光学镜面离子束修形理论与工艺研究
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摘要
随着光学性能要求的不断提高,武器装备、太空观测、激光核聚变、极紫外光刻等领域对光学元件的精度要求越来越高,且数量要求越来越大,使光学元件的加工面临严峻的挑战。目前的计算机控制光学表面成形(CCOS)工艺虽然与传统的加工相比能大大提高加工效率,但是仍然不能满足要求,主要是加工精度低、面形收敛慢、容易产生中高频误差、存在边缘效应等。离子束修形(IBF)工艺利用离子源发射的离子束轰击光学镜面时发生的物理溅射效应,达到去除光学元件表面材料的目的。由于IBF工艺独特的材料去除方式,使IBF工艺的去除函数非常稳定,对加工距离、工件表面起伏、环境振动、工件支撑都不敏感,并且去除函数形状好、无边缘效应。这些优点决定了IBF工艺加工光学镜面精度高、面形收敛快,使其成为了高精度光学镜面特别是高精度非球光学镜面加工的有效方法。
虽然国外从90年代初以来就有IBF技术的成功应用,但由于IBF技术工艺相对复杂、成本相对较高,国内基本未开展相关研究。由于IBF技术在军事上和商业上的巨大应用价值,必须对相关的理论和工艺进行研究,力争实现高精度光学镜面的IBF加工。论文针对IBF工艺的去除函数、驻留时间、修形能力、加工误差和加工工艺等关键问题展开深入研究,并进行了充分的试验验证。论文的研究工作包括以下几部分：
1.对去除函数进行了建模和分析。利用Sigmund溅射理论建立了去除函数的理论模型,根据建立的理论模型分析了去除函数的特性,主要分析了表面曲率和入射角度偏差对去除函数的影响；讨论了利用试验估计去除函数的方法,提出了线扫描试验法；在自研的IBF设备KDIFS-500上进行了去除函数试验,研究了去除函数的形状、稳定性和保形性。
2.驻留时间求解问题是IBF工艺中的关键问题,为了解决驻留时间求解中的边缘效应问题和参数优化问题,本文研究了两种驻留时间求解方法。首先引入了CEH模型,该模型能完全消除边缘效应,采用了TSVD正则化算法求解该模型,定义了加工预测曲线(加工时间Vs.加工残差),发现该曲线具有字母“L”形状,利用加工预测曲线的这一性质可以确定出TSVD算法中合理的正则化参数。其次由于TSVD算法计算速度慢,研究了计算速度快的迭代算法,使用了边缘平滑延拓方法减小了迭代法中的边缘效应,应用加工预测曲线实现了迭代法中的参数优化,使迭代法进一步实用。
3.对修形能力进行了理论研究和试验验证。针对确定性抛光工艺过程对不同频率误差的修正能力,即修形能力,提出了量化评价指标——材料去除有效率,它定义为期望去除的材料量体积与实际去除的材料量体积之比；首先分析了高斯型去除函数的修形能力,分析得出IBF工艺对不同频率误差的修正能力与离子束直径有关,并得出了定量关系；然后进一步分析了任意形状去除函数的修形能力,并具体分析了回转对称型去除函数的修形能力和一维加工情况下的修形能力；最后进行了3个正弦面形的刻蚀试验,验证了修形能力分析的预测结果。
4.对IBF工艺中的主要误差源进行了分析。以确定性抛光工艺过程的二维卷积模型为基础分析了定位误差和去除函数误差对加工结果的影响,分析得出：定位误差引起的加工残差近似等于面形梯度矢量和定位误差矢量的内积,去除函数误差引入的加工残差正比于加工量。
5.对加工工艺进行了改进。为了减小定位误差,提出并实现了定位优化方法；为了缩短加工时间,实现了速度加工模式；为了优化加工路径,提出并实现了等面积增长螺旋线加工路径。这些工艺的改进有利于提高面形收敛比和提高加工精度。
6.最后进行了大量的IBF试验和应用,所加工的光学镜面包括平面镜、球面镜和非球面镜,材料包括微晶玻璃和SiC,形状包括圆形和椭圆形,加工结果的面形精度(RMS值)都小于10nm(最好为3.1nm),试验结果验证了本文研究所得出的结论。
With the ever-increasing demands on performances, optics used in modern optical systems such as weapons, telescopes, laser fusion systems and extreme ultraviolet lithography (EUVL) systems demand higher accuracy and more quantity. The present widely used computer controlled optical surfacing (CCOS) technique, although gains more efficiency than conventioanal polishing methods, can not satisfy the critical demands due to its lower accuracy and lower convergence ratio. Moreover, it often causes high-middle frequency error and edge effects on optical surface. Ion beam figuring (IBF), which removes surface material by physical sputtering, hold very stable beam removal function (BRF) due to its unique manner to remove material. It is insensitive to machining distance, surface curvature, environment vibration and optics support. Moreover, its BRF is in Gaussian shape and is free of edge effect. Consequently, IBF process can obtain high accuracy and high convergence ratio than other deterministic process, which makes it an effective and applicable technique to produce high accuracy optical surfaces, especially aspheric surfaces.
