Design of thicknesses and refractive indexes measurement system combined with auto-focus system for multilayer transparent samples

The representative measurement techniques for determining the thickness and refractive index of transparent materials include ellipsometry, interferometry, and confocal methods. However, these methods are limited by the thickness range they can measure and do not account for non-parallel layers in multilayer transparent materials. In order to improve the deficiencies of these techniques, this study proposes a novel optical measurement system based on the fundamental theorem of geometrical optics. Through a simple optical structure, it can measure not only the thicknesses and refractive indexes of multilayer transparent samples, but also the inclination angles of non-parallel layers simultaneously. In addition, the measurement system, when combined with the auto-focusing system, can enhance the focusing efficiency. Firstly, we establish a mathematical model of the proposed measurement system using homogeneous transformations and the skew ray tracing method. The characteristic of the proposed measurement system is to use two lasers at different incident angles as the light sources. And then an image sensor would capture images of the spots reflected from each surface of the sample. After image processing, we obtain the positional information of the spots. Furthermore, the information is substituted into the mathematical model to determine the unknown sample properties. According to the determined properties, the defocus distance can be calculated in order to achieve auto-focusing. In this study, we utilize ZEMAX, an optical simulation software, to establish the system structure, analyze the system characteristics, and evaluate the system feasibility. Accordingly, a laboratory-built prototype is constructed, and the installation errors are compensated for by the proposed calibration method. Finally, experiments and result analysis are conducted to verify the feasibility of the proposed measurement system.