Characterization of integrating-sphere systematic effects for photon calibration of the KAGRA gravitational wave detector
Photon calibration (Pcal) systems are essential for accurately reconstructing gravitational-wave strain in laser interferometric detectors. In the KAGRA Pcal system, the laser power applied to the end test mass is measured using integrating-sphere power sensors. During the first part of the fourth observing run (O4a), repeated calibration measurements showed scatter larger than expected from the uncertainties assigned to individual measurements. Although this excess scatter was empirically reflected in the previously reported calibration uncertainties, its physical origin was not identified. In this study, we experimentally characterize the response of the integrating spheres used in the KAGRA calibration chain with respect to three incident-beam conditions: incidence angle, polarization, and beam position. Based on these measurements and the reproducibility of the integrating-sphere placement in each calibration configuration, we evaluate the corresponding systematic uncertainties and explicitly incorporate them into the uncertainty model for the O4a Pcal-X calibration measurements. The inclusion of these previously unmodeled effects substantially improves the consistency between the estimated uncertainties and the observed scatter, particularly for calibration parameters measured at the KAGRA end station, where the reduced chi-square values decrease from values as large as $10^3$ to values of order unity to several. These results indicate that variations in the incident-beam conditions of integrating-sphere power sensors account for a substantial part of the previously unexplained scatter and establish a more physically motivated framework for evaluating Pcal laser-power calibration uncertainty. They also provide a basis for future reduction of the calibration uncertainty through improved control of the incident-beam conditions.