The evolution of the crystallization wave front and convective structures in a horizontal layer of supercooled water bounded by tempera- ture-controlled flat surfaces is visualized using methods of Hilbert optics. The phase transition is manifested by the occurrence of a crys- tallization wave and is accompanied by a positive energy release, which, in turn, affects the dynamic distribution of the optical phase density gradient in supercooled water and induces phase perturbations in the probing light field. The results of measurements of the phase velocity and the shape of the crystallization front approximated by Bezier curves are presented. The wave front velocity is obtained using modified time-of-fight method. The phase velocity field is found to exhibit spatio-temporal quasi-periodicity that can be related to the existence of oscillatory phenomena in the crystallization process.