Although IBF process has been successfully applied since the early 90s, there is little work on it at home due to its relative complexity and its high cost. Because it is a key technology to produce high precision optical surfaces used in both military and commerce, we should develop it. This thesis is dedicated to the theory and technology of IBF process, including removal function, dwell time, error correcting ability, error sources, processing technique and plentiful experiments. The major research efforts include the following points.
1. The BRF in IBF process is modeled and studied. First, the theoretical model of BRF is founded using the Sigmund theory. Then the characteristics of BRF are investigated according to the model. The methods to estimate BRF by experiments are discussed and a new method named line scan method is proposed. Using line scan method the stability of BRF can be investigated. Finally, some experiments are performed on KDIFS-500 to test the shape, stability and conformability of BRF.
2. In order to determine dwell time, which is the key input variable for successful figuring processes, two approaches are investigated with emphases on edge effect and parameter optimization. First, the CEH model is introduced, which can completely eliminate edge effect. The TSVD regularization algorithm is also introduced in order to solve the CEH model, and to determine a reasonable regularization parameter in the TSVD algorithm. A new curve named figuring prediction curve is proposed and applied, which is defined as process time vs. residual accuracy. Lastly, the iterative method to determine dwell time is also investigated due to its less computing time. Some improvements are proposed to reduce edge effect and to determine a reasonable dwell time, which makes the iterative method more practical.
3. To evaluate the correcting ability of a figuring process to different spatial frequency figure error, a quantitative criterion named material removal availability (MRA) is proposed, which is defined as the ratio of the volume of desired material removal to that of the real material removal. First, the correcting ability of a Gaussian BRF is investigated and the investigation indicates that the correcting ability of an IBF process is determined by the diameter of the ion beam, and the quantitative relationship is given. Then, the correcting ability of an arbitrary BRF is investigated. Furthermore, the correcting ability of circular symmetrical BRF and the correcting ability of one dimensional figuring process are discussed. Lastly, three sine figures are etched by IBF processes and the figuring results agree with the theoretical predictions.
4. The major error sources, the positioning error and the BRF's error, are discussed based on the two-dimensional convolution model. The investigation shows that the residual error resulted from positioning error is the dot product of the figure error gradient vector and the positioning error vector, and the residual error resulted from a constant bias error of BRF is proportional to the material removal.
5. Several improvements are made on processing technique. A positioning method is proposed and realized in order to reduce positioning error. The velocity process mode is realized in order to reduce processing time. And a novel spiral scan path named uniform-area-growth-ratio spiral path is proposed and realized to optimize processing path. These improvements are of great benefits to IBF process with higher convergence ratio and less residual error.
6. Finally, IBF experiments are performed on a variety of optical surfaces including flats, sphere and aspheres, on materials including Zerodur glass and SiC, and on shapes including circle and ellipse. The final residual errors after IBF process are all less than 10nm RMS (the best value is 3.1 nm RMS). The successful figuring results prove the validity and advantages of the proposed algorithms and the proposed process improvements.
虽然国外从90年代初以来就有IBF技术的成功应用,但由于IBF技术工艺相对复杂、成本相对较高,国内基本未开展相关研究。由于IBF技术在军事上和商业上的巨大应用价值,必须对相关的理论和工艺进行研究,力争实现高精度光学镜面的IBF加工。论文针对IBF工艺的去除函数、驻留时间、修形能力、加工误差和加工工艺等关键问题展开深入研究,并进行了充分的试验验证。论文的研究工作包括以下几部分：
1.对去除函数进行了建模和分析。利用Sigmund溅射理论建立了去除函数的理论模型,根据建立的理论模型分析了去除函数的特性,主要分析了表面曲率和入射角度偏差对去除函数的影响；讨论了利用试验估计去除函数的方法,提出了线扫描试验法；在自研的IBF设备KDIFS-500上进行了去除函数试验,研究了去除函数的形状、稳定性和保形性。
2.驻留时间求解问题是IBF工艺中的关键问题,为了解决驻留时间求解中的边缘效应问题和参数优化问题,本文研究了两种驻留时间求解方法。首先引入了CEH模型,该模型能完全消除边缘效应,采用了TSVD正则化算法求解该模型,定义了加工预测曲线(加工时间Vs.加工残差),发现该曲线具有字母“L”形状,利用加工预测曲线的这一性质可以确定出TSVD算法中合理的正则化参数。其次由于TSVD算法计算速度慢,研究了计算速度快的迭代算法,使用了边缘平滑延拓方法减小了迭代法中的边缘效应,应用加工预测曲线实现了迭代法中的参数优化,使迭代法进一步实用。
3.对修形能力进行了理论研究和试验验证。针对确定性抛光工艺过程对不同频率误差的修正能力,即修形能力,提出了量化评价指标——材料去除有效率,它定义为期望去除的材料量体积与实际去除的材料量体积之比；首先分析了高斯型去除函数的修形能力,分析得出IBF工艺对不同频率误差的修正能力与离子束直径有关,并得出了定量关系；然后进一步分析了任意形状去除函数的修形能力,并具体分析了回转对称型去除函数的修形能力和一维加工情况下的修形能力；最后进行了3个正弦面形的刻蚀试验,验证了修形能力分析的预测结果。
4.对IBF工艺中的主要误差源进行了分析。以确定性抛光工艺过程的二维卷积模型为基础分析了定位误差和去除函数误差对加工结果的影响,分析得出：定位误差引起的加工残差近似等于面形梯度矢量和定位误差矢量的内积,去除函数误差引入的加工残差正比于加工量。
5.对加工工艺进行了改进。为了减小定位误差,提出并实现了定位优化方法；为了缩短加工时间,实现了速度加工模式；为了优化加工路径,提出并实现了等面积增长螺旋线加工路径。这些工艺的改进有利于提高面形收敛比和提高加工精度。
6.最后进行了大量的IBF试验和应用,所加工的光学镜面包括平面镜、球面镜和非球面镜,材料包括微晶玻璃和SiC,形状包括圆形和椭圆形,加工结果的面形精度(RMS值)都小于10nm(最好为3.1nm),试验结果验证了本文研究所得出的结论。
