凹透镜的焦距测量误差与光心指示偏差间关系

Relationship between Measurment Error of Focal Distance of Concave Lens and Optical Center Instructions Deviation

透镜加工很难避免光心不出现偏离,同时在测量透镜的焦距过程中需要将透镜利用支架置于光具座上,这些因素必然导致光心的实际位置与轨道刻度尺上的指示位置出现偏差(简称光心指示偏差),最终必然给焦距测量带来误差。实际测量过程中经常发现,即便是同一套光学仪器,多次测量结果间时常出现很大的偏差。通过分析研究,对辅助法测量凹透镜焦距系统建立了数学模型,推导出透镜的焦距与物距、光心指示偏差之间的函数关系式,总结了光心指示偏差对焦距测量误差的影响规律,即物距越大焦距测量误差越小,并且光心指示偏差左偏情形导致焦距测量值大于标称值;反之,小于标称值。实验验证显示,依据该规律可显著提高焦距的测量精度。

The deviation of optical center of lens is hard to avoid in the preparation of lens. Besides, lens are placed in optical benches to measure its focal length. All these factors will lead to a divergence between the actual position of optical center and the indicated value based on the ruler of optical benches（referred to as tile optical center instructions deviation） and finally inevitable errors of focal length measurement appear. The actual measurement reveals that, even for the same set of optical instruments,the measured results of focal length often have a great difference with the true value of lens. By the analysis of auxiliary approach to measure the focal length, a mathematical model was established, which displayed the function equation between the focal length with the object distant and optical center instructions deviation. Besides, the influence law of the optical center instructions deviation on the focal length measurement error, i. e. the greater the object distant from, the smaller the measurement error of focal length was theoretically analysed. Moreover, if the optical center instructions deviation is located in the right side of the lens, the focal length measured values will be greater than the nominal value. Conversely, the values will be smaller. The experiment results reveal that the law could significantly improve the accuracy of the focal length measurement.