离轴非球面反射镜检测技术的研究
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摘要
离轴三反光学系统可实现宽覆盖，获得接近理想的成想性能和效果，是空间光学遥感系统的重要发展方向，但是普遍认为其制造和装调技术比较难。高精度离轴非球面光学元件的制造需要与之精度相适应的检测技术，离轴非球面镜的高精度测量技术一直都是先进光学制造领域的前沿课题，仍然面临着很多挑战。
本文研究工作的主要任务就是有效地解决离轴非球面检测的关键理论和技术问题，从真正意义上掌握离轴非球面光学元件的测量技术。本文以XX离轴三反相机中的主镜和三镜的检测为主线开展了以下几个方面的研究工作。
1.基于Zernike多项式推导了光学系统的出瞳变换矩阵以及波前绕自身几何中心旋转的变换矩阵。出瞳变换矩阵是研究光学系统的出瞳经缩放和偏心后，系统波像差的变换关系。在非球面检测系统中，被检镜从母镜到离轴非球面镜，相当于系统光瞳从母镜经缩放和偏心后变换到离轴子镜身上，因此，出瞳变换矩阵是研究母镜和离轴子镜检测系统波像差之间关系的桥梁。
2.本文基于三级像差理论，针对Offner、Dall和无光焦度补偿法，建立了相应的初始结构设计理论，考察了补偿器的结构参数对检测系统残余波像差的影响，明确了各参数的选取原则和范围。并结合XX三反相机中的离轴主镜和三镜，进行了实际检测光路的设计。
3.补偿器设计结果的工艺性是其能否得到实施的关键因素之一。本文以离轴三镜的检测系统为例，在现有的工艺水平下，对补偿器的制造、装调误差进行了详细的分析。
4.阐述了全息法检测非球面的原理及其对准方法。建立了单块离轴非球面镜检测系统的初始结构设计理论，对于大非球面度的离轴非球面镜，仅采用简单的单个补偿透镜是不能满足高精度非球面检测的要求，故在补偿法中引入计算全息，利用单个球面反射镜补偿由离轴非球面镜产生像散和慧差的主要量，计算全息片补偿剩余的像差，由于全息片所承担的像差量较少，因此其制作难度也可以降低，而且也简化了补偿器的结构。文中也给出了单块离轴非球面镜检测系统的设计实例。
5.根据离轴非球面面形偏差的数学表达式，通过分析离轴量误差引入的面形误差，指出离轴量误差主要是由母镜检测系统的非对称性像差—彗差引入的。由本文的分析可知，在小视场范围内，离轴量误差与检测视场成线性关系。同时基于Zernike旋转变换矩阵分析离轴非球面自旋角度误差对检测系统波像差的影响，给出自旋角度误差的计算公式。
6.针对补偿法和无像差点法检测离轴非球面，利用光线追迹法，分析非球面干涉检测系统中，由被检镜的调整误差引入的系统波像差，建立调整误差分离的数学模型。将该分离模型应用于XX离轴三反相机的主镜、三镜以及XX空间遥感相机的离轴三镜实际检测光路的调整中，最终检测结果都优于1/40λ RMS (Root Mean Square, λ=632.8nm)，试验结果验证了本文提出的调整误差分离方法的正确性。
本文通过对离轴非球面检测中若干关键技术的研究，对离轴非球面镜检测方案的确定、精度分析以及检测方案的实施提供了理论和技术指导，并成功制备出XX离轴三反相机中的主镜和三镜，为离轴相机最终的研制成功提供了关键基础技术保障。
Off-axis three-mirror system is with no obstruction. It is for this reason that onecan expect diffraction limited quality over a wide field of view. It should be clear thatOff-axis telescope is the next generation of earth observation telescopes. However, itis well known that fabrication of off-axis apsheres and alignment of off-axis systemare quite difficult. The fabrication of off-axis optical element requires thecorresponding testing method. The optical measurement of off-axis mirrors for thenext generation telescopes present a serious challenge.
This thesis is dedicated to solve the key theoretical and technical problems forthe test of off-axis aspheric optics. Here, the following researches in the test arecarried out:.
