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摘要:光学自由曲面因其表面自由度较多而难于进行检测。干涉检测法具有高精度非接触的特点，但传统干涉仪中的静态补偿器在自由曲面加工过程中未知面形不断变化的情况下，难以实现原位检测。因此，可编程控制的大动态范围自适应补偿器成为近年来自由曲面干涉检测中的研究热点。结合课题组在自由曲面自适应干涉检测领域的工作，介绍了光学自由曲面自适应干涉检测的最新研究进展，详细分析了基于可变形镜和空间光调制器的自适应干涉检测技术，介绍了针对干涉图目标的自适应控制算法，总结了两大类自适应检测方法的优点以及发展瓶颈，并对未来自由曲面的自适应检测技术进行了展望。Abstract:Optical free-form surfaces are difficult to detect due to their rich degrees of freedom. Interference detection methods are both highly precise and non-contact. However, the static compensator in a traditional interferometer faces difficulty in achieving in-situ tests of unknown surface shapes or those changing during fabrication. Therefore, programmable adaptive compensators for large dynamic ranges have become a well-researched topic in recent years. Combined with the research work in the field of freeform surface metrology, we introduce the latest research progress in adaptive interferometry for optical freeform surfaces. Adaptive interferometers based on a Deformable Mirror (DM) or Liquid Crystal Spatial Light Modulator (LC-SLM) are analyzed in detail. An adaptive controlling algorithm in the adaptive interferometer is introduced as well. Finally, the advantages and development bottleneck of the above two kinds of adaptive interferometry are summarized and the prospects for the future development of freeform surface adaptive interferometers are proposed.
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Key words:
- freeform surface testing/
- adaptive interferometry/
- DM/
- LC-SLM
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图 2LC-SLM替代泰曼格林干涉仪的参考镜时的薄膜检测结果。（a）补偿前干涉图，（b）LC-SLM产生的参考相位，（c）补偿后的干涉图，（d）SLM波前调制量[33]
Figure 2.Thin-film interferometry results when LC-SLM replaces the reference mirror in the Twyman-Green interferometer. (a) The pre-compensated interferogram, (b) the reference phase generated by the LC-SLM, (c) the compensated interferogram, (d) the final detection result[33]
图 4基于SLM的自适应波前干涉仪对大面形误差自由曲面检测示意图。（a）利用静态零位镜对自由曲面进行的常规检测；（b）全孔径干涉图中部分条纹不能分辨；（c）表面面形误差分布具有部分数据缺失；（d）基于SLM的自由曲面检测；（e）局部区域的初始不能分辨干涉图；（f）被SLM补偿的局部区域的最终干涉图；（g）局部区域的曲面面形误差；（h）全孔径曲面面形误差图拼接结果[38]
Figure 4.Illustration of the SLM-based Adaptive Wave-front Interferometer (AWI) for freeform surfaces with severe surface figure error. (a) The conventional test of a freeform surface utilizing a static null. (b) The full aperture interferogram when the upper region cannot be resolved by the interferometer. (c) The surface figure error map when the upper region is not available. (d) The SLM-based AWI. (e) The initial interferogram of the local region. (f) The final interferogram of the local region nulled by the SLM. (g) The surface figure error of the local region. (h) The full aperture surface figure error map stitching result[38]
图 9基于薄膜DM的非球面动态干涉检测。（a）干涉检测系统布局；（b）驱动电压与DM反射波前PV的模型预测值和实际测量值之间的关系；（c）不同驱动电压下DM全口径形变量（截面）[47]
Figure 9.Aspheric dynamic interferometer based on a thin film DM. (a) Layout of the system; (b) the relationship between the model predicted value and the actual measured value for PV of the DM- reflected wavefront with applied voltage and (c) the DM’s full aperture shapes (section) under different driving voltages[47]
图 17SPGD搜索过程中，以优化指标J作为条纹恢复判据的一维演示。（a）为条纹缺失状态，（b）为优化中间过程，（c）为最终条纹及其J值[50]
Figure 17.One-dimensional demonstration showing the judgment valueJas the fringe restoration criterion during the SPGD search process. (a) The case without the fringe, (b) the middle of the restoration process, and (c) the final fringe with itsJvalue[50].
图 18实验中优化收敛曲线。（a） SPGD算法的收敛曲线(第二步) ；（b） 最后一步采用牛顿迭代算法时的收敛曲线；（c） 最后一步采用SPGD算法时的收敛曲线[72]
Figure 18.Experimental convergence curves between the second and final steps. (a) The convergence curve using the SPGD algorithm (the second step); (b) the convergence curve using the Newton iteration algorithm in the final step; (c) the convergence curve using the SPGD algorithm in the final step[72]
图 19MV-GA和SSD-SPGD算法对比[71]。（a） 500次实验中MV-GA和SSD-SPGD算法优化后的目标函数值（最终干涉图中不可分辨条纹子区域的像素数），（b） MV-GA法中500个试验目标函数值的均值变化，（c） SSD-SPGD算法500次试验目标函数值的均值随迭代次数的变化
Figure 19.Comparison of the MV-GA and SSD-SPGD algorithms[71]. (a) The objective function values optimized by MV-GA and SSD-SPGD in 500 experiments. (b) Variation of the mean value & standard deviation of the 500 trials’ objective function values with a generation number for the MV-GA method. (c) Variation of the mean value & standard deviation of the 500 trials’ objective function values with the iteration number for the SSD-SPGD method.
表 1相关文献研究中使用的SLM参数及自由曲面检测指标
Table 1.SLM parameters used in relevant literatures and freeform surface detection indexes
口径/mm 像素数 像素尺寸 (μm/pixel) 补偿自由曲面偏离度/μm rms精度/nm SLM in [32] 10×10 640×480 100×300 ~1 ~6 SLM in [33] 20×15 1024×768 19 ~12 ~16 SLM in [36] R=13.65 R=500 13.65 ~2 rad ~28 SLM in [40] 36.8×27.6 1024×768 36 ~15 ~20 SLM in [41] 9.22 4160×2464 3.74 ~150 ~50 注：文献[41]中rms精度0.08λ为SLM波前量化误差，真实自由曲面检测误差目前无实验报道。 
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表 2相关文献研究中使用的DM参数及自由曲面检测指标
Table 2.DM parameters used in relevant literatures and freeform surface detection indexes
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