🔭 astrophysics

From the Virgo interferometer calibration to the bias and uncertainty of the h(t) detector strain during the O4 run

This paper outlines the Virgo interferometer's calibration procedures for the O4b run, detailing how intercalibrated Photon Calibrators achieved 0.48% mirror displacement precision and how a new frequency-dependent method enabled online unbiasing of the h(t) strain signal to reach 2% modulus and 30 mrad phase accuracy across the 10 Hz to 2 kHz band.

Original authors: Cervane Grimaud, Florian Aubin, Benoît Mours, Thierry Pradier, Loïc Rolland, Monica Seglar-Arroyo, Hans Van Haevermaet, Pierre Van Hove, Didier Verkindt

Published 2026-07-16

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CC BY 4.0

Original authors: Cervane Grimaud, Florian Aubin, Benoît Mours, Thierry Pradier, Loïc Rolland, Monica Seglar-Arroyo, Hans Van Haevermaet, Pierre Van Hove, Didier Verkindt

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 universe as a giant, invisible ocean. Most of the time, it's calm, but sometimes, massive objects like black holes or neutron stars crash into each other, sending out ripples that travel across space at the speed of light. These ripples are called gravitational waves. They are so faint that by the time they reach Earth, they stretch and squeeze space itself by a distance smaller than the width of a single atom. To catch these whispers, scientists built giant, ultra-sensitive ears called interferometers. These machines use lasers to measure the tiny distance between hanging mirrors. If a gravitational wave passes through, it changes the distance between the mirrors just a tiny bit, and the laser light tells us about it. But here's the tricky part: the machine itself is noisy. It vibrates from earthquakes, traffic, and even the wind. To hear the universe's ripples, scientists have to be incredibly precise about how their machine moves and reacts. If they don't know exactly how their "ear" is tuned, they might think a noise from a passing truck is a signal from a black hole, or worse, they might miss the real signal entirely. This is the challenge of calibration: making sure the instrument's reading matches reality perfectly.

This paper is about the team behind the Virgo interferometer, a massive detector in Italy, and how they tuned their instrument for a new listening period called the O4 run, which started in April 2024. Think of the detector's output as a song recorded on a tape. The "song" is the gravitational wave signal, but the tape recorder (the detector) has its own quirks and distortions. The authors explain how they fixed these distortions to ensure the song sounds exactly as it was played. They describe a process of "tuning" the detector using two special tools. The first is like a giant, spinning weight that creates a known gravitational tug on the mirrors, acting as a ruler for very low frequencies. The second is a "Photon Calibrator," which uses the gentle push of a laser beam to nudge the mirrors. This laser push is like a tiny, precise finger tapping the mirror to see how it responds. By comparing how the mirrors move when pushed by the laser versus how they move when controlled by the machine's own motors, the team could build a perfect map of how the detector behaves.

The main finding of this paper is that the team successfully created a new, smarter way to correct the detector's data in real-time. Before, the data might have had a slight "bias," meaning the recorded signal was a little too big or too small, or slightly out of sync in time. The authors developed a method to measure this bias using special test signals (called "lines") that are injected into the system constantly or weekly. They found that by using these test signals, they could correct the data online, removing the bias so that the final signal is much truer to reality. Specifically, they achieved a precision where the size of the signal (modulus) is accurate to within 2% and the timing (phase) is accurate to within 30 milliradians across a wide range of frequencies (from 10 Hz to 2 kHz). They also created a new way to calculate the "uncertainty" or the margin of error for every single frequency, rather than just giving one average number for the whole range. This means scientists now have a much clearer picture of how sure they can be about the signals they are detecting. The paper confirms that this new method works, showing that the remaining errors after correction are very small, less than 2% for the signal size in the most important frequency range. This improvement is crucial because it ensures that when the Virgo detector hears a cosmic event, the story it tells us about the universe is as accurate as possible.

Technical Summary: Virgo Interferometer Calibration and $h(t)$ Strain Reconstruction in O4

Problem Statement
Since the first gravitational wave detection in 2015, the sensitivity of ground-based interferometers has improved significantly, necessitating highly precise calibration to ensure the accurate reconstruction of the detector strain signal, $h(t)$ . The Virgo interferometer measures tiny length variations (on the order of $10^{-18}$ m) between suspended test masses. To detect these signals, the interferometer must be maintained in a specific observing configuration using feedback loops and electromagnetic (EM) actuators. The reconstruction of $h(t)$ from the dark fringe signal requires accounting for all control signal contributions and the frequency response models of the mirror actuators. These models rely on independent references for mirror displacement. A primary challenge is achieving precise, frequency-dependent calibration across the observation band (10 Hz to 2 kHz) and accurately quantifying the bias and uncertainty of the reconstructed strain to support low-latency and offline data analysis.

