A broad absorption band around 0.72 eV, assigned to the absorption of Nb4+ polarons, is observed in strontium barium niobate (SBN) crystals (nominally pure or Cr- or Ce-doped) either under illumination at low temperature or after a previous reduction treatment. The absorption spectra of Nb4+ polarons at low temperature show considerable dichroism, which in reduced SBN crystals exists even far above room temperature. The peak position of the Nb4+ polaron absorption in reduced SBN crystals shifts to higher energies with decreasing temperature. The dependence on light intensity and temperature of the Nb4+ polaron absorption during the build-up process under illumination and the decay process after the illumination is switched off are investigated in detail. Compared with pure SBN, doping with Ce or Cr creates additional absorption bands in the visible (2.6 eV) and red (1.9 eV for Cr doping) spectral regions. Illumination in these absorption bands at low temperature gives rise to strong Nb4+ polaron absorption in the NIR (0.72 eV), giving evidence of the enhanced sensitivity even in the red spectral region for SBN:Cr. The light-induced charge transfer process and formation of Nb4+ polarons in SBN are briefly discussed.