🔬 optics

A 3D passive ring gyroscope for seismology

This paper presents a prototype of a transportable three-dimensional free-space passive ring gyroscope that achieves micro rad/s/sqrt(Hz) sensitivity across all spatial dimensions, demonstrating its capability to reconstruct the rotational components of simulated seismic events as a promising complement to existing seismological sensor technology.

Original authors: Thomas Gereons, Jannik Zenner, Thorsten Groh, Simon Stellmer

Published 2026-06-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thomas Gereons, Jannik Zenner, Thorsten Groh, Simon Stellmer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Earth as a giant, slightly wobbly spinning top. When an earthquake happens, the ground doesn't just shake up and down or side-to-side (like a person jumping); it also twists and turns. For a long time, scientists could only measure the "jumping" part. But to truly understand the earthquake, they need to measure the "twisting" part too.

This paper introduces a new, portable device designed to catch those twists in all three directions (up-down, left-right, and forward-backward) at the same time.

Here is a breakdown of how it works and what they found, using simple analogies:

The Problem: The "Blind" Seismometer

Traditional earthquake sensors are like a person standing on a boat who can only feel the boat bobbing up and down. They miss the boat rocking side-to-side or spinning around. To get the full picture of a seismic wave, you need a sensor that can feel all six ways the ground can move (three translations and three rotations).

The Solution: The "Tetrahedral" Gyroscope

The team built a prototype sensor shaped like a pyramid with four triangular faces (a tetrahedron).

The Shape: Imagine a hollow pyramid made of stainless steel rods. Inside each of the four triangular faces, there is a loop of light.
The Light: Instead of using a laser beam that generates its own light inside the loop (which can be messy and unstable), they use a "passive" approach. Think of it like a race track. They shine a very steady, external laser beam into the track.
The Race: They send two beams of light racing around the same triangular track: one clockwise and one counter-clockwise.
The Twist: If the track is perfectly still, both beams finish the lap at the exact same time. But if the track rotates (like the Earth twisting during an earthquake), the beam racing with the rotation has a slightly longer path to run, while the one racing against it has a shorter path. This creates a tiny difference in their arrival times.

How They Measure the Twist

The device doesn't just "see" the light; it listens to the beat between the two racing beams.

The Analogy: Imagine two singers holding the exact same note. If one singer speeds up slightly, you hear a "wah-wah-wah" sound (a beat frequency). The faster the track spins, the faster the "wah-wah" sound becomes.
The Tech: The scientists use a high-tech electronic system (called PDH locking) to keep the lasers perfectly tuned to the track. If the Earth twists, the system has to adjust the speed of the light to keep it in sync. By measuring how much they have to adjust the speed, they can calculate exactly how fast the ground is twisting.

What They Tested

To prove it worked, they didn't wait for an earthquake. Instead, they put the whole pyramid on a table and physically shook and tilted the table to simulate an earthquake.

They compared their new device to a standard, commercial sensor (a MEMS gyroscope) sitting right next to it.
The Result: Their new device tracked the twisting motion almost perfectly, matching the commercial sensor but with much higher sensitivity. It successfully reconstructed the 3D rotation of the table in real-time.

How Sensitive Is It?

The device is incredibly sensitive.

The Scale: It can detect rotations as small as a few microradians per second. To visualize this: imagine the Earth is a giant clock. This sensor is sensitive enough to detect if the second hand moved a tiny fraction of a hair's width.
The Noise: Like any sensitive instrument, it hears some background noise.
- Low Frequencies: It hears "flicker" noise (like a slow, drifting hum).
- High Frequencies: It hears "white" noise (like static on a radio).
- Specific Noises: They found that the device was sensitive to air currents from a lab fan (HEPA filter) and vibrations from the electronics. This suggests that if they put the device in a vacuum (no air) and stabilized the temperature better, it could become even more sensitive.

Why This Matters (According to the Paper)

The authors claim this is a portable version of a technology that usually requires massive, room-sized machines.

Transportability: Unlike the giant ring lasers that are bolted into the ground in specific locations, this device is small enough to be carried to different sites.
The Goal: This allows scientists to set up temporary "sensor arrays" in different places to map out exactly how seismic waves twist the ground, which helps them understand the physics of earthquakes better.

In summary: The team built a portable, pyramid-shaped "light race track" that can detect the tiniest twists in the ground. They proved it works by shaking a table and showed that it can measure 3D rotation with high precision, offering a new tool for understanding earthquakes without needing a massive, permanent installation.

Technical Summary: A 3D Passive Ring Gyroscope for Seismology

Problem Statement
In seismology and geodesy, a complete physical description of ground motion requires the measurement of all six degrees of freedom (6 DoF), including both translational and rotational components. While traditional sensors capture translation, rotational measurements are essential for the full reconstruction of seismic wavefields and the understanding of complex ground motion. Current solutions face a trade-off: large-scale active ring laser gyroscopes (RLGs) offer unmatched sensitivity but lack transportability, while fiber-optic gyroscopes (FOGs) are compact but suffer from limitations such as Rayleigh backscattering and thermally induced refractive-index fluctuations. There is a need for compact, transportable rotational sensors that can achieve sensitivities comparable to large-scale installations to enable flexible deployment in diverse seismic environments.

