基于Talbot-Moiré法的长焦透镜焦距测量的极限精度分析

Limit precision analysis of focal length measurement of lens based on Talbot-Moiré

长焦距测量的Talbot-Moiré法是研究热点,目前很多方法虽然都是基于Talbot现象和Moiré技术,但基本原理和实验方案各不相同,因此焦距计算公式也不相同。基于透镜位相变换作用,利用Talbot效应和Moiré条纹,通过图像处理的方法获得条纹的斜率变化,根据焦距与莫尔条纹斜率之间的关系求得透镜焦距。由于长焦透镜的焦距相对于被测透镜厚度大得多,完全可以看作是薄透镜对光束的变换,可用薄透镜对球面波的变换作用来近似表示其对高斯光束的变换。因此,该方法测量长焦透镜焦距对于高斯光束与非高斯光束焦距测量结果无差别,均适用。最后全面分析了该测量方法的误差及精度极限。在影响测量精度的各个误差因素中,光栅节距误差对焦距测量的影响最为显著。

Talbot-Moiré based methods utilizes Talbot self-image effect and amplification of Moiré fringe for long focal length measurement.Because of the phase transformation of lens,the measurement based on Talbot effect and Moiré fringes of Ronchi gratings is suitable to long focal length.The focal length of measured lens is calculated according to its relation to the slope coefficient of Moiré fringes taken with CCD camera.Since the focal length of measured lens is much greater than its thickness,the phase transformation of lens to Gauss light beams is approximately expressed by the phase transformation of thin lens to spherical wave.Therefore,the measurement of long focal length is applicable for both Gauss and non-Gasussian lights.Finally,the concept,error and precision limit are analyzed,and the pitch error of the grating is the major contributor.