Additional Error of Optical Path Measurement Caused by Radial GRIN Lens With Mispositioned Sample

Radial gradient index (GRIN) lens is widely used in optical path measurement based on white light interferometry (WLI), yet the additional error caused by the GRIN lens when the sample under test (SUT) is not at the ideal position has rarely been discussed. To deal with this problem, a ray-tracing model is established to reveal the influence of angular tilt and axial offset of SUT when GRIN lens is applied. Simulations based on WLI are done using the parameters of a real GRIN lens. The results show that the maximum additional optical path change is as larger as $0.99~\mu \text{m}$ within the range of ±0.1° angular tilt and $\pm 2000~\mu \text{m}$ axial offset of SUT, which can be regarded as additional error if the influence of GRIN lens is ignored. Experimental results of optical path change and insertion loss at different tilt angles of SUT simultaneously agree well with one set of simulation.