Methodology
The paper outlines the calibration procedures and reconstruction monitoring strategies implemented for the O4 run (specifically O4b, starting April 2024).

Actuator Calibration References:
- Newtonian Calibrator (NCal): Uses rotating masses to induce a known gravitational field, serving as the absolute reference for mirror displacement with an uncertainty of 0.12%. However, it is limited to frequencies up to 150 Hz and single-frequency operation.
- Photon Calibrator (PCal): Uses radiation pressure from an auxiliary laser to induce displacement. It complements the NCal for the 10 Hz to 2 kHz band with a precision of 0.48%. The displacement $\Delta x_{PCal}$ is calculated using the mechanical response model, laser incidence angle, reflected power, and sensor chain response.
- Calibration Process: The PCal is used to calibrate the EM actuators. This is achieved by comparing the interferometer's response to injections from the reference actuator (PCal) and the actuator under test, allowing the extraction of the new actuator's response model.
Strain Reconstruction ( $h(t)$ ):
- The reconstruction algorithm, Hrec, subtracts the contributions of longitudinal control signals from the dark fringe signal using the calibrated actuator responses.
- Monitoring: The reconstruction quality is monitored via the transfer function $h_{raw}/h_{inj}$ , where $h_{raw}$ is the reconstructed strain and $h_{inj}$ is the strain computed using only the actuator's calibration model. Deviations from unity (modulus) and zero (phase) indicate reconstruction bias.
- Injection Signals: Two types of signals are used for monitoring:
  - Permanent Lines: 16 sinusoidal signals (16 Hz to 1 kHz) injected continuously.
  - Weekly Lines: 27 sinusoidal signals (18 Hz to 1158 Hz) injected for one minute weekly.
Bias and Uncertainty Computation:
- A new method was developed to compute frequency-dependent bias and uncertainty, enabling online unbiasing of the strain.
- Bias Calculation: Uses data from the Weekly Lines. The modulus and phase values are averaged over a time period (typically one month). A Gaussian distribution is generated for each line, and random sets of points are selected to perform linear interpolation across the frequency range (10 Hz to 10 kHz). This yields a frequency-dependent bias estimate used to correct $h_{raw}$ to $h_{unbias}$ .
- Uncertainty Calculation: Uses data from the Permanent Lines applied to the unbiased strain ( $h_{unbias}$ ). This approach captures systematic uncertainties arising from short-timescale variations (e.g., alignment or optical response changes < 1 hour).
- Total Uncertainty: The reconstruction uncertainty is combined quadratically with calibration uncertainties (including a conservative 0.6% PCal uncertainty and 0.5% actuator model uncertainty for modulus, and 5 mrad for phase). Additional errors near 50 Hz and 150 Hz (power supply harmonics) are included.

Key Results

Precision: In the 10 Hz to 2 kHz band, the reconstructed strain achieves a precision of 2% in modulus and 30 mrad in phase.
Unbiasing Performance: The online unbiasing process reduces the residual bias to < 2% (modulus) over 10 Hz to 1 kHz and < 1% over 30 to 500 Hz. The residual phase bias is < 15 mrad from 10 to 1 kHz.
Stability: The reconstruction bias was found to be very stable over time, requiring updates only twice over a 16-month period.
Overall Uncertainty: The total strain reconstruction uncertainty is below 2.5% in modulus for the 10 Hz to 1 kHz band. For phase, it remains within 25 mrad below 200 Hz, increasing to 100 mrad at 1 kHz.

Significance and Claims
The paper claims that the primary significance of this work lies in the implementation of online unbiasing and the development of a frequency-dependent uncertainty computation method for the Virgo detector.

Unlike the O3 run, where such online corrections were not performed, O4 features an $h(t)$ strain that is unbiased in real-time (with a latency of ~10 s) before distribution to low-latency analysis pipelines.
The methodology improves upon previous O3 practices by replacing frequency-independent uncertainty estimates with a conservative, frequency-dependent reconstruction uncertainty over the 10 Hz to 2 kHz band.
The system allows for monthly monitoring of residual bias and uncertainties, ensuring that data quality is tracked and that periods of poor quality can be identified (where $h(t)$ is set to zero).
The work establishes a robust framework for the Virgo interferometer to provide high-fidelity strain data to the LIGO-Virgo-KAGRA (LVK) collaboration, essential for accurate gravitational wave source characterization.

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