , which characterizes the phase difference error originated from the fiber coil caused by temperature variations. Figure 3a shows the optics module containing all the optical components except the light source and the PM fiber. A 1310 nm superluminescent light-emitting diode (SLED) with a linewidth of 40 nm and an output power of 1 mW acted as the light source. The PD signals were amplified using a four-channel low-noise transimpedance amplifier board developed in house. Data acquisition and processing were performed using a low-cost digital signal processing board equipped with multiple analog-to-digital converters. It was necessary to package the entire P-FOG in an enclosure to fully characterize its performance using a rotation stage and a temperature chamber. The packaged unit comprises the optics module, electronic circuit, light source, and PM fiber (Fig. 3(b)). It also has a UART interface, outputting 200 Δϕ data points per second.
The ability of the P-FOG to sense rotation was evaluated using a high-precision rotation table that can generate rotation rates between 0.001 and 1000°/s. The rotation table was programmed to rotate back and forth with a gradually increasing rate of 0 to 1000°/s. Figure 4(a) shows the output of the P-FOG over time. The device correctly detected the varying rotation rates. The scale factor was obtained by plotting the P-FOG output Δϕ as a function of the input rotation rate Ω and linearly fitting the curve (Fig. 4(b)). The linear fit gave the scale factor as a slope of 0.0144, in agreement with the value calculated using Eq. (3) (Δϕ = 0.0143Ω (Ω in °/s)) for the PM fiber coil chosen. The output of the P-FOG remained linear even at ± 1000°/s, despite the fact that the rotation induced phase difference reached 14.3 rad (~4.55π) at a rotation rate of 1000°/s. This result demonstrates the phase unwrapping capability and, consequently, unlimited dynamic range of the P-FOG. This dynamic range is a clear enhancement over those reported for OP-FOG [32,33] and open-loop I-FOG devices [2,22], which were limited to a fraction of π, and rivals that of a closed-loop I-FOG [22,23].
To evaluate the detection sensitivity of the P-FOG, it is necessary to generate highly accurate rotation at slow rates ranging within fractions of degrees per hour, which is beyond the capability of our rotation table. To achieve these slow rates, we exploited the earth’s rotation by vertically mounting the P-FOG on a leveled rotation stage  (Fig. 5(a)). The rotation rate Ω experienced by the P-FOG can be expressed as Figure 5(b) shows the measured rotation rate as a function of the rotation stage angle using a value of 12.82° (15*cos31.3°) to calibrate the measurement data. The measured rotation rate varies sinusoidally with respect to angle θ, consistent with Eq. (7). Finally, a subdegree per hour angular rate sensitivity is observed, however, drift, which mainly results from the temperature dependence of the optical head and the electronic circuit, restricts further sensitivity enhancement. We anticipate that refining the optomechanical design of the optical head and receiving electronics could increase sensitivity by up to ten times.
Bias instability and angular random walk (ARW) are the most important parameters for a gyroscope , which describe the instability of the bias offset and the average error as a result of random noise of the gyroscope, respectively. We measured the bias instability of the P-FOG at room temperature and in variable temperature environments. The setup for measuring the bias instability and ARW included a temperature chamber with low vibration designed specifically for FOG testing. The rotation table for measuring the scale factor in Fig. 4 was enclosed inside the temperature chamber. For P-FOG testing, the prototype P-FOG was placed on the rotation table and connected with a power supply and a notebook computer outside the chamber. Using the scale factor obtained in Fig. 4, the computer convert Δϕ data into rotation rates. These data were then further averaged to obtain the bias instability. The ARW was obtained by processing the data with an Allen Variance  analysis program we developed in the laboratory.
For I-FOG test, only the fiber coil was placed inside the chamber. The rest of the I-FOG, including the light source, PIN-FET detector, the IOC, the electronics, and the data interfaces, were all enclosed in a compact package and were placed outside of the chamber. The fiber leads connecting the fiber coil inside the chamber and the I-FOG package outside the chamber were well protected with goose neck tubes to prevent wind induced fiber vibrations.
The bias instability at 25°C averages 0.09°/h over a 100s period and slightly drifts downward over time (Fig. 6(a)). Figure 6(b) shows the bias instability under variable temperature conditions at heating/cooling rates of 1°C/min (dashed line). The maximum peak-to-peak bias instability approximates 0.85°/h, which is considered to be outstanding for a gyroscope without temperature compensation or control. The angular random walk  of the P-FOG measures 0.0015°/ with a 1s integration time at 25°C, which is indicative of a low-noise device.
