Problems on design of computer-generated holograms for testing aspheric surfaces: principle and calculation

Interferometric optical testing using computer-generated hologram (CGH) has provided an approach to highly accurate measurement of aspheric surfaces. While designing the CGH null correctors, we should make them with as small aperture and low spatial frequency as possible, and with no zero slope of phase except at center, for the sake of insuring lowisk of substrate figure error and feasibility of fabrication. On the basis of classic optics, a set of equations for calculating the phase function of CGH are obtained. These equations lead us to find the dependence of the aperture and spatial frequency on the axial diszance from the tested aspheric surface for the CGH. We also simulatethe ptical path difference error of the CGH relative to the accuracy of controlling laser spot during fabrication. Meanwhile, we discuss the constraints used to avoid zero slope of phase except at center and give a design result of the CGH for the tested aspheric surface. The results ensure the feasibility of designing a useful CGH to test aspheric urface fundamentally.     

计算全息检测离轴非球面的离散相位计算

为了设计检测离轴非球面的计算全息图（CGH）,需要对采样点的相位进行计算。通过平移和旋转,将离轴非球面几何中心的法线作为检测光路光轴。在此基础上,采用光线追迹法,对离轴非球面上采样点的相位分布进行了研究,详细推导了离散相位的计算方法,给出了在3维空间坐标系中,离轴非球面上任意一采样点的相位计算公式,并通过计算、对比同一旋转对称非球面的相位分布对该算法进行了验证。结果表明该计算方法正确,且计算精度能够满足CGH的要求。     

变步长搜索的计算全息图编码方法

基于计算全息图(Computer-Generated Hologram,CGH)的非球面检测技术通过控制衍射光相位来生成所需要的参考波前,从而实现非球面的零位检测,近年来,该技术已经发展成为非球面的主流检测技术。对于CGH编码,采用传统编码方法实现高精度编码,其数据量往往高达几十甚至上百GB。因此,为同时确保编码精度高及编码数据量小,本文提出了一种变步长CGH编码方法。该方法首先通过寻找等相位面的方法得到CGH条纹分布,然后通过计算相位分布梯度选取不同的取样步长,使CGH能利用尽可能少的点实现高精度编码。利用变步长搜索的编码方法进行编码并制作了CGH对非球面样品进行检测,检测结果为3.142 nm(RMS)。为验证检测结果可信度,本文设计并制作了补偿器对同一非球面进行检测,其检测结果为3.645 nm(RMS)。对两检测结果点对点做差,RMS值为1.291 nm,结果表明该编码方法可满足非球面高精度检测需求。     

Aspheric surface reconstruction for scanning interference

A simplified reconstructing method for the aspheric surface testing based on scanning interference technology is presented. The aspheric normal intersects the optical axis at different points with different angles, which is called normal congruence; a normal congruence can identify an aspheric surface. In this method, the test aspheric surface is shifted along the optical axis to scan the tested aspheric surface; meanwhile a series of interferograms and phase maps are obtained. The angles between the normal lines and the aspheric axis are obtained using the positions of zero-phase points, according to the image-forming principle of the camera. Here, Zernike polynomials are applied to analyze the phase maps and extract the zero-phase points. Finally, the absolute coordinates of the test surface is rebuilt through iterative integration. Because both the system deformation and amplification do not affect the reconstruction result, this method can avoid complicated stitching algorithm in the subaperture stitching interferometric method. Experimental results show that the method has high accuracy and reliability.     

Study on the Phase Detecting Laser Interferometric System with Computer Generated Hologram

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Measurement accuracy verification of aspheric surface test with computer-generated hologram

A convex aspheric surface using a computer-generated hologram(CGH) test plate fabricated with novel techniques and equipment is tested.However,the measurement result is not verified via comparison with other methods.To verify the accuracy of the measurement,a perfect sphere surface is measured by the following.The measurement result is quantified into four parts:the figure error from the tested spherical surface;the figure error from the reference spherical surface;the error from the hologram;and the adjustment error from misalignment.The measurement result,removed from the later three errors,shows agreement to 4-nm RMS with the test by Zygo interfermeter of the same surface.Analysis of the CGH test showed the overall accuracy of the 4-nm RMS,with 3.9 nm from the test plate figure,0.5 nm from the hologram,and 0.74 nm from other sources,such as random vibration,various second order effects,and so on.Thus,the measurement accuracy using the proposed CGH could be very high.CGH can therefore be used to measure aspheric surfaces accurately.     

一种离轴计算全息图在凹非球面检测中的应用

为了精确检测大口径非球面面型质量,将CGH作为补偿器应用于凹非球面的离轴全息检测系统中.根据计算全息图的离轴全息检测系统检测凹非球面的基本原理,分析了离轴CGH的计算、制作过程,实现了对口径为150 mm,近轴半径为1499.7 mm,非球面系数为-1的凹非球面镜的检测.实验结果与轮廓仪检测结果吻合得很好.     

用于非球面检测的计算全息设计及其精度分析

介绍了用于非球面检测计算全息(Computer-generated hologram,CGH)的设计方法和步骤,对CGH位相分布求取、载频选取、CGH与干涉仪配合校准所涉及的关键问题展开了讨论,提出了一些全新的设计理念和方法。从理论上定量分析了CGH片基面型误差、全息图样偏差、刻蚀深度不均匀性和线宽不均匀性对再现波面的影响,得出了相应的误差公式指导计算全息元件加工环节的公差分配。给出了一个设计实例,检测不确定度达到λ/20。     

Shack-Hartmann波前传感器非零位在轴检测离轴非球面反射镜

在离轴非球面反射镜研磨后期和粗抛光阶段,被测反射镜面形与理想面形存在着较大的偏差,表面反射率较低,采用干涉测量会因局部区域干涉条纹过密或条纹对比度过低,造成普通干涉仪无法进行全口径测量,而普通接触式轮廓仪测量精度此时已经不能满足加工要求。鉴于Shack-Hartmann波前传感器较大的动态范围和较高的测量精度,提出了采用Shack-Hartmann波前传感器非零位在轴检测离轴非球面面形,研究了该方法的检测原理并搭建了检测系统,分析了系统误差来源,并制作了用于在轴检测离轴非球面的参考波前,对两个不同加工精度的离轴非球面反射镜进行了测量,并与干涉仪的测量结果进行了对比。对比结果表明,Shack-Hartmann波前传感器的测量结果是正确可靠的,并且可以弥补轮廓仪测量和干涉仪测量的不足,从而证明了采用Shack-Hartmann波前传感器在轴检测离轴非球面的可行性和正确性。     

Null test of aspheric surface based on digital phase-shