The optical-fiber-based dosimeter of the LUMINA project was deployed in August 2021 in the International Space Station in the framework of the Alpha mission. The sensing elements of the dosimeter are P-doped optical fibers, which were proven to be excellent candidates for dosimetry applications. The twofold objective of this paper is to provide a theoretical model for the radiation response of the dosimeter and to report on the experimental work carried out at CERN for the qualification and calibration of the engineering model of the LUMINA dosimeter. Combining the theoretical response and experimental data, the calibration curve of the flight model is obtained. Finally, this study broadens the investigation of the room temperature radiation response of P-doped optical fibers in a range of dose rates 104 times lower than previously reported, from 21µGy(SiO2)/h to145mGy(SiO2)/h.