为了同时同位测量石英管的外径和壁厚, 建立了激光透射成像系统, 对系统测量原理进行研究。基于几何光学和菲涅尔公式, 分别导出平行光垂直照射石英管后的透射光线偏向角、相对光强与入射光线离轴距离之间的关系; 通过数值计算, 分析了偏向角、相对透射光强随入射光线离轴距离的变化特点; 针对物方远心光路, 分析了光阑对偏向角和相对光强的限制; 基于CCD成像原理, 通过引入标定系数和补偿因子, 导出石英管外径与壁厚的计算公式。实验结果表明: 外径绝对误差和相对误差的平均值分别为0.119mm和0.91%, 壁厚绝对误差和相对误差的平均值分别为0.153mm和6%。

For measuring the outer diameter and wall thickness of quartz tube at the same time and position, a laser transmission imaging system is established and the measuring principle of the system is investigated. Based on the geometry optics and Fresnel formula, the theory relationship of the transmission beam deviation angle, the relative intensity and the off-axis distance of the incident beam are derived. By numerical calculation, the resultant variation of the deviation angle and the relative intensity with the off-axis distance of the incident beam is analyzed. For the infinite objective of the telecentric optical path system, the restriction of the stop to the deviation angle and relative intensity is analyzed. Based on CCD imaging principle, by defining the calibration coefficient and compensation factor, the formula of the outer diameter and wall thickness of the quartz tube are derived. The experiment results show that the average of the absolute and relative error of the outer diameter is 0.119mm and 0.91% , and the average of the absolute and relative error of the wall thickness is 0.153mm and 6%, respectively.