1. The transformation matrix of Zernike aberration coeffients is developedbetween scaled and decentered pupils. So is rotaion matrix for rotation of wavfront.When the test piece changed from the rotationally symmetric parent asphere to theoff-axis asphere, it means that the pupil of the test system is scaled and decentered.Therefore, the transformation matrix is the theorical base for analysis of therelationship between the off-axis aspheric mirror and its parent mirror in the test.
2. Based on the third order theory, design theory is established for Offner, Dalland Zero power null lens. The impact of structure parameter of the null lens on theresidual aberration is discussed, and the principle and value scope of parameterselecting is determined.
3. Tolerance analysis is performed for the null corrector of the tertiary off-axisaspheric mirror. Optical fabrication errors, alignment errors and environmental effectsare all considered.
4. The measurement of aspheric surface with CGH (Computer generatedhologram) and the alignment technology of the CGH are illustrated. The design ofoptical null testing off-axis aspheric mirror is developed. To test the steep off-axisaspheric, the null optics are often expensive to produce accurately. We can combine aspherical mirror and a CGH. The spherical mirror is tilted to compensate much of theastigmatism and some coma, and the CGH compensates rest of aberrations. At last wegive the design example for an off-axis parabolic mirror.
5. Based on the mathematic description for surface departure of the off-axisasphere from the paraxial sphere, misfigure induced by the error on the off-axis distance is analyzed. The coma observed in the test for rotationally symmetric parentaspheric is the source of the distance error. In our discussing off-axis interferometrictest for off-axis aspheric mirror, we showed that the error on the distance of theoff-axis aspheric is linear with the field of view. Meanwhile, a way to fine thetolerance on the allowable rotation error is developed by use of rotation matrix.
6. In interferogram the null lens test and stigmatic null test for off-axis asphericmirror, we analyze the effects of alignment error with optical path method by ray trace.An expression for wavefront aberrations induced by misalignment of the test piece isderived, and an optimum method for separating misalignment from misfigure ininterferograms on off-axis aspheres is developed. The method are applied to thealignment of two off-axis mirrors in the null lens test and one off-axis mirrors instigmatic null test. The test result of all the three off-axis mirrors can reach up to1/40λ (λ=632.8nm).
The research in this thesis is as a theoretical and technical guide for off-axisasphere test. Finally, the primary and tertiary off-axis aspheric mirrors in XX cameraare successfully fabricated. This supplies a basic technical guarantee for finalsuccessful development and manufacture of the off-axis telescope.
本文研究工作的主要任务就是有效地解决离轴非球面检测的关键理论和技术问题，从真正意义上掌握离轴非球面光学元件的测量技术。本文以XX离轴三反相机中的主镜和三镜的检测为主线开展了以下几个方面的研究工作。
1.基于Zernike多项式推导了光学系统的出瞳变换矩阵以及波前绕自身几何中心旋转的变换矩阵。出瞳变换矩阵是研究光学系统的出瞳经缩放和偏心后，系统波像差的变换关系。在非球面检测系统中，被检镜从母镜到离轴非球面镜，相当于系统光瞳从母镜经缩放和偏心后变换到离轴子镜身上，因此，出瞳变换矩阵是研究母镜和离轴子镜检测系统波像差之间关系的桥梁。
2.本文基于三级像差理论，针对Offner、Dall和无光焦度补偿法，建立了相应的初始结构设计理论，考察了补偿器的结构参数对检测系统残余波像差的影响，明确了各参数的选取原则和范围。并结合XX三反相机中的离轴主镜和三镜，进行了实际检测光路的设计。
3.补偿器设计结果的工艺性是其能否得到实施的关键因素之一。本文以离轴三镜的检测系统为例，在现有的工艺水平下，对补偿器的制造、装调误差进行了详细的分析。
4.阐述了全息法检测非球面的原理及其对准方法。建立了单块离轴非球面镜检测系统的初始结构设计理论，对于大非球面度的离轴非球面镜，仅采用简单的单个补偿透镜是不能满足高精度非球面检测的要求，故在补偿法中引入计算全息，利用单个球面反射镜补偿由离轴非球面镜产生像散和慧差的主要量，计算全息片补偿剩余的像差，由于全息片所承担的像差量较少，因此其制作难度也可以降低，而且也简化了补偿器的结构。文中也给出了单块离轴非球面镜检测系统的设计实例。
5.根据离轴非球面面形偏差的数学表达式，通过分析离轴量误差引入的面形误差，指出离轴量误差主要是由母镜检测系统的非对称性像差—彗差引入的。由本文的分析可知，在小视场范围内，离轴量误差与检测视场成线性关系。同时基于Zernike旋转变换矩阵分析离轴非球面自旋角度误差对检测系统波像差的影响，给出自旋角度误差的计算公式。
6.针对补偿法和无像差点法检测离轴非球面，利用光线追迹法，分析非球面干涉检测系统中，由被检镜的调整误差引入的系统波像差，建立调整误差分离的数学模型。将该分离模型应用于XX离轴三反相机的主镜、三镜以及XX空间遥感相机的离轴三镜实际检测光路的调整中，最终检测结果都优于1/40λ RMS (Root Mean Square, λ=632.8nm)，试验结果验证了本文提出的调整误差分离方法的正确性。