With the ever-increasing demands on performances, optics used in modern optical systems such as weapons, telescopes, laser fusion systems and extreme ultraviolet lithography (EUVL) systems demand higher accuracy and more quantity. The present widely used computer controlled optical surfacing (CCOS) technique, although gains more efficiency than conventioanal polishing methods, can not satisfy the critical demands due to its lower accuracy and lower convergence ratio. Moreover, it often causes high-middle frequency error and edge effects on optical surface. Ion beam figuring (IBF), which removes surface material by physical sputtering, hold very stable beam removal function (BRF) due to its unique manner to remove material. It is insensitive to machining distance, surface curvature, environment vibration and optics support. Moreover, its BRF is in Gaussian shape and is free of edge effect. Consequently, IBF process can obtain high accuracy and high convergence ratio than other deterministic process, which makes it an effective and applicable technique to produce high accuracy optical surfaces, especially aspheric surfaces.
Although IBF process has been successfully applied since the early 90s, there is little work on it at home due to its relative complexity and its high cost. Because it is a key technology to produce high precision optical surfaces used in both military and commerce, we should develop it. This thesis is dedicated to the theory and technology of IBF process, including removal function, dwell time, error correcting ability, error sources, processing technique and plentiful experiments. The major research efforts include the following points.
1. The BRF in IBF process is modeled and studied. First, the theoretical model of BRF is founded using the Sigmund theory. Then the characteristics of BRF are investigated according to the model. The methods to estimate BRF by experiments are discussed and a new method named line scan method is proposed. Using line scan method the stability of BRF can be investigated. Finally, some experiments are performed on KDIFS-500 to test the shape, stability and conformability of BRF.
2. In order to determine dwell time, which is the key input variable for successful figuring processes, two approaches are investigated with emphases on edge effect and parameter optimization. First, the CEH model is introduced, which can completely eliminate edge effect. The TSVD regularization algorithm is also introduced in order to solve the CEH model, and to determine a reasonable regularization parameter in the TSVD algorithm. A new curve named figuring prediction curve is proposed and applied, which is defined as process time vs. residual accuracy. Lastly, the iterative method to determine dwell time is also investigated due to its less computing time. Some improvements are proposed to reduce edge effect and to determine a reasonable dwell time, which makes the iterative method more practical.
3. To evaluate the correcting ability of a figuring process to different spatial frequency figure error, a quantitative criterion named material removal availability (MRA) is proposed, which is defined as the ratio of the volume of desired material removal to that of the real material removal. First, the correcting ability of a Gaussian BRF is investigated and the investigation indicates that the correcting ability of an IBF process is determined by the diameter of the ion beam, and the quantitative relationship is given. Then, the correcting ability of an arbitrary BRF is investigated. Furthermore, the correcting ability of circular symmetrical BRF and the correcting ability of one dimensional figuring process are discussed. Lastly, three sine figures are etched by IBF processes and the figuring results agree with the theoretical predictions.
4. The major error sources, the positioning error and the BRF's error, are discussed based on the two-dimensional convolution model. The investigation shows that the residual error resulted from positioning error is the dot product of the figure error gradient vector and the positioning error vector, and the residual error resulted from a constant bias error of BRF is proportional to the material removal.
5. Several improvements are made on processing technique. A positioning method is proposed and realized in order to reduce positioning error. The velocity process mode is realized in order to reduce processing time. And a novel spiral scan path named uniform-area-growth-ratio spiral path is proposed and realized to optimize processing path. These improvements are of great benefits to IBF process with higher convergence ratio and less residual error.
6. Finally, IBF experiments are performed on a variety of optical surfaces including flats, sphere and aspheres, on materials including Zerodur glass and SiC, and on shapes including circle and ellipse. The final residual errors after IBF process are all less than 10nm RMS (the best value is 3.1 nm RMS). The successful figuring results prove the validity and advantages of the proposed algorithms and the proposed process improvements.
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