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摘要
为实现激光棒透射波前的测量，改善一般泰曼型或斐索型干涉仪测量小口径激光棒透射波前时的边缘衍射效应，研究了一种变倾角移相马赫-曾德尔干涉仪。通过调整移相反射镜的倾斜姿态，改变入射到马赫-曾德尔干涉光路的光束倾角，参考光束与测试光束的光程差随之变化，从而在相干光之间引入相移，实现了相移干涉测量。利用该干涉仪测量一根口径为Ф6 mm、长度为60 mm激光棒(Nd:YAG)的透射波前，测量结果的峰谷值(PV)为0.391λ，均方根值(RMS)为0.056λ；使用ZYGO激光干涉仪测量同一根激光棒，其透射波前的峰谷值(PV)为0.370λ，均方根值(RMS)为0.064λ。对比结果表明该干涉仪能实现光学元件透射波前的高精度检测，测试结果的一致性验证了该方案的可行性。该变倾角移相方法具有较高的移相精度和较大的移相范围，且该变倾角干涉系统中光束仅一次透过待测激光棒，可有效抑制多光束干涉现象，改善小口径激光棒的边缘衍射效应。
Abstract
In order to measure the transmission wavefront of laser rods and to improve the edge diffraction effect of small-aperture laser rods measured by Tayman or Fizeau interferometer, a variable-inclination Mach-Zehnder interferometer was proposed. The incident angle was changed by adjusting the tilting attitude of the phase shifting reflector, then the optical path difference was changed that the phase shift was introduced to the coherent light and the phase shifting interferometry was realized. The transmission wavefront of a laser rod (Nd:YAG) with the diameter of 6 mm and the length of 60 mm was measured by this interferometer, the peak-valley (PV) and root mean square (RMS) of the wavefront were 0.391λ and 0.056λ. The same laser rod was measured by ZYGO GPI XP interferometer, the peak-valley (PV) and root mean square (RMS) were 0.370λ and 0.064λ. The comparison results show that the interferometer can achieve high-precision detection of transmission wavefront of laser robs. The variable-inclination Mach-Zehnder interferometer has high phase-shifting precision and wide phase-shifting range, and the beam in the system can pass through the laser rod only once, which can suppress the multi-beam interference and improve the edge diffraction effect of the small-aperture laser rods.
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Overview
Overview: In order to measure the transmission wavefront of laser rods and to improve the edge diffraction effect of small-aperture laser rods measured by a general Tayman or Fizeau interferometer, a variable-inclination phase shifting Mach-Zehnder interferometer was proposed. In the proposed interferometer, the phase shifting reflector was placed on the electric linear rotating table. By adjusting the tilting attitude of the phase shifting reflector, the incident angle into the Mach-Zehnder interference cavity was changed. A laser rod with a certain length was placed in the test optical beam as the test object, and it could be used as a retarder in the equal optical path Mach-Zehnder interferometer to increase the optical path difference between the reference beam and the test beam, so the proposed interference system met the requirement of phase shifting. The optical path difference between the reference beam and the test beam changed each time the incident angle into the Mach-Zehnder interference cavity was transformed by the phase shifting reflector placed on the electric linear rotating table, thereby the phase shifting quantity was introduced to the coherent light. The phase shifting interferometry was realized under the interaction of phase shifting reflector and laser rob. The transmission wavefront of a laser rod (Nd:YAG) with the diameter of 6 mm and the length of 60 mm was measured by this interferometer, the peak-valley value (PV) and root mean square value (RMS) of the wavefront are 0.391λ and 0.056λ. The same laser rod is measured by ZYGO GPI XP interferometer, the peak-valley (PV) and root mean square (RMS) of the wavefront are 0.370λ and 0.064λ. The surface shape and numerical values of the two measurements are consistent, the comparison results show that the proposed interferometer can achieve high precision measurement of transmission wavefront of the laser robs. The proposed variable-inclination phase shifting Mach-Zehnder interferometer can realize periodic phase shifting only by using a reflector with adjustable inclination angle in the traditional Mach-Zehnder interferometer. It has high phase shifting precision and wide phase shifting range. The high precision phase modulation can be achieved by using conventional precision stepping motor. The proposed interferometer system is cheap and compact. The transmission wavefront of a small aperture laser rod can be measured by the variable-inclination phase-shifting system. The beam in the system can pass through the laser rod only once, therefore, the interferometer has obvious advantages in measuring the transmission wavefront of a small-aperture optical element with a certain length. It can effectively suppress the multi-beam interference and improve the edge diffraction effect of small-aperture optical elements.
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图 1 (a) 变倾角移相的原理光路图；(b)透射式等倾干涉示意图
Figure 1. (a) Schematic diagram of variable-inclination phase shifting; (b) Diagram of transmissivity equal inclination interference
图 2 最小二乘求解线性回归模型迭代算法流程图
Figure 2. Flow chart of least squares iterative algorithm for solving linear regression model
图 3 变倾角时间移相马赫-曾德尔干涉仪系统光路图
Figure 3. Schematic optical diagram of variable-inclination phase shifting Mach-Zehnder interferometer
图 5 变倾角时间移相马赫-曾德尔干涉仪中得到的激光棒透射波前
Figure 5. Transmission wavefront of laser rob measured by variable-inclination Mach-Zehnder interferometer
图 6 ZYGO GPI XP干涉仪中得到的激光棒透射波前
Figure 6. Transmission wavefront of the same laser rob measured by ZYGO GPI XP interferometer
图 7 系统移相量与反射镜倾角的关系图
Figure 7. Relationship between system phase shift and inclination of reflector
图 8 ZYGO干涉仪测量激光棒透射波前光路图
Figure 8. Optical diagram for testing laser robs in ZYGO interferometer
图 9 (a) ZYGO干涉仪中反射平晶距激光棒10 cm的干涉图；(b) ZYGO干涉仪中反射平晶距激光棒30 cm的干涉图；(c)马赫-曾德尔干涉仪中得到的干涉图
Figure 9. (a) Interferogram of reflection flat 10 cm away from the laser rob in ZYGO interferometer; (b) Interferogram of reflection flat 30 cm away from the laser rob in ZYGO interferometer; (c) Interferogram in M-Z interferometer
表 1 随机移相算法计算移相量与理想移相量对比
Table 1. Comparison of the phase shift quantity calculated by random phase shift algorithm and the ideal quantity
干涉图序号 理想的系统移相量/rad 随机移相算法计算的移相量/rad 1 0 0 2 0.079 0.075 3 0.317 0.308 4 0.712 0.710 5 1.266 1.264 6 1.978 1.978 7 2.849 2.853 8 3.878 3.881 9 5.065 5.063 10 6.376 6.382 
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