Luminosity measurements for the R scan experiment at BESIII

By analyzing the large-angle Bhabha scattering events $e^{+}e^{-}$ $to$ ($gamma$)$e^{+}e^{-}$ and diphoton events $e^{+}e^{-}$ $to$ $gammagamma$ for the data sets collected at center-of-mass (c.m.) energies between 2.2324 and 4.5900 GeV (131 energy points in total) with the upgraded Beijing Spectrometer (BESIII) at the Beijing Electron-Positron Collider (BEPCII), the integrated luminosities have been measured at the different c.m. energies, individually. The results are the important inputs for R value and $J/psi$ resonance parameter measurements.