Influence of eccentricity and tilt of radial GRIN lens on its thickness measurement by chromatic confocal technology

The chromatic confocal technology (CCT) has ultra-high distance measurement resolution and the characteristics of multi-surface tomography. Based on the principle of optical dispersion and confocal, the technology achieves accurate axial position or micro-displacement measurement. The radial gradient index (GRIN) lens is a typical important inhomogeneous material. Its refractive index gradually decreases from the center to the edge along the radial direction. We propose to measure the thickness of the radial GRIN lens based on CCT. The thickness measurement model is established by the ray-tracing method, the optical Lagrange function, and the ray arc differential in the Cartesian coordinate system. The refractive index distribution makes the eccentric tilt of the lens change the propagation of the probe light and affects the extraction of the peak of the spectral response causing the thickness measurement error. The influence of eccentricity and tilt of the radial GRIN lens on its thickness measurement is studied. The precision shift table drives the radial GRIN lens movement to simulate the eccentric tilt state of the lens under the dispersion probe. According to the comparative analysis between the experimental and simulation results, it is concluded that the greater the eccentric distance and inclination degree of the radial GRIN lens is, the greater the influence on the thickness measurement is. The larger the lens thickness is, the greater the measurement error is. For the radial GRIN lens with a thickness of 2.36 mm, the measurement error is about 20 μm when the eccentricity is 0.1 mm and the tilt is 6 deg. The research results have significance for optimizing the system structure and further improving the system performance for the application of the CCT in measuring non-homogeneous materials or optical thin film. And the research will encourage the development of GRIN lens instrument preparation and application technology by improving the thickness measurement accuracy and precision of the GRIN lens.