Why Does a Fiber Optic Gyroscope Start at 0.1°/h but Stabilize at 0.01°/h?

A fiber optic gyroscope (FOG) is specified with a bias stability of 0.01°/h.

You power it on, start recording data, and calculate the Allan variance. The result is surprising: during the startup period, the bias drifts to around 0.1°/h—ten times worse than the specification.

Then, about 30 minutes later, the bias gradually settles into the expected 0.01°/h range.

Does this mean the gyroscope is defective?

Not necessarily.

The specification may be completely correct. The problem is that a steady-state specification is being compared with a transient startup measurement.

For a high-precision FOG, the internal components have not yet reached thermal equilibrium immediately after power-on. Temperature changes in the light source, multifunction integrated optical chip (MIOC), fiber coil, detector, and electronics can generate transient errors in both bias and scale factor.

In other words:

The first 30 minutes may not represent the intrinsic stability of the gyroscope. They may primarily represent its thermal transient.

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What Does a 0.01°/h Bias Stability Specification Actually Mean?

A bias stability specification such as 0.01°/h should not automatically be interpreted as:

“The gyroscope will show 0.01°/h immediately after power-on.”

Instead, the measurement is normally performed under specified operating conditions after the device has reached the required operating state.

For FOG testing, startup time is itself an important parameter. GJB 2426A-2015, Test Methods for Fiber Optic Gyroscopes, defines startup time as the period from power-on until the gyroscope reaches the specified performance under the prescribed operating conditions.

Therefore, when evaluating a 0.01°/h-class FOG, the measurement procedure matters just as much as the instrument specification.

If the gyroscope is still heating up, the measured bias may contain significant thermal-transient components.

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Thermal Source 1: Laser Wavelength Drift Changes the Scale Factor

The optical source is one of the first components to become thermally active after power-on.

For a fiber optic gyroscope, the scale factor can be expressed approximately as:

$$SF=\frac{2\pi LD}{c\lambda}$$

where:

• $L$ is the fiber length

• $D$ is the fiber coil diameter

• $c$ is the speed of light

• $\lambda$ is the mean optical wavelength

Therefore:

$$\frac{\Delta SF}{SF}\approx-\frac{\Delta\lambda}{\lambda}$$

The important point is that the scale factor depends directly on the optical source wavelength.

If the source temperature changes after power-on, its mean wavelength can drift. The scale factor therefore changes with it.

The source material notes that optimized ASE sources can achieve very low wavelength temperature coefficients, while typical SLD/ASE sources can exhibit substantially higher temperature coefficients.

This means that immediately after startup, the source may still be moving toward its thermal operating point.

If you place the FOG on a rate table immediately after power-on and measure its scale factor, you may be measuring a transient scale factor, rather than the final steady-state value.

Once the optical source reaches thermal equilibrium, the scale factor gradually converges.

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Thermal Source 2: MIOC Thermo-Optic Effects Shift the Bias Point

The multifunction integrated optical chip (MIOC) is another important thermal source.

A typical MIOC based on lithium niobate ($\mathrm{LiNbO_3}$) integrates several optical functions, including:

• polarization control

• optical coupling

• phase modulation

The refractive index of lithium niobate changes with temperature. As a result, parameters such as the modulator half-wave voltage $V_\pi$ and phase bias point can also shift with temperature.

During startup, the MIOC temperature is still changing, so its optical operating point can move.

This can appear directly as a change in FOG bias.

The source cites research showing that thermal treatment of lithium-niobate MIOCs can significantly reduce temperature-dependent bias drift.

The engineering interpretation is straightforward:

The optical path is not necessarily malfunctioning—the MIOC may simply not have reached its final thermal operating point.

Although an MIOC is relatively small and has a low thermal mass, its package and thermal interfaces couple it to the fiber coil, substrate, and surrounding components. Consequently, its thermal stabilization still occurs on a timescale of minutes.

