The working principle of fiber optic gyroscope

September 27, 2023

The basic working principle of fiber optic gyro comes from the Sagnac effect. The Sagnac effect is a universal correlation effect that interrupts propagating light with respect to a closed-loop optical path rotating in inertial space, that is, two beams of light with the same characteristics emitted from the same light source in the same closed optical path are transmitted in opposite directions to each other and finally converge To the same detection point; if there is a rotation angular velocity relative to the vertical line that is perpendicular to the plane where the closed optical path is located, the optical path traveled by the two beams of light is different, and the optical path difference occurs. Theoretically, it can be proved that the optical path difference is proportional to the rotation angular velocity, that is

Where L is the length of the fiber; D is the diameter of the fiber ring; λ is the wavelength of light; c is the speed of light in vacuum; Ω is the angular velocity of rotation.
The low-loss single-mode fiber is used to form a ring, and its total length L can reach hundreds of meters or even thousands of kilometers, which can greatly improve the sensitivity of the ring interferometer, and even a slight rotation can produce a detectable phase difference. Because the single-mode fiber in the fiber ring is in a double-beam interference state, its output light intensity can be expressed as

In the formula, I0 is Imax / 2. From equations (1) and (2), the output light intensity is a cosine function of angular velocity, as shown in Figure 1. It can be seen from Figure 1 that regardless of whether Ω is positive or negative, the I value reading remains unchanged, that is, the output light intensity cannot reflect the direction of rotation. At the same time, the small signal sensitivity is low, the Sagnac phase shift is very small in most cases, and the system sensitivity dI / dΩ is 0 at Ω = 0. For this reason, a phase difference of 90o is introduced between the two beams of reverse transmission, resulting in the output light intensity becoming I = I0 (1−sinϕs). Obviously, the sensitivity of the gyroscope at 90Ω, ie, dI / dΩ, reaches the maximum value after a 90 ° phase difference, and at the same time solves the problem that the output I can reflect the direction of rotation.
The reciprocity structure shown in Fig. 2 is the basic principle structure of the fiber optic gyroscope, which can completely ensure that the optical paths of the clockwise and counterclockwise light waves of the gyroscope in the static state are equal. The function of the coupler is to couple a part of the return light to the detector as the light output of the gyro. The polarizer is located between the fiber ring and the coupler, which keeps the single-mode light in a single-polarized state, thereby eliminating the effect of fiber birefringence changes on the performance of the gyro. When the two light waves clockwise and counterclockwise pass through the fiber ring, the paths are inconsistent, causing them to pass through the phase modulator at different times. Let the time difference be τ and the result of the phase modulator is Substituting equation (3) into equation (2), the optical output of the gyro has

Figure 2 Schematic diagram of fiber optic gyro Taking sinusoidal signal modulation as an example, set ϕ (t) = ϕm sin (ωt), and substitute into (4), then

Where η = 2ϕmsin (ωτ / 2). When the gyro is stationary, its output has only even harmonics of the modulation frequency ω; when rotating, its output will have odd harmonics. Using a lock-in amplifier to detect the first harmonic, the gyro output is Where K is the voltage gain, usually the value of η is 1.84 rad, the Bessel function J1 (η) takes the maximum value of 0.53, and the sine wave modulation is shown in Figure 3. Using equation (6), according to the detected Iω, ϕs can be solved, and then using equation (1) to obtain the angular velocity Ω. The integrated optical phase modulator in Figure 2, one is used for bias signal modulation and the other is used for feedback signal modulation to provide a feedback phase shift to form a closed-loop gyro.