Performance of the KAGRA photon calibrators during the fourth joint observing run with LIGO and Virgo

The KAGRA detector, located in Kamioka, Japan, is a kilometer-scale cryogenic gravitational-wave (GW) interferometer. It joined the fourth joint observing run (O4) in May 2023 in collaboration with the Laser Interferometer GW Observatory (LIGO) in the USA and the Virgo observatory in Italy. After one month of observations, KAGRA entered a break period to enhance its sensitivity to GWs, and has rejoined O4 in June 2025, which is currently ongoing and planned to continue until November 2025. To accurately recover the information encoded in the GW signals, it is essential to properly calibrate the telescope output signals. A photon calibration (Pcal) system was employed as a reference displacement injector to calibrate the output signals obtained from the telescope. In this paper, we present the methods used to estimate the uncertainty in the Pcal systems employed at KAGRA during O4. We investigated and quantified the uncertainty in the Pcal laser power sensors, which had the highest impact on the Pcal uncertainty, and measured the beam positions on the KAGRA end mirror, which had the second highest impact. We report an estimated overall system uncertainty of 0.63%, which is more than a factor of four lower than the uncertainty achieved in the previous third joint observing run (O3) in 2020. This estimate included, for the first time, correction for the Pcal-induced apparent displacement caused by unintended rotation of the end test mass, based on measured beam positions on the mirror surface. The Pcal systems in KAGRA are the first fully functional calibration systems for a cryogenic GW telescope. To avoid interference with the KAGRA cryogenic systems, the Pcal systems incorporate unique features regarding their placement and the use of telephoto cameras, which can capture images of the mirror surface at almost normal incidence. These images are used to quantify the laser beam positions on the mirror surface enabling correction for the impact of unintended rotation of the mirror caused by Pcal forces. As future GW telescopes, such as the Einstein Telescope, are expected to adopt cryogenic techniques, the performance of the KAGRA Pcal systems can serve as a valuable reference.