基于多次平移的平面绝对检测仿真

将待测面形表示为多项式的和,通过分别沿x,y向多次平移待检光学元件得到移动前后待测元件面形差,采用最小二乘法拟合多项式系数,得到待检光学元件的绝对面形。推导了多次平移法的理论公式,并进行了仿真实验,模拟了移动次数、移动间隔和采样点数对测量精度的影响。仿真结果表明:待测平面与初始平面残差图的均方根值为5.118×10~(-13)λ,理论误差达到高精度平面面形检测要求。     

基于单次旋转的旋转非对称面形误差绝对检测技术研究

绝对检测技术是剔除干涉仪系统误差进而提高面形检测精度的有效手段。基于单次旋转的绝对检测技术由被测球面绕光轴旋转前后的检测数据,采用基于最小二乘法的Zernike多项式拟合,剔除系统误差,获得被测面的旋转非对称面形误差。详细推导了理论计算公式,分析了单次旋转角度对算法检测精度的影响,并和多次旋转法作了对比,其残差均方根(RMS)值约为1.5nm。该方法只需一次旋转两次检测,在保证检测精度的同时简化了检测过程。     

非球面非零位检测的逆向优化面形重构

非球面的非零位检测较其零位检测而言具有更强的通用性,但非零位检测偏离了零位条件,所产生的回程误差给被测非球面的面形重构带来一定困难。针对非球面非零位检测中回程误差的校正与面形重构问题,提出了基于检测系统理论建模的非球面面形逆向求解技术。该方法对实际检测系统进行理论建模,设置被测面面形为变量,以实际检测到的波前作为目标函数,通过拟合优化得到的结果进而重构出被测面面形。对逆向优化重构技术进行了仿真验证、实际检测和误差分析,实际测量口径为101.0mm的凹抛物面反射镜,检测结果与标准零位法测得结果一致,峰谷值和均方根值误差分别优于λ/20和λ/50。     

基于有限元法的面形反演模型

为利用有限元法和面形检测结果反演出光学元件的面形,对面形检测结果进行分解,并对旋转平均法面形检测原理进行分析,讨论采用忽略光学元件自身面形的理想几何模型对其旋转非对称项面形误差进行有限元计算的理论可行性.在此基础上提出了基于有限元法反演光学元件面形的反演模型.以三点球支撑6inch平面镜为例,建立接触有限元模型计算旋转非对称项面形误差,对比了数值法和N步旋转平均法所获得的镜面旋转非对称项面形误差,结果显示,二者的旋转非对称项面形均方根值为分别为2.944nm和2.762nm,两种方法获得的面形相减结果分别为二者的6.31%和6.73%.最后对比了面形反演的面形结果与N步旋转平均法所获得的面形检测结果,结果显示,二者的面形均方根值分别为3.535nm和3.351nm,两种方法获得的面形相减结果分别为二者的11.67%和11.06%.证明提出的反演模型准确可靠.     

基于光学偏折的微小透镜双曲面同步测量

针对自由曲面微小透镜检测中无法同时高精度检测前后表面的问题，提出一种基于光学偏折的微小透镜前后曲面同步测量方法。该方法基于高精度的透射波前检测系统建立理想光线追迹模型，并在利用光学偏折高精度测得的含有被测微小透镜面形信息的透射波前像差基础上，以被测微小透镜的前后两个曲面为优化变量，进行数值迭代优化求解，最终基于优化结果重构出被测微小透镜各表面面形误差。对所提出的面形测量方法进行仿真与实验验证，并通过Zygo干涉仪进行比对实验，结果显示对于口径为6 mm的微小透镜，所提方法的检测结果与比对实验的检测结果高度一致，面形偏差的均方根误差值仅为几十纳米。     

两位置球面面形检测方法研究

三位置球面面形绝对检测方法在一定的条件下可以简化为两位置球面面形检测方法.本文在研究三位置绝对检测原理的基础上,提出了基于菲索干涉系统新的两位置球面面形检测方法.该方法的简化条件分为参考面面形误差偶对称或被检面面形误差偶对称两种不同的情况.实验结果表明,两位置检测方法可以有效实现PVr值λ/30的高准确度检测,且检测结...     

基于N次图像旋转法的两平晶三面互检技术研究

光学平面面形的绝对检验技术规避了干涉仪参考面形精度的制约,能够有效提高平晶面形的检测精度。采用N次图像旋转法的两平晶三面互检的绝对检验技术,求解待测平晶的三维绝对面形分布,结果中包含了中频波段的信息。利用递推公式构造旋转变化项的N次虚拟旋转结果,求和平均后得到旋转变化项,叠加旋转不变项结果后得到待测波面面形。推导了算法的理论误差,针对旋转角度进行优化并增加虚拟旋转次数,提高了算法精度,优化后的仿真结果的残差波面的均方根值精度为0.14 nm。对150 mm口径平晶进行两平晶三面互检实验,并将实验结果与传统三面互检法结果进行比对,均方根值偏差小于0.5 nm,验证了算法的准确性。     

基于液面旋转平移法的绝对检验技术研究

绝对检验作为一种光学元件高精度检测方法,其中的两平晶绝对检验无法精确测量平移过程中的倾斜误差,导致恢复的面形中二次项出现偏差.液面在位置变化前后能够保持水平,在旋转平移过程中不会产生倾斜误差.推导了平移过程中倾斜误差和恢复面形中离焦项的关系,并通过仿真分析加以验证,当不存在倾斜误差时,残差面PV值小于1nm.在300m...     

同步辐射用光学元件面形绝对检测方法的研究

为实现同步辐射用光学元件面形的绝对检测,发展了镜面旋转对称三平板检测法。该方法将菲佐干涉法检测到的波前函数关于y轴分解成镜面对称部分与镜面非对称部分,再利用N次旋转取平均值消除镜面非对称部分,从而通过计算获得待测平面的绝对面形分布。推导了镜面旋转对称法检测矩形平面镜面形的公式,应用该方法设计了高精度矩形平面镜的测试实验,并进行了误差分析。实验结果表明,与传统三平板绝对测量方法相比较,两种方法在高度轮廓误差和斜率误差方面的计算结果都符合较好,其对比后的残差均方根(RMS)值分别为λ/500(λ=632.8nm)与0.93μrad。     

基于迭代算法的两平板互检求解方法

提出了一种基于两平板绝对检验的迭代面形恢复算法。算法基于两平板互检方法,通过分别翻转和旋转其中一块平板,获得4次两两测量结果。对测量得到的4个结果数据进行翻转和旋转逆操作,直接推导出三个面形与测量结果及相互之间的关系公式。设置初始面形,逐次迭代逼近4次测量结果。实验表明,该方法仅需要50次以内迭代,即可得到偏差小于0.1nm均方根值的绝对面形。详细分析了实验过程中的各项误差来源,并对每项误差进行了定量计算,获得总的测量误差为1.417nm。     

Absolute surface figure testing by shift-rotation method using Zernike polynomials

In surface figure testing, most of them are relative tests, and the reference surface usually limits the accuracy of test results. Absolute calibration is one of the most important and efficient techniques to reach subnanometer accuracy in surface figure testing. An absolute testing method, a shift-rotation method using Zernike polynomials, is presented, which can be used to calibrate both flat and spherical surfaces (concave or convex). Calibration contains at least three position measurements: one basic position, one rotation, and one lateral shift of the test surface. Experiments show that the repeatability of this method is 0.13?nm RMS, and pixel-to-pixel comparison with the two-sphere method is 0.2?nm RMS.     

Absolute measurement of flats with the method of shift-rotation

We present an absolute measurement of flats in a Fizeau interferometer with the method of shift-rotation, which only requires rotational measurements and shift measurement with a translation. Experiments have been carried out to verify the validity of the absolute testing method, and the results show that the reference surface deviation measured with the shift-rotation method agrees well with that of another calibration result with traditional three-flat absolute procedure; the root-mean-square (RMS) of the residual figure between them is ～0.4 nm.     

An absolute test for axicon surfaces

We present a method for absolute testing of axicon surfaces in a null test setup. The absolute test exploits the symmetry of axicons, which allows us to introduce a shift of the surface under test in both the axial and rotational directions while still maintaining the null test condition. With two shifts of the surface under test and four measurements, the interferometer and null optics error can be removed. The absolute surface local deviation can be obtained by wavefront reconstruction with a double-side spiral-path direct integration method. A simulation of the method, including typical systematic as well as statistical errors as input, is presented to estimate the error propagation. Experimental absolute test results of a 90° axicon surface are given.     

Absolute spherical test towards an accuracy of one-hundredth of the wavelength

Two dominant systematic errors in the absolute interferometric test of high numerical-aperture sphericals are discussed and measured experimentally in pursuit of an accuracy of λ=100. Gravitational sag deformation of a 4-inch spherical concave surface was measured in a vertical phase-shifting Fizeau interferometer. The surface shapes of two identical transmission spherical concaves were measured via the two-surface comparison method using three positional measurements. One of the surfaces was then rotated around the optical axis and the interference phases were averaged to extract a rotationally symmetric component of the aberration. The gravitational sag was then determined by the aberration component independent of the rotation. The geometrical error in the phase shift is also estimated theoretically and corrected in the experiment. Experimental results show that the both errors amount to 6 to 7 nm peak-to-valley lengths, the magnitudes of which are comparable to that of the total aberration of the spherical surface.     

Nuclear magnetic relaxation by quadrupole interactions in non-spherical molecules

The nuclear magnetic relaxation times associated with quadrupole interactions are investigated by an analytical method for molecules that may be linear or symmetric rotators, or may be totally asymmetric. The molecules are subject to random thermal couples, and it is supposed that the consequent rotational motion is Brownian. The results are in agreement with those obtained otherwise by Hubbard for the special case of spherical molecules.     

Modified Rocard relation for complex permittivity

It is shown that to a high degree of accuracy the complex relativity permittivity for a gas dielectric or for a liquid dielectric in very dilute solution in a nonpolarsolvent is given theoretically for symmetric polar molecules by the modification of a relation, which essentially goes back to Rocard. When the molecules are linear or spherical, the modified relation is particularly simple. There is no simple relation for complex permittivity when the polar molecules are asymmetric. Thus in comparing the theory of rotational Brownian motion with the results of dielectric relaxation experiments it would seem advisable at the present stage to focus attention on experiments performed with symmetric polar molecules, preferably spherical or linear.     

非球面检测中最佳入射球面波和最佳参考球面波的确定

为了能够对非球面光学元件面型进行高精度的干涉检测,提出了一种确定最佳入射球面波和最佳参考球面波的新方法。该方法通过计算分析入射球面波与非球面反射波干涉条纹密度,确定最佳入射球面波的波源位置;通过计算分析在干涉图记录平面CCD上干涉条纹的密度,确定非球面检测时参考球面波波源的最佳位置。应用该理论与方法,不仅可明确非球面检测时CCD等光路元件选型的具体策略,而且可用于指导非球面检测调试过程,并能够通过对干涉图的深入分析,获得更多被测非球面的信息。     

自由曲面成像光学系统设计:理论、发展与应用

传统球面以及非球面可供光学系统设计使用的自由度较少。自由曲面打破了旋转对称以及平移对称的几何约束,特别适用于校正非旋转对称系统的像差,同时可以减少系统中元件的数量,减小系统的体积与质量,实现传统光学系统难以实现的系统参数、结构与功能。自由曲面为光学设计的发展注入了巨大潜力,但同时也带来了全新的困难与挑战。概括性地总结了自由曲面成像系统设计的研究现状。简要介绍了自由曲面的常用数学描述与自由曲面成像系统的像差理论,总结了自由曲面成像系统的设计方法,并对自由曲面在各类成像系统中的应用进行概述。最后,对自由曲面成像光学设计的未来发展方向进行了讨论与展望。     

Rapid and reliable reference sphere calibration for Fizeau interferometry

I describe and demonstrate a rapid and simple technique for calibrating spherical reference surfaces in Fizeau interferometry. A flat mirror at the focus of the test wavefront and a partial occlusion of the test beam enable a double-pass measurement of one half of the surface against the other, which gives an error map for half the aperture. Subsequent rotations of the beam stop and stitching together of several measurements yields the full-aperture calibration file. The method always produces point-symmetrical surface maps and is therefore not exact. However, most actual reference surfaces are approximately point symmetric and therefore the trade-off of accuracy for expediency is reasonable in practice.     

Calibration of geometrical systematic error in high-precision spherical surface measurement

Geometric aberrations in interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surface, in which obvious high-order aberrations introduced by wavefront defocus could be observed and they cannot be removed with the traditional calibration method. A technique based on the rigorous model for the analysis of geometric aberrations introduced by wavefront tilt and defocus, is presented for the calibration of the corresponding geometrical systematic error. The calibration method can be carried out either with or without a prior knowledge of the spherical surface under test. The feasibility of the proposed method has been demonstrated by computer simulation, and the residual error less than 0.001λ is obtained. Experimental validation is carried out by testing a high-numerical-aperture spherical surface with the ZYGO interferometer, and an accuracy RMS about 0.003λ with the proposed calibration technique is achieved. The effect of geometric aberrations on the measurement is discussed in detail. The proposed calibration method provides a feasible way to lower the requirement on the adjusting precision of mechanical device, and is of great practicality for the high-precision measurement of high-numerical-aperture spherical surface.