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Photon Calibration Performance of KAGRA during the 4th Joint Observing Run (O4)

This paper reports that KAGRA's photon calibration system achieved a record-low uncertainty of 0.79% during the O4 observing run, representing a threefold improvement over O3 and establishing a critical reference for future cryogenic gravitational-wave detectors.

Original authors: Dan Chen, Shingo Hido, Darkhan Tuyenbayev, Dripta Bhattacharjee, Nobuyuki Kanda, Richard Savage, Rishabh Bajpai, Sadakazu Haino, Takahiro Sawada, Takahiro Yamamoto, Takayuki Tomaru, Yoshiki Moriwaki

Published 2026-05-25

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CC BY 4.0

Original authors: Dan Chen, Shingo Hido, Darkhan Tuyenbayev, Dripta Bhattacharjee, Nobuyuki Kanda, Richard Savage, Rishabh Bajpai, Sadakazu Haino, Takahiro Sawada, Takahiro Yamamoto, Takayuki Tomaru, Yoshiki Moriwaki

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

The Big Picture: Tuning the Cosmic Microphone

Imagine KAGRA as a giant, ultra-sensitive microphone designed to "hear" the ripples in space-time caused by colliding black holes. These ripples are called gravitational waves.

However, this microphone is so sensitive that even the tiniest vibration from the Earth or a passing truck could drown out the cosmic signal. To make sure the microphone is working correctly, the scientists need to "calibrate" it. Calibration is like checking a ruler: you need to know exactly how long a "tick" on the ruler is so you can measure things accurately.

In this paper, the team explains how they calibrated KAGRA during its 2023 observing run (called O4) and proved that their "ruler" is incredibly accurate—much better than it was in previous years.

The Problem: How Do You Measure the Unmeasurable?

Gravitational waves stretch and squeeze space itself. To measure this, KAGRA uses lasers bouncing between mirrors. But how do you know the laser is measuring the stretch correctly? You can't just ask the mirror, "Did you move?"

The Solution: The "Photon Calibrator" (Pcal)
The scientists used a clever trick called Photon Calibration.

The Analogy: Imagine you have a very delicate scale. To test if it's working, you gently blow on it with a known amount of air to see how much it moves.
The Reality: The KAGRA team shot a special, modulated laser beam at the main mirror. Because light carries momentum, when the laser hits the mirror, it gives the mirror a tiny, known "push" (radiation pressure).
The Result: By knowing exactly how hard the laser pushed, they could calculate exactly how much the mirror should have moved. They then compared this expected movement to what the detector actually recorded. If they matched, the detector was calibrated correctly.

The Challenge: The Frozen Mirror

KAGRA is unique because its mirrors are kept at cryogenic temperatures (colder than -250°C) to reduce noise. This is like trying to tune a violin while wearing thick winter gloves; you can't touch the strings directly without messing up the temperature.

Because the mirrors are frozen, the scientists couldn't put their calibration equipment right next to them. They had to set up the laser system 34.9 meters away (about the length of a bus) to avoid warming up the mirrors.

The Analogy: Imagine trying to hit a bullseye on a dartboard from across a football field, but you can't walk closer because the floor is slippery ice.
The Fix: They used special "telephoto cameras" (like a high-powered zoom lens) to take pictures of the mirror from that distance. This allowed them to see exactly where the laser beam was hitting the mirror, even from far away.

The Results: A Sharper Ruler

The main goal of the paper was to figure out how much "fuzziness" or uncertainty exists in their measurement.

Previous Attempt (O3): In 2020, their measurement had an uncertainty of about 3%. This is like saying, "This ruler is 1 meter long, give or take 3 centimeters."
New Attempt (O4): In 2023, they improved the process and reduced the uncertainty to 0.79%. Now, they can say, "This ruler is 1 meter long, give or take less than 1 centimeter."

Why is this important?
The paper states that this level of precision is three times better than before. This means when KAGRA detects a signal from a black hole collision, the scientists can be much more confident about the details of that event (like how heavy the black holes were).

What Caused the Errors?

The scientists broke down where the tiny errors came from. They found two main "culprits":

The Power Sensor: Measuring exactly how much power the laser beam had was the biggest source of error. It's like trying to guess the exact volume of water in a cup just by looking at it.
The Beam Position: Knowing exactly where the laser hit the mirror was the second biggest source of error. If the laser hits the edge of the mirror instead of the center, the "push" is different.

The Takeaway

This paper doesn't claim to find new black holes or change how we treat diseases. Instead, it is a technical report on quality control.

The authors successfully demonstrated that KAGRA's "calibration system" works perfectly in a frozen environment. They proved that by using long-distance lasers and zoom cameras, they can measure the movement of a mirror with extreme precision. This success serves as a blueprint for future, even bigger telescopes (like the Einstein Telescope) that will also need to operate in freezing conditions to hear the faint whispers of the universe.

