In-orbit calibration to the point-spread function of Insight-HXMT

We make the in-orbit calibration to the point-spread functions (PSFs) of the collimators of the Hard X-ray Modulation Telescope with the scanning observation of the Crab. We construct the empirical adjustments to the theoretically calculated geometrical PSFs. The adjustments contain two parts: a rotating matrix to adjust the directional deviation of the collimators and a paraboloidal function to correct the inhomogeneity of the real PSFs. The parameters of the adjusting matrices and paraboloidal functions are determined by fitting the scanning data with lower scanning speed and smaller intervals during the calibration observations. After the PSF calibration, the systematic errors in source localization in the Galactic plane scanning survey are 0^∘ . 010, 0^∘ . 015, 0^∘ . 113 for the Low-Energy Telescope (LE), the Medium-Energy telescope (ME) and the High-Energy telescope (HE), respectively; meanwhile, the systematic errors in source flux estimation are 1.8%, 1.6%, 2.7% for LE, ME and HE, respectively.