The two refractive indices in the flow of a colloidal birefringent liquid are measured separately by means of a Mach-Zehnder interferometer. For a quantitative evaluation of the resulting interferograms it is not necessary to linearize the respective equations relating the refractive index distribution to the deformation velocity in the flow. Therefore it becomes possible to perform velocity measurements in the non-Newtonian flow range. An additional measurement of the mean flow rate enables one to determine the velocity field without the need of a calibration of the observed interference fringes.