Technical Summary: Photon Calibration Performance of KAGRA during the 4th Joint Observing Run (O4)

Problem Statement
Accurate calibration of gravitational-wave (GW) detector signals is essential for recovering the physical information encoded in GW events. As detector sensitivity increases, the uncertainty in calibration becomes a critical factor in the parameter estimation of GW sources. KAGRA, a cryogenic GW detector, faced unique challenges in implementing a calibration system due to its low-temperature environment. The primary challenge was to design a Photon Calibration (Pcal) system that could inject reference signals without interfering with the cryogenic infrastructure surrounding the End Test Mass (ETM) mirrors. Furthermore, the system required rigorous uncertainty quantification to ensure that calibration errors did not dominate the overall data uncertainty, particularly given that previous observing runs (O3) exhibited higher uncertainty levels.

Methodology
The study details the configuration, operation, and uncertainty estimation of the KAGRA Pcal system during the O4a observing period (May–June 2023). The system utilizes two laser beams (Path 1 and Path 2) projected onto the ETM to induce calibrated displacements via radiation pressure.

System Configuration:
- Placement: To avoid thermal interference with the cryogenic ducts and coolers, the Pcal system components (transmitter and receiver modules) are located 34.9 meters away from the ETM.
- Beam Geometry: Two beams are used to minimize the excitation of the drumhead mode of the ETM, which couples strongly to the interferometer's average length. The beams are positioned near the nodal circle of this mode.
- Optical Setup: A Yb fiber laser (1047 nm) generates stable beams modulated by Acousto-Optic Modulators (AOMs). An Optical Follower Servo (OFS) stabilizes the laser power.
- Beam Position Monitoring: A telephoto camera (Tcam) system, consisting of a high-sensitivity CMOS camera and a 1,500 mm focal length telescope, captures images of the ETM surface to estimate beam positions.
Calibration and Uncertainty Estimation:
- Power Sensor Calibration: The laser power sensors (TxPDs and RxPD) were calibrated using a traceable chain: NIST $\rightarrow$ LIGO Gold Standard (GSK) $\rightarrow$ KAGRA Working Standard (WSK) $\rightarrow$ KAGRA End Station Sensors. This involved comparative measurements using integrating spheres to determine responsivity ratios ( $\alpha$ ).
- Power Estimation: The total laser power ( $P$ ) on the ETM was estimated by combining measurements from TxPDs and RxPDs, accounting for optical efficiencies ( $e$ ) and separation ratios ( $s$ ) of the two paths.
- Beam Position Estimation: The positions of the Pcal beams ( $\vec{a}$ ) and the main interferometer beam ( $\vec{b}$ ) were determined by analyzing Tcam images. The ETM geometry and suspension wires served as references for pixel-to-millimeter conversion.
- Uncertainty Propagation: The total relative uncertainty was calculated by propagating errors from all parameters in the displacement equation, including laser power ( $P$ ), beam positions ( $\vec{a} \cdot \vec{b}$ ), ETM mass ( $M$ ), moment of inertia ( $I$ ), and incident angle ( $\theta$ ).

Key Results

Total Uncertainty: The estimated relative uncertainty for the Pcal-X system (the primary calibration system used in O4a) is 0.73%.
Improvement over O3: This represents a reduction by a factor of approximately three compared to the 3% uncertainty achieved during the O3GK run.
Uncertainty Breakdown:
- Laser Power ( $P$ ): The dominant contributor to the total uncertainty (0.67%), primarily limited by the stability of the power sensor calibration parameters.
- Beam Position ( $\vec{a} \cdot \vec{b}$ ): The second-largest contributor (0.30%), derived from the Tcam image analysis.
- Incident Angle ( $\cos \theta$ ): Contributed minimally (0.0019%) due to the long baseline (34.9 m) between the Pcal system and the ETM, which results in a very small incident angle close to normal incidence.
- Mass and Inertia: Contributions from ETM mass ( $M$ ) and moment of inertia ( $I$ ) were negligible (<0.05%).
Stability: The calibration parameters (responsivity ratios, optical efficiencies, and separation ratios) demonstrated stability over a six-month period, with variations generally less than 0.6%.

Significance and Claims
The paper asserts that the KAGRA Pcal system is the first fully functional calibration system for a cryogenic GW telescope. Its successful operation demonstrates that high-precision calibration can be achieved despite the constraints imposed by cryogenic shielding and the need for remote placement of optical components.

The authors claim that the achieved uncertainty of 0.73% is sufficiently low to ensure that calibration errors do not significantly impact the estimation of GW source parameters, given the signal-to-noise ratios of observed events. Furthermore, the performance and design strategies of the KAGRA Pcal system serve as a valuable reference for future third-generation cryogenic GW detectors, specifically the Einstein Telescope (ET) and Cosmic Explorer (CE), which are expected to adopt similar low-temperature techniques. The study highlights that while beam position monitoring remains a challenge, the current methodology using telephoto cameras is effective, and future improvements could involve more continuous monitoring during observation runs.