本文通过对离轴非球面检测中若干关键技术的研究，对离轴非球面镜检测方案的确定、精度分析以及检测方案的实施提供了理论和技术指导，并成功制备出XX离轴三反相机中的主镜和三镜，为离轴相机最终的研制成功提供了关键基础技术保障。
Off-axis three-mirror system is with no obstruction. It is for this reason that onecan expect diffraction limited quality over a wide field of view. It should be clear thatOff-axis telescope is the next generation of earth observation telescopes. However, itis well known that fabrication of off-axis apsheres and alignment of off-axis systemare quite difficult. The fabrication of off-axis optical element requires thecorresponding testing method. The optical measurement of off-axis mirrors for thenext generation telescopes present a serious challenge.
This thesis is dedicated to solve the key theoretical and technical problems forthe test of off-axis aspheric optics. Here, the following researches in the test arecarried out:.
1. The transformation matrix of Zernike aberration coeffients is developedbetween scaled and decentered pupils. So is rotaion matrix for rotation of wavfront.When the test piece changed from the rotationally symmetric parent asphere to theoff-axis asphere, it means that the pupil of the test system is scaled and decentered.Therefore, the transformation matrix is the theorical base for analysis of therelationship between the off-axis aspheric mirror and its parent mirror in the test.
2. Based on the third order theory, design theory is established for Offner, Dalland Zero power null lens. The impact of structure parameter of the null lens on theresidual aberration is discussed, and the principle and value scope of parameterselecting is determined.
3. Tolerance analysis is performed for the null corrector of the tertiary off-axisaspheric mirror. Optical fabrication errors, alignment errors and environmental effectsare all considered.
4. The measurement of aspheric surface with CGH (Computer generatedhologram) and the alignment technology of the CGH are illustrated. The design ofoptical null testing off-axis aspheric mirror is developed. To test the steep off-axisaspheric, the null optics are often expensive to produce accurately. We can combine aspherical mirror and a CGH. The spherical mirror is tilted to compensate much of theastigmatism and some coma, and the CGH compensates rest of aberrations. At last wegive the design example for an off-axis parabolic mirror.
5. Based on the mathematic description for surface departure of the off-axisasphere from the paraxial sphere, misfigure induced by the error on the off-axis distance is analyzed. The coma observed in the test for rotationally symmetric parentaspheric is the source of the distance error. In our discussing off-axis interferometrictest for off-axis aspheric mirror, we showed that the error on the distance of theoff-axis aspheric is linear with the field of view. Meanwhile, a way to fine thetolerance on the allowable rotation error is developed by use of rotation matrix.
6. In interferogram the null lens test and stigmatic null test for off-axis asphericmirror, we analyze the effects of alignment error with optical path method by ray trace.An expression for wavefront aberrations induced by misalignment of the test piece isderived, and an optimum method for separating misalignment from misfigure ininterferograms on off-axis aspheres is developed. The method are applied to thealignment of two off-axis mirrors in the null lens test and one off-axis mirrors instigmatic null test. The test result of all the three off-axis mirrors can reach up to1/40λ (λ=632.8nm).
The research in this thesis is as a theoretical and technical guide for off-axisasphere test. Finally, the primary and tertiary off-axis aspheric mirrors in XX cameraare successfully fabricated. This supplies a basic technical guarantee for finalsuccessful development and manufacture of the off-axis telescope.
引文
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