轴上物点经双凸对称球面透镜成像偏差分析  

Imaging deviation analysis of object points on axis through biconvex symmetrical spherical lens

作　　者：于晨曦 冯立峰[1] 孙文军[1] YU Chen-xi;FENG Li-feng;SUN Wen-jun(College of Physics and Electronic Engineering,Harbin Normal University,Harbin,Heilongjiang 150025,China)

机构地区：[1]哈尔滨师范大学物理与电子工程学院,黑龙江哈尔滨150025

出　　处：《大学物理》2024年第7期81-84,共4页College Physics

基　　金：黑龙江省大学生创新创业训练计划(S202210231058);黑龙江省高等教育教学改革研究项目(SJGY20190370);哈尔滨师范大学高等教育教学改革研究重点项目(XJGZ2022002);哈尔滨师范大学课程思政教学改革示范项目(XKCSZ2022001)资助。

摘　　要：为确定轴上物点经双凸对称球面透镜所成的像与理想像的差异,便于检验成像器件能否达到实际成像应用要求,本文利用解析几何方法推导了轴上物点经双凸对称球面透镜的成像区域边界方程,计算分析了入射光线倾角及透镜参数对成像区域的影响.结果表明当轴上物点位置与透镜曲率半径确定时,如物距取30.0 cm、曲率半径为15.0 cm、透镜的半厚度≤0.300 cm时,表示成像区域边界轴上像点偏离理想像点程度的轴上偏差小于等于2.02%;当轴上物点位置与透镜参数确定,如物距取30.0 cm、透镜半通光孔径为3.00 cm、入射光线倾角≤4.85°时,表示成像区域边界像点离轴程度的离轴偏差小于等于10.0%.此方法同样可以分析其他类型像差,理论推导与计算结果为相关后续研究提供了理论支持与技术借鉴.In order to determine the difference between the ideal imaging and the real imaging produced by the object point on the axis passing through the biconvex symmetric spherical lens,and to verify whether the imaging device can meet the requirements of practical imaging application,the boundary equation of the imaging region of the object point on the axis passing through the biconvex symmetric spherical lens is derived by using the analytical geometry method,and the influence of the Angle of incident ray and the lens parameters on the imaging region is calculated and analyzed.The results show that when the object point position on the axis and the radius of curvature of the lens are determined,for example,the object distance is 30.0 cm,the radius of curvature is 15.0 cm and the half thickness of the lens L≤0.300 cm,the deviation on the axis representing the degree of deviation from the ideal imaging point on the boundary axis of the imaging region is less than or equal to 2.02%;when the object point position on the axis and the lens parameter are determined,for example,the object distance is 30.0 cm,the lens half-aperture h=3.00 cm and the angle of incident ray α≤4.85°,the off-axis deviation representing the off-axis degree of imaging points at the boundary of the imaging region is less than or equal to 10%.This method can also analyze other aberrations.The theoretical derivation and calculation results provide theoretical support and technical reference for the subsequent research.

关 键 词：几何光学 双凸球面透镜 理想成像 成像区域 

分 类 号：O435.2[机械工程—光学工程]