Methodology
The authors present a prototype of a transportable, three-dimensional free-space passive ring gyroscope (PRG). The system utilizes a tetrahedral geometry consisting of four corner blocks connected by twelve stainless-steel rods, forming four independent triangular ring cavities.

Optical Design: Each cavity has a perimeter of 1.5 m (side length $L=0.5$ m) and is formed by plano-concave mirrors with a transmission of $\approx 30$ ppm. The system operates with a free spectral range of 200 MHz and cavity finesse values between 25,000 and 45,000.
Laser Source & Stabilization: A commercial single-frequency fiber laser (1550 nm, <100 Hz linewidth) serves as the external source. Light is split into clockwise (CW) and counter-clockwise (CCW) directions. The system employs the Pound-Drever-Hall (PDH) technique for frequency stabilization, controlled by a field-programmable gate array (FPGA).
Frequency Control: To lock the laser to the cavity resonance, the light is frequency-shifted by acousto-optic modulators (AOMs). The rotation signal is derived electronically from the difference in the radio-frequency drive signals applied to the AOMs in the two propagation directions, rather than relying on optical beat detection.
3D Reconstruction: The tetrahedral layout provides four independent cavity signals. Three non-coplanar cavities are used to reconstruct the full 3D rotation vector via a transformation matrix based on the cavity normal vectors. The fourth cavity serves as an overconstrained element for potential noise reduction and consistency checks.
Slow Feedback: To compensate for perimeter drifts caused by environmental factors and machining tolerances, one mirror in each angled cavity is mounted on a piezoelectric actuator with a slow feedback loop, reducing average drift from 1 MHz/min to 8 kHz/min.

Key Contributions

Prototype Development: The successful construction of a transportable, three-dimensional free-space PRG system capable of measuring rotation in all spatial dimensions.
Signal Processing: Implementation of an electronic readout scheme where the Sagnac frequency is determined by the difference in AOM drive frequencies, allowing for compact fiber-based operation without bulky free-space optics for detection.
Performance Demonstration: Validation of the system's ability to reconstruct rotational components of simulated seismic events and characterize its noise floor.

Results

Sensitivity: The system achieves sensitivities in the $\mu\text{rad/s}/\sqrt{\text{Hz}}$ regime across all three spatial dimensions. Specifically, the white-noise-limited sensitivities are $A_x = 7$ , $A_y = 2$ , and $A_z = 3 \, \mu\text{rad/s}/\sqrt{\text{Hz}}$ . The best overall sensitivity reaches $6 \, \mu\text{rad/s}$ at an integration time of 0.4 s for the vertical axis.
Validation: Controlled tilting of the optical table to simulate seismic events (rotations around x, y, and z axes, and translation) demonstrated that the reconstructed rotation vector shows good agreement with a commercial MEMS gyroscope reference.
Noise Characterization:
- Low Frequency: The z-axis exhibits $1/f$ flicker noise below 1 Hz, while the y-axis shows flicker noise up to 10 Hz. The x-axis displays a steeper slope indicative of Brownian noise ( $1/f^2$ ) below 1 Hz, likely due to environmental temperature fluctuations affecting the refractive index of air.
- High Frequency: The system is dominated by white noise at higher frequencies.
- Specific Peaks: Distinct noise peaks were identified at 15 Hz (piezo vibrations), 50 Hz (electronic interference), 64 Hz (HEPA filter fan), and 77 Hz (FPGA electronics).
Limitations: The authors note that the x-axis performance is lower than the others, attributed to the reconstruction algorithm requiring data from all three cavities (accumulating noise) and the inclusion of a cavity with lower finesse (25,000). The current sensitivity is limited by air movements and temperature instabilities affecting the refractive index of the air.

Significance and Claims
The paper claims that this prototype demonstrates the feasibility of compact, transportable three-dimensional free-space PRG systems for rotational seismology. While the current sensitivity is in the $\mu\text{rad/s}/\sqrt{\text{Hz}}$ range—below the theoretical $n\text{rad/s}/\sqrt{\text{Hz}}$ limit predicted for a system limited solely by shot noise—the authors assert that the device successfully resolves controlled rotational excitations mimicking seismic signals.

The significance lies in the potential to combine the high sensitivity of ring laser technology with the transportability of fiber-optic systems. The authors suggest that enclosing the system in a vacuum and implementing active thermal stabilization could enhance performance by orders of magnitude, potentially approaching the theoretical limit. Such instruments could enable local full-vector reconstruction of seismic wavefields, improve seismic source characterization, and facilitate the deployment of distributed international arrays for rotational ground-motion monitoring in regions with sparse instrumentation.