A simple and sensitive interferometric technique which yields accurate measurements of the 2nd- , 4th-, and 6th-order coefficients of the series expansion for the radial distribution of the dielectric constant of SELFOC or other GRIN rods is reported. Such data are required, for example, in predicting temporal dispersion in SELFOC fiber waveguides. The interferometer directly measures the relative phase delay along meridional-ray paths of different initial field angles. The mathematical analysis consists of finding the 2nd-, 4th-, and 6th-order coefficients which yield the best least squares fit to the measured phase shifts. The 4th-order results are found to be in good agreement with those of I. Kitano and co-workers. As an experimental application we describe a small, mechanically stable, diffraction-limited collimator for use with an optical fiber waveguide.