Design of the full-sky scanning strategy and systematic effect control in a cosmic microwave background probe

The quest for primordial $B$-mode polarization signatures in the Cosmic Microwave Background (CMB) is a major goal of contemporary cosmology. Detecting these signatures would confirm primordial gravitational waves and allow precise determination of the tensor-to-scalar ratio, $r$, which is crucial for distinguishing between inflationary models. This requires high-precision, full-sky observations from space-based platforms to avoid atmospheric fluctuations and windows. Since $B$-mode signatures are much fainter than CMB temperature anisotropies, their detection requires well-designed calibration and mitigation strategies. Next-generation space observatories such as LiteBIRD, which use Half-Wave Plate (HWP) modulation technology, represent a significant advance. This technology allows single-detector observations, eliminating the need for pair-differential detection and its associated systematic complexities. The study begins with the optimization of scanning strategy parameters for missions with HWP to improve in-flight calibration, suppress systematic effects, and develop robust null-test methods. In addition, we present a method for calculating the impact of systematic effects on the estimation of $r$ using the SBM (Spin-Based Map-making) software framework, which performs fast map-making in spin space. This method allows the decomposition and elimination of systematic effects in terms of spins, and we demonstrate the elimination of several systematic effects.