"Dead-zone" Effect in Tri-axial Fiber Optic Gyroscopes: Mechanism, Modeling, and Suppression

As three-axis fiber-optic gyroscopes (FOGs) increasingly aim for miniaturization and high precision, the "dead-zone" effect—triggered by inter-axis optical crosstalk—has become a critical bottleneck limiting performance in low-angular-rate measurements. A dead zone occurs when the gyroscope's output ceases to respond to changes in input angular velocity below a certain threshold. For applications such as satellite attitude control that require operation near zero angular velocity, the nonlinear bias error introduced by the dead zone directly compromises system accuracy. This paper focuses on the issue of inter-axis optical crosstalk in three-axis FOGs utilizing a shared-light-source architecture; it analyzes the underlying physical mechanisms, quantifies the impact on threshold characteristics, and comparatively evaluates current primary mitigation strategies.

**Physical Origins of the Dead Zone and the Inter-Axis Optical Crosstalk Model**

The dead zone is a nonlinear effect characteristic of digital closed-loop FOGs. Conventionally, the primary source of interference causing the dead zone is identified as the electrical cross-coupling of the staircase voltage applied to the phase modulator into the detector signal. However, in a three-axis shared-source architecture, the problem is more complex: a single superluminescent diode (SLD) source drives three orthogonal axes simultaneously after being split by a 1×3 coupler. Back-reflected light creates optical crosstalk channels between the axes; at low angular rates, this optical intensity crosstalk superimposes onto the interference intensity, potentially overwhelming the useful signal.

To quantitatively characterize this effect, a study proposed an open-loop excitation method to measure the optical back-reflection crosstalk coefficients between axes. Incorporating these coefficients into a closed-loop control model reveals that an increase in the crosstalk coefficient causes the gyroscope's threshold to expand multiplicatively, directly resulting in a wider dead-zone range. This mechanism can be formalized as follows: when the phase of the periodic disturbance in the feedback channel and the equivalent phase of the crosstalk satisfy specific conditions, the system enters the dead zone, and the output phase locks to zero.

**Quantitative Characterization of Dead-Zone Thresholds**

The impact of the dead zone on the system lies not only in the existence of an "insensitive range" but also in the fact that the boundaries of this range shift dynamically due to environmental factors such as space radiation and temperature fluctuations. Space radiation causes a decrease in light source power and an increase in fiber loss, thereby reducing the system gain (K₁) and expanding the dead-zone range. Experimental data indicate that the dead-zone threshold of an uncompensated triaxial gyroscope can reach the order of 0.2°/h, a level unacceptable for high-precision applications requiring the resolution of extremely low angular velocities.

It is worth noting that the dead zone arises from multiple mechanisms. In addition to inter-axis optical crosstalk, electrical cross-coupling constitutes another significant cause. The analog drive voltage signal of the phase modulator—subjected to resets via a digital feedback staircase wave—generates distinct operating modes; the resulting crosstalk, manifesting as variations in the amplitude and phase of the detector output signal, becomes particularly pronounced during state transitions in the four-state modulation scheme. Since these two mechanisms often act concurrently in triaxial systems, modeling the dead zone requires accounting for both optical and electrical dimensions.

Comparative Analysis of Suppression Schemes

To address the aforementioned causes of dead zones, three primary suppression strategies have been developed, each differing in mechanism and effectiveness:

 Static operating point flipping (bias switching) method. Targeting the physical root cause of inter-axis optical crosstalk, this method actively flips the gyroscope's static operating point so that the crosstalk signal no longer superimposes onto the closed-loop residual phase. Experimental results are impressive: this approach reduces the threshold from 0.2°/h to below 0.01°/h, effectively enhancing measurement accuracy at low rotation rates. Its advantage lies in directly addressing the optical crosstalk mechanism without introducing additional bias errors.

 Periodic perturbation superposition method (dithering). A zero-mean periodic perturbation phase, φ₀, is introduced into the system to break the dead-zone locking condition through "dithering." When the dither amplitude is sufficiently large (φ₀ ≥ φ₁), the dead zone can be completely eliminated. In practical engineering applications, triangular-wave phase dithering technology has suppressed the dead-zone error of high-precision gyroscopes from 0.08°/h to below 0.001°/h. The method's effectiveness has been validated in a triaxial system utilizing 900 meters of optical fiber; suppression performance depends on the specific combination of dither amplitude, frequency, and loop gain. However, excessive dither amplitude may introduce additional noise, necessitating a careful trade-off.

 Combined method of analog additive feedback and ratio-based four-state demodulation. This method addresses the issue starting with the electrical cross-coupling path: in traditional four-state modulation, the reset operations associated with each modulation state are a primary cause of the dead zone. The analog additive feedback method significantly reduces the frequency of reset operations by resetting only the feedback phase during modulation; experiments demonstrate that this can lower the dead zone to below the measurement threshold of 0.022°/h. However, due to the inherent nature of electrical crosstalk, this method still introduces an additional bias of approximately -0.06°/h. To mitigate this, the method is further combined with the ratio-based four-state demodulation technique; by adjusting the demodulation ratio of the feedback signal, the correlation between the modulation and demodulation sequences is weakened, thereby controlling the additional bias while simultaneously suppressing the dead zone.

Overall, these three types of schemes are suited to different application scenarios: the optical crosstalk suppression scheme is most effective for tri-axial architectures sharing a common light source; the dithering method is simple to implement but requires noise management; and electrical crosstalk suppression schemes are better suited for single-axis and discrete systems. For silicon-photonic gyroscopes aiming for ultra-high integration, recent research has introduced a joint suppression algorithm that integrates phase-shift hopping with sample rejection; this approach suppresses the dead zone while reducing angle random walk by over 26%, reflecting a trend toward combining multiple strategies rather than relying on a single method.

In summary, the dead zone effect in tri-axial fiber-optic gyroscopes is a systemic issue resulting from the coupling of multiple factors. Inter-axis optical crosstalk and electrical cross-coupling constitute the physical root causes of the dead zone, with their effects significantly amplified in architectures featuring common light sources and high levels of integration. Currently, the static operating point bias-flipping method offers the best performance for optical crosstalk suppression, the dithering method boasts the broadest applicability, and combined modulation schemes represent the cutting edge of electrical crosstalk suppression. As tri-axial gyroscopes evolve toward chip-scale integration, the combination of inter-waveguide crosstalk suppression (e.g., germanium-doped silica waveguide chips achieving crosstalk levels below -40 dB) and algorithmic joint suppression strategies may well become the key pathway to completely resolving the dead zone problem.