Two-dimensional refractive index distribution measurement of a GRIN lens

Based on the Fresnel's equations and the phase-shifting method, an alternative method for measuring the refractive index distribution of a GRIN lens is presented. A linearly/circularly polarized light in order enters a modified Twyman-Green interferometer, in which an electro-optical modulator is used as a phase shifter. In the interferometer, the light beam is divided by a beam-splitter into two beams, a reference beam and a test beam. After they are reflected by a plane mirror and the tested GRIN lens, respectively, they are combined together and pass through an analyzer. The analyzer extracts the same polarized components to interfere each other, and the full-field interference signals produced by the components of the s- and the p-polarizations can be obtained. The full-field interference signals are taken by a CMOS camera. The phase differences can be obtained by using the four-step phase-shifting interferometric method. Substituting these two groups of data into special equations derived from Fresnel equations, and the two-dimensional refractive index distribution of the GRIN lens can be calculated. Its validity is demonstrated and has some merits such as simple optical configuration, easy operation and high resolution.