The annealing process of an amorphous silicon (a-Si) film has been studied by means of spectroscopic ellipsometry (SE). Measured SE spectra were analyzed using an empirical dielectric function (EDF) proposed in a previous paper and a refractive index function proposed by Forouhi and Bloomer (FB). We found several remarkable facts : (1) our EDF fits to measured spectra much better than FB; (2) the FB refractive index function does not satisfy Kramers-Kronig relations; (3) an adsorption layer should be taken into account to improve the fitting of SE spectra measured in air; (4) the thickness of a-Si deposited by r.f. glow discharge at 250 degrees C decreases more than 10% by annealing at 550 degrees C due to hydrogen evolution; (5) peak position and peak height of the dielectric function changes systematically with the annealing so that an analysis using the effective medium approximation (EMA) with a-Si and voids cannot explain these changes; (6) the EMA interface layer model cannot explain the optical behavior of a rough surface.