A cross-calibration approach for polarisation-sensitive detectors in CMB experiments: application to LiteBIRD's polarisation angle calibration
One of the current challenges in observational cosmology is obtaining high-precision polarisation maps of the CMB to measure primordial $B$-modes and constrain the tensor-to-scalar ratio ($r$). The weakness of this signal compared to foregrounds and $E$-to-$B$ leakage makes this task particularly challenging, requiring large detector arrays operating at multiple frequencies and extremely precise calibration. We present a cross-calibration algorithm to determine relative calibration of detectors within the same frequency band of a CMB experiment. The method iteratively compares single-detector maps with band-averaged maps and can be applied to any calibration parameter that can be observed and corrected at the map level, relaxing pre-flight calibration requirements and enabling post-processing validation. We validate the pipeline by calibrating the polarisation angle of simulated LiteBIRD observations, including both random detector miscalibration and wafer-level rotations. The algorithm converges to correct values with arcminute precision. Finally, we propagate residual calibration uncertainties through component separation and tensor-to-scalar ratio estimation pipelines using both parametric (FgBuster) and blind (HILC) methods. The induced bias on $r$ remains well below the LiteBIRD systematics budget of $\delta r < 6.5\times10^{-6}$, demonstrating that the method is suitable for next-generation CMB experiments.