毛细管干涉仪的理论分析

从几何光学出发,推导了毛细管干涉仪的从柱面透镜到接收屏的光线的光程．对光线追迹模拟,结果表明毛细管干涉仪的干涉条纹的形成可用双光束的干涉来解释．从柱面不同位置入射的两条光线可能具有相同的光程,而且从柱面透镜不同位置出发的两条光线可能到达接收屏的同一点,当它们满足相干条件时,就会形成干涉条纹．建立了干涉条纹的计算机模拟程序, 模拟了毛细管中液体折射率、毛细管内径、外径对干涉条纹的影响. 结果表明实验中应使用薄壁毛细管, 由于干涉条纹对柱面透镜到毛细管之间的距离非常敏感, 为提高精度, 建议在实验中用已知折射率的标样来确定这一距离.

Theoretical Analysis of a Capillary Tube Interferometer

Geometrical optical analysis of a capillary tube interferometer was presented. The optical path length (OPL) was deduced from a cylindrical lens to a screen. Ray tracing and simulating of the capillary tube interferometer was presented. The results show that the fringe pattern produced by the capillary tube interferometer can be explained by two-beam interference. Two rays coming from two different positions on the cylindrical lens may have the same OPL. And, two rays coming from two different positions on the cylindrical lens may get to the same point on the screen. When the interference condition matches, the interferogram will be formed. A computer program to simulate the interference fringe pattern was established. The influences caused by the refractive indices of the liquids in the capillary tube, the outer and inner radii of the capillary tubes were given by computer simulation. This simulation shows that a capillary tube with thin wall should be used in experiment and the fringe pattern is very sensitive to the distance between the cylindrical lens and the capillary tube. For enhancing accuracy, this distance should be determined by fitting a standard liquid with known refractive index in experiment.