For comparison, we modified a LiNbO3 IOC-based commercial closed-loop I-FOG classified as a high-end tactical-grade gyroscope  by replacing its original fiber coil with the 585 m-long PM fiber coil used in the P-FOG and measured its bias instability at 25°C. Measurements were conducted using a 1310 nm SLED as a light source and a PIN photodiode combined with a high-impedance field-effect transistor preamplifier as a low-noise optical detector. Light source power and spectral width were optimized by the I-FOG manufacturer along with the detector bandwidth and gain. The modulation frequency used by the I-FOG’s electronic circuit to drive the IOC was readjusted to match the eigenfrequency of the fiber coil . The results are shown in Fig. 6(c). The technically mature I-FOG shows lower bias instability than the proof-of-concept P-FOG (0.037 vs. 0.09°/h). However, its angular random walk measures 0.0069°/ for a 1s integration, which is 4.6 times higher than that of the P-FOG (0.0015°/).
Low bias instability in varying temperature environments is also critical for a gyroscope to achieve in order to assure its accuracy at all times. The bias instability of the P-FOG under variable temperature conditions (Fig. 6(b)) includes contributions from the PM fiber coil [22,50] and the P-FOG body, which consists of the optical head, electronic circuitry, and mechanical package. We are more interested in the contribution from the P-FOG body because it reflects the temperature behavior of the P-FOG concept. The contribution of the fiber coil, which results from the Shupe effect , can be independently determined and be excluded from the total bias instability of the P-FOG to obtain the contribution from the P-FOG body alone. To evaluate fiber coil’s contribution under variable temperature conditions, we separated the fiber coil from the closed-loop I-FOG main body containing the optics and electronics components (Fig. 6(c), inset) and placed it alone in a temperature chamber for testing. These measurements show that the peak-to-peak and average bias instabilities of the fiber coil resulting from the temperature ramps (Fig. 6(d), dashed line) approximate 0.4°/h and 0.056°/h, respectively. The peak-peak bias instability of the coil is 0.45°/h lower than that of the entire P-FOG, which includes contributions from the fiber coil, optical assembly, and electronic circuit (Fig. 6(b)).
High data output rate of the P-FOG at 200 points/s is also attractive for vehicle navigation and control, because this low-latency positioning information is critical to high speed vehicles, robots, and drones. For example, at 100 km/h, a vehicle moves 0.14 m between 200 Hz position reports.
Table 2 compares the key performance data of our proof-of-concept P-FOG with those of the modified commercial closed-loop I-FOG. The P-FOG displays somewhat worse bias instability but superior angular random walk performance than the technically mature I-FOG. Nonetheless, according to the gyroscope classification of Table 1 , these performance parameters would qualify the P-FOG device as a high-end tactical-grade instrument. It is difficult to specify the required performance parameters of gyroscopes for autonomous and robotic vehicles, because the exact specifications is likely to highly depend on engineering trade-offs in vehicle’s navigation system designs. Nevertheless, a market survey  indicates that low-end tactical-grade gyroscopes with a bias instability on the order of 1-5°/h are sufficient. Therefore, the performance of the proof-of-concept P-FOG is already sufficient for autonomous and robotic vehicles. We believe that our continued efforts to optimize the optical assembly and electronics can significantly reduce the bias instabilities of the P-FOG for more demanding applications.
It is important to emphasize that the intend of our paper on P-FOG is to develop a low cost alternative to the I-FOG, targeted for cost sensitive applications with adequate performance, not to compete with the I-FOG for high performance applications, such as Astrix 200 by Airbus. It should point out that the I-FOG performance listed in Table 2 is typical of a high end tactical grade gyroscope, which may not represent the best performance of commercial I-FOGs in the same performance class.
In summary, we have proposed, theoretically analyzed, and experimentally demonstrated a different concept to measure rotation rates by analyzing the SOP of the output signal from a Sagnac loop. Unlike the traditional I-FOG, this P-FOG approach does not measure the interference between the counter-propagating signals in the Sagnac loop and, consequently, does not require phase modulation and the associated high-speed electronics. In contrast to the OP-FOG approach, it also exhibits an unlimited dynamic range for rotation rate sensing according to theory and validated by experiment. The proof-of-concept P-FOG displays key performance parameters comparable to a high-end tactical-grade gyroscope, suggesting that it meets the requirements for autonomous vehicles. The simplicity of the P-FOG approach facilitates its implementation in silicon optical benches or, potentially, PICs for the low-cost production of autonomous vehicles and other high-performance robotics applications. Continued development efforts are expected to substantially improve P-FOG performance for more demanding applications at low cost, such as drones, boats, underwater crafts, self-navigating robots, and military vehicles.
Technology Foundation for Selected Overseas Chinese Scholar of MOHRSS (CG2015003006); Research Start-up Foundation of High-level Talents Introduction (8012605); Internal development funding of NuVision Photonics and Suzhou Optoring Co. Ltd.
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