Method for measuring the refractive index distribution of a GRIN lens with heterodyne interferometry

Abstract

Based on the Fresnel's equations and the heterodyne interferometry, an alternative method for measuring the refractive index distribution of a GRIN lens is presented. A light coming from the heterodyne light source passes through a quarter-wave plate and is incident on the tested GRIN lens. The reflected light passes through an analyzer and an imaging lens; finally it enters a CMOS camera. The interference signals produced by the components of the s- and the p-polarizations are recorded and they are sent to a personal computer to be analyzed. In order to measure the absolute phases of the interference signals accurately, a special condition is chosen. Then, the interference signals become a group of periodic sinusoidal segments, and each segment has an initial phase psi with the information of the refractive index. Consequently, the estimated data of psi are substituted into the special equations derived from Fresnel's equations, and the refractive index distribution of the GRIN lens can be obtained. Because of its common-path optical configuration, this method has both merits of the common-path interferometry and the heterodyne interferometry. In addition, the phase can be measured without reference signals.