光学仪器  2020, Vol. 42 Issue (2): 8-13 PDF

Comparison of single and double pass methods in laser rod interferometric measurement
QI Bingyun, ZHANG Zeyu, ZHOU Kanghu, CHEN Lei
School of Electronic and Optical Engineering, Nanjing University of Science & Technology, Nanjing 210094, China
Abstract: Due to the special shape characteristic of a laser rod, the traditional double-pass test method, which has high sensitivity, tends to have obvious diffraction effect and edge black ring caused by multiple imaging. The result leads to the reduction of the effective measurement area, which has a negative impact particularly on the measurement of small aperture optical components. To avoid these problems, the wavefront aberration of laser rod is measured by the single-pass method. The right-angle prism is used as the reflection part to ensure the test light passes through the laser rod only once, so that the number of equivalent circular holes and the imaging times can be reduced. We use the expanded multi-hole model to discuss the diffraction effect and analyze the cause of edge overlap from the perspective of imaging to derive the advantages of the single-pass method. In addition, considering the matching of the reference light and the test light, it is necessary to rotate the right-angle prism by at least 5.40° to improve the contrast of the interferogram. Finally, the measurement result of the laser rod wavefront was as follows: the peak−valley value is 0.068λ and the root mean square is 0.012λ.
Key words: wavefront aberration    laser rod    single pass    diffraction effect    multiple imaging

1 原　理

 图 1 单通法原理图 Figure 1 Single-pass system diagram

 $I(x,y,t) = {I_{\rm{d}}}(x,y) + {I_{\rm{a}}}(x,y)\cos [\phi (x,y) - \delta (t)]$ (1)

 $\phi (x,y) = \arctan \left[\frac{{I(x,y,{t_4}) - I(x,y,{t_3})}}{{I(x,y,{t_1}) - I(x,y,{t_2})}}\right]$ (2)

 图 2 双通法原理图 Figure 2 Double-pass system diagram
2 实　验 2.1 测量结果

 图 3 单通法测试结果 Figure 3 Test results of single-pass method

2.2 单通双通实验结果对比

1）双通法得到的干涉图边缘厚度约为单通法的两倍（图4），系多重成像导致。设边缘重叠区域环宽为d，标定干涉区域半径为R，引入一个比例变量 $\gamma {\rm{ = }}d/R$ 来衡量边缘信息的缺失程度，下标s和d分别表示单通法和双通法。经计算， ${\gamma _{\rm{d}}} \approx 1.8{\gamma _{\rm{s}}}$

 图 4 干涉图样边缘重影对比 Figure 4 Comparison of ghosting at the edge of the interferogram

2）双通法有多层衍射环而单通法无肉眼可见的衍射环。设反射件（直角棱镜或标准平晶）离激光棒前表面A的距离为Lm，如图5所示，随着Lm的增加，双通法的衍射环存在范围扩大。因此对于双通法，反射平晶必须紧贴激光棒才能够降低衍射效应，且在相同掩模下，不同的Lm会导致不同的测量结果；单通法由于抑制了衍射效应，对反射棱镜无距离限制。

 图 5 不同情况下衍射效应的对比图 Figure 5 Comparison of diffraction effects under different conditions

3 讨　论

3.1 衍射效应的对比分析

 图 6 不同情况下的小孔等效图 Figure 6 Small-hole equivalent diagram under different conditions
3.2 多重成像的对比分析

 $l' = \frac{{f'l}}{{l - f}}{\rm{ = }}f' + \frac{{ff'}}{{l - f}}$ (3)
 $\beta {\rm{ = }} - \frac{f}{{f'}}\frac{{l'}}{l}{\rm{ = }} - {\left(\frac{1}{f} - \frac{1}{l}\right)^{ - 1}}$ (4)

 图 7 双通法成像变形示意图 Figure 7 Imaging deformation diagram in double-pass method

 图 8 单通法成像变形示意图 Figure 8 Imaging deformation diagram in single-pass method

3.3 干涉对比度调整

 图 9 直角棱镜内部光路示意图 Figure 9 Internal light path of right angle prism

 图 10 反射率与入射角关系拟合图 Figure 10 Fitting chart of reflectivity and incident angle

 图 11 旋转前后干涉条纹对比 Figure 11 Comparison of interference fringes before and after rotation
4 结　论

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