It is well known that a continuous wave laser beam impinging on a nematic liquid crystals film can induce a change in the orientation of the molecular director. In the case of homeotropic alignment and for a p-polarized obliquely incident beam, the reorientation process has no threshold and the sample exhibits a giant optical nonlinearity due to the laser-induced change in refractive index of the medium. In the small distortion approximation the phase change is governed by a linear differential equation whose coefficients depend on the ratio between the elastic constants. In this paper we describe an interferometric technique based on high precision two-dimensional spatial fringe analysis Fourier method for measuring the elastic constants of nematic liquid crystals. Since the determination of the elastic anisotropy relies on the measurement of the ratios between the elastic constants, this technique provides a powerful and high accuracy method for characterizing nematic liquid crystals.