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Thermal Source 3: The Shupe Effect Converts Temperature Gradients into Bias Drift

The fiber coil is at the heart of a FOG.

Ideally, the Sagnac effect allows the gyroscope to distinguish rotation from other effects. However, temperature gradients along the fiber coil can introduce an additional non-reciprocal phase shift.

This is known as the Shupe effect.

The physical mechanism is important.

When the fiber coil has a temperature gradient, the clockwise and counter-clockwise optical waves experience slightly different changes in refractive index and optical path length.

This produces an additional phase difference.

The gyroscope cannot inherently distinguish this thermally induced non-reciprocal phase from a phase difference caused by rotation.

The result appears as bias drift.

The key point is:

The Shupe effect is driven primarily by temperature gradients and temperature changes—not simply by the absolute temperature.

During startup, heat generated by the optical source, modulator, detector, and electronics propagates through:

package → substrate → adhesive → coil structure → fiber layers

This creates both radial and axial temperature gradients inside the fiber coil.

The source cites experimental work in which temperature variation rates of approximately ±1.5°C/min produced thermal errors on the order of 0.1°/h in a three-axis IFOG. Symmetric winding structures, such as sixteen-fold symmetric winding, can suppress the Shupe effect, although they cannot eliminate it completely.

This explains why a gyroscope can show apparently poor bias stability during warm-up even though its steady-state performance is much better.

As the temperature field inside the coil becomes more uniform, the thermally induced non-reciprocal phase error decreases.

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Thermal Source 4: Detector Dark Current and Electronic Components Also Drift

The detector and analog electronics contribute another, usually smaller, thermal component.

Photodetector dark current is temperature dependent, while resistors and other electronic components also exhibit temperature coefficients.

Immediately after power-on, the detector temperature may continue to rise, causing the dark current and electrical baseline to change.

This can appear as a gradual drift in the FOG output.

Modern FOG electronics typically include temperature compensation, but the compensation circuit itself also needs to reach a stable operating condition.

For lower-performance gyroscopes, this contribution may be relatively insignificant.

For a 0.01°/h-class system, however, even a relatively small electronic drift can become visible during startup.

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Why Does It Take About 30 Minutes?

The answer is thermal time constants.

A FOG is not a single thermal system. It contains multiple components, each with its own thermal mass and thermal resistance.

Typical thermal processes include:

Component	Typical thermal behavior
Optical source	Tens of seconds to several minutes
MIOC	Approximately 1–5 minutes
Fiber coil	Several minutes to more than 10 minutes
System substrate/enclosure	Tens of minutes

These processes interact rather than occurring independently.

The overall system therefore needs several times the largest relevant thermal time constant before its temperature field becomes sufficiently stable. The source notes that approximately 30 minutes of warm-up is a common engineering practice for high-precision FOG measurements.

So:

The gyroscope does not suddenly become better after 30 minutes.

Instead, the thermal environment inside the instrument has gradually reached a much more stable condition.

The first 30 minutes contain meaningful information—but that information primarily describes the startup thermal behavior, not necessarily the gyroscope's steady-state bias stability.

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Why Allan Variance Can Be Misleading During Startup

Allan variance is widely used to characterize gyroscope stability.

However, the quality of the Allan deviation curve depends strongly on the data segment being analyzed.

If the dataset contains a large startup thermal transient, the calculated result can be dominated by that transient rather than by the underlying stochastic noise processes of the gyroscope.

For example:

Immediately after power-on

→ source temperature changes
→ MIOC bias point moves
→ fiber-coil temperature gradients develop
→ detector/electronics drift
→ FOG bias changes

After thermal stabilization

→ temperature gradients decrease
→ optical parameters stabilize
→ bias becomes much more stationary
→ Allan deviation better represents the intrinsic steady-state behavior

Therefore, simply collecting a long dataset from the instant of power-on and calculating Allan variance does not automatically produce a valid assessment of the specified steady-state bias stability.

The startup portion must be treated according to the applicable test procedure.

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A Practical Test Procedure for 0.01°/h-Class FOGs

1. Allow Sufficient Warm-Up Time

Before measuring bias stability or scale factor, allow the gyroscope to reach the specified operating condition.

For systems where the manufacturer's specification or test procedure calls for approximately 30 minutes of warm-up, do not begin the final performance measurement immediately after power-on.

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2. Record Temperature Together with Gyroscope Output

Do not monitor only the gyro output.

Record:

• FOG output

• internal temperature, if available

• enclosure temperature

• ambient temperature

• temperature rate of change

The source recommends verifying that the temperature change rate has fallen to approximately 0.1°C/min or below before starting the steady-state Allan variance analysis.

This provides a much stronger indication that the measurement is no longer dominated by thermal transients.

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3. Remove the Startup Segment When Evaluating Steady-State Stability

If the objective is to evaluate the steady-state bias stability, exclude the startup period—or more precisely, the period during which the thermal state has not stabilized—from the final Allan variance analysis.

The source specifically recommends removing the first approximately 30 minutes, or otherwise excluding the temperature-unstable segment.

The exact duration should follow the manufacturer's specification and applicable test standard rather than being treated as a universal 30-minute rule.

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4. Consider Temperature Compensation for Fast-Start Applications

If the application requires the FOG to achieve high accuracy shortly after power-on, simply increasing the warm-up time may not be practical.

Temperature compensation can then become important.

The source cites a 2025 experiment in which a third-order compensation model incorporating both temperature and temperature rate reduced the reported FOG bias-stability figure from 0.0200°/h to 0.0055°/h, corresponding to an approximately 75% reduction in error.

However, compensation does not eliminate the underlying thermal physics.

The model must first be calibrated, and unmodeled thermal transients can still produce residual errors.

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What Can Be Done at the Hardware Design Stage?

If short startup time is an important requirement, the solution should be considered during the mechanical and optical design stage.

Potential approaches include:

Reduce Thermal Coupling

Minimize unwanted heat transfer from high-power or temperature-sensitive components to the fiber coil.

Optimize Fiber-Coil Winding

Highly symmetric winding structures can reduce the sensitivity of the coil to temperature gradients and therefore suppress the Shupe effect.

Improve MIOC Thermal Stability

Thermally optimized or appropriately treated lithium-niobate MIOCs can reduce temperature-dependent bias drift.

Improve Thermal Management

The overall package, substrate, heat paths, and thermal isolation should be designed as a complete system rather than optimizing individual components independently.

These approaches can reduce the effective thermal stabilization time, but they must be implemented during the design stage. They cannot be fully compensated for by changing the test procedure after the instrument has been built.

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The Key Engineering Lesson

When a FOG is specified at 0.01°/h but shows approximately 0.1°/h immediately after startup, the first question should not be:

“Is this gyroscope defective?”

Instead, ask:

“Has the gyroscope reached thermal equilibrium?”

During startup, several thermal mechanisms can contribute simultaneously:

Laser wavelength drift
→ scale-factor variation

MIOC thermo-optic drift
→ phase-bias variation

Temperature gradients in the fiber coil
→ Shupe non-reciprocal phase error

Detector and electronic temperature drift
→ baseline variation

These effects can make a high-precision FOG appear significantly less stable during the first several minutes of operation.

After the thermal state stabilizes, the measured bias can gradually approach the specified steady-state performance.

Therefore:

A 0.01°/h specification should be evaluated under its specified operating conditions—not immediately after power-on.

For high-precision FOG testing, warm-up time, temperature monitoring, data selection, and test methodology are part of the measurement itself.

The difference between “0.1°/h at startup” and “0.01°/h after stabilization” is not necessarily a contradiction in the specification.

It may simply be the difference between measuring the thermal transient and measuring the steady-state gyroscope.