Objective A resonant fiber optic gyroscope (RFOG) is a rotation rate sensor based on the Sagnac effect. The rotation rate is measured by determining the resonant frequency difference between the clockwise and counterclockwise waves propagating in a multiturn fiber ring resonator. Since the Sagnac effect is very weak, signal modulation and demodulation techniques are indispensable for improving the detection accuracy of the RFOG. The sinusoidal wave-phase modulation and demodulation techniques are widely used in the RFOG, in which the modulation index is set as 2.405 to reduce the backscattering noise. The modulation frequency is conventionally optimized to maximize the demodulation slope at the resonant point, which yields the highest sensitivity. However, the shot-noise-limited theoretical sensitivity of the RFOG depends on the signal-to-noise ratio (SNR) rather than the most sensitive working point. Angle random walk (ARW) is one of the basic parameters of the RFOG, which is used to evaluate the shot-noise limit.
Aiming at the optimum theoretical ARW, the influences of the modulation parameters, including the modulation index, modulation frequency, and demodulation phase, on the theoretical ARW are analyzed. This study provides insights into the optimization of the modulation parameters to improve the theoretical sensitivity of RFOGs. Our experiments verify the simulation results.
Methods Here, we introduce the basic operating principle of the RFOG based on the sinusoidal phase modulation and demodulation techniques. Thereafter, the theoretical ARW is derived in detail. The relationship between the theoretical ARW and the modulation parameters is analyzed. We find that the modulation parameters for the optimum ARW are different from those for the most sensitive working point. Subsequently, we set up a practical RFOG system based on the sinusoidal phase modulation and demodulation techniques and determine the influences of the modulation parameters on the ARW. We employ the power spectral density (PSD) analysis method to calculate the ARW of the gyro output data.
Results and Discussions In the practical RFOG system, the diameter of the fiber ring resonator is 12 cm and the total fiber length is 29 m. The measured fineness is 14.7. All the simulation results are obtained using the same fiber ring resonator as that in the practical RFOG system, and the peak output power of the resonator is 30 μW. Figure 5 shows the relationship between the amplitude of the demodulation output at a given rotation rate and the modulation-demodulation parameters. Two modulation indexes are calculated, i.e., 1.080 and 2.405. The relationship between the maximum demodulation output and the modulation parameters is further investigated, as shown in Fig. 6. When the modulation index is greater than 1, the maximum demodulation output remains almost unchanged with the variation of the modulation frequency. For example, when the modulation index is 1.1, the optimal modulation frequency is approximately 180 kHz and the maximum amplitude of the demodulation output corresponding to a rotation rate of 1 (°)/s is approximately 1.44×10 -3. When the modulation index is 2.2, the optimal modulation frequency is 80 kHz and the maximum amplitude is 1.5×10 -3. The difference is only approximately 4%. This is because when the modulation index is greater than 1, the maximum demodulation slope at the resonant point remains almost unchanged as the modulation index increases. The RFOG based on the sinusoidal modulation-demodulation technique can achieve the optimum theoretical sensitivity by resorting to match three parameters, including the modulation index, modulation frequency, and demodulation phase. The optimum sensitivity is related to the demodulation slope at the resonant point, as well as the output power of the fiber ring resonator. The relationship between the output power and the modulation parameters is shown in Fig. 7. It can be observed that the output power decreases as the modulation frequency or index increases. A set of optimal modulation-demodulation parameters (Figs. 8 and 9) related to the fiber ring resonator is observed, which enables the achievement of the best ARW. When the modulation frequencies are set as 1 MHz, 600 kHz, and 240 kHz, the calculated ARWs are 0.010 (°)/h, 0.007 (°)/h, and 0.005 (°)/h, respectively; for the practical RFOG system, the measured ARWs are 0.0124 (°)/h, 0.0072 (°)/h, and 0.0052 (°)/h (Fig. 10), respectively.
Conclusions An RFOG based on the sinusoidal modulation and synchronous demodulation technique is optimized to improve its shot-noise-limited theoretical sensitivity. The optimal modulation parameters, including the modulation frequency, modulation index, and demodulation phase, corresponding to a certain fiber ring resonator are obtained. Thereafter, an experimental system is set up to verify the simulation results. When the peak output power of the fiber ring resonator is 30 μW, the measured ARW of the RFOG is 0.0052 (°)/h, which is close to the theoretical value.
