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<p>To address the limitations of current technologies and equipment in simultaneously measuring multiple parameters of spherical transparent materials, this study proposes an innovative optical measurement system to simultaneously measure the radius of curvature, thickness, and refractive index of spherical transparent materials. While existing methods for measuring spherical transparent materials can independently determine the radius of curvature, thickness, and refractive index, they are typically costly and limited in scope. Using image processing techniques, such as the maximum value and centroid methods, the positions of reflected and refracted light spots under different incident beam angles are extracted for analysis. Moreover, the skew ray tracing method combined with homogeneous coordinate transformation matrices is employed to establish measurement algorithms. Furthermore, simulations and experimental verifications are also conducted. According to the verification results, the accuracy and measurement ranges of each parameter are as follows: radius of curvature (100–940&#xa0;mm, ± 0.01&#xa0;mm), central thickness (1–10&#xa0;mm, ± 0.0001&#xa0;mm), and refractive index (1–3.6, ± 0.001). Finally, it is worth emphasizing that the proposed robust and cost-effective measurement system achieves high accuracy and stability.</p>

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Design of a measurement system for the radius of curvature, thickness, and refractive index of spherical transparent materials

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Fan-Hsi Hsu,
  • Chien-Sheng Liu,
  • Yi-Chi Li

摘要

To address the limitations of current technologies and equipment in simultaneously measuring multiple parameters of spherical transparent materials, this study proposes an innovative optical measurement system to simultaneously measure the radius of curvature, thickness, and refractive index of spherical transparent materials. While existing methods for measuring spherical transparent materials can independently determine the radius of curvature, thickness, and refractive index, they are typically costly and limited in scope. Using image processing techniques, such as the maximum value and centroid methods, the positions of reflected and refracted light spots under different incident beam angles are extracted for analysis. Moreover, the skew ray tracing method combined with homogeneous coordinate transformation matrices is employed to establish measurement algorithms. Furthermore, simulations and experimental verifications are also conducted. According to the verification results, the accuracy and measurement ranges of each parameter are as follows: radius of curvature (100–940 mm, ± 0.01 mm), central thickness (1–10 mm, ± 0.0001 mm), and refractive index (1–3.6, ± 0.001). Finally, it is worth emphasizing that the proposed robust and cost-effective measurement system achieves high accuracy and stability.