The in situ measurement of the crystallization of amorphous silicon at 600 degreesC was carried out during the annealing of amorphous silicon-on-oxide samples inside a vertical furnace using spectroscopic ellipsometry. The ellipsometer arrangement was adapted to the furnace geometry using a special beam-guiding system to have a minimum impact on the furnace process performance. Modifications in the furnace geometry were restricted as far as possible, to show that a fast integration in an existing industrial equipment with minor costs can be done. The dielectric function of the changing structure was calculated using the Bruggeman-effective medium approximation (B-EMA). Two optical models were compared. In the first model, the crystallinity was described by the 'mixture' of single-crystalline silicon and amorphous silicon. A better fit was obtained using the second model, in which fine-grained polycrystalline silicon and amorphous silicon are used. The high-temperature reference data were obtained by a measurement on the annealed samples at the beginning and at the end of the annealing process. Using this method the crystallization can be monitored by the change of the ratio of amorphous and fine-grained polycrystalline silicon in the best-fit model.