The dependence functions of relative optical air mass on apparent solar zenith angle θ have been calculated over the θ < 87°range for the vertical profiles of wet-air molecular number density in the Arctic and Antarctic atmospheres, extinction coefficients of different aerosol types, and molecular number density of water vapor, ozone, nitrogen dioxide, and oxygen dimer. The calculations were made using as weight functions the seasonal average vertical profiles of (i) pressure and temperature derived from multiyear sets of radiosounding measurements performed at Ny-Ålesund, Alert, Mario Zucchelli, and Neumayer stations; (ii) volume extinction coefficients of background summer aerosol, Arctic haze, and Kasatochi and Pinatubo volcanic aerosol measured with lidars or balloon-borne samplings; and (iii) molecular number concentrations of the above minor gases, derived from radiosonde, ozonesonde, and satellite-based observations. The air mass values were determined using a formula based on a realistic atmospheric air-refraction model. They were systematically checked by comparing their mutual differences with the uncertainties arising from the seasonal and daily variations in pressure and temperature conditions within the various ranges, where aerosol and gases attenuate the solar radiation most efficiently. The results provide evidence that secant-approximated and midlatitude air mass values are inappropriate for analyzing the Sun photometer measurements performed at polar sites. They indicate that the present evaluations can be reliably used to estimate the aerosol optical depth from the Arctic and Antarctic measurements of total optical depth, after appropriate corrections for the Rayleigh scattering and gaseous absorption optical depths.