A method for the absolute measurement of population densities of selected atomic helium levels, which has been applied on the tokamak TEXTOR at the Forschungszentrum Jülich in Germany, is presented. The method is based on the resonant excitation of selected levels by a high-power, narrow-band, pulsed laser beam saturating the optical pumping process. Observation of the fluorescence response is performed at the laser wavelength and elsewhere in the spectrum: this gives information on collisional population transfer between some excited levels. Data analysis, as required for the derivation of absolute population densities, includes due consideration of the Zeeman splitting of spectral lines in a strong magnetic field. The first results of the measured population densities are compared with those provided by simulation based on the collisional-radiative model for atomic helium in the edge of fusion plasmas. This code has been extended to include the laser interaction with atomic helium, in order to simulate the measured time traces of radiation from the laser-perturbed levels. A combination of this simulation procedure with laser-induced fluorescence measurements is suggested as a possible method for determining the electron density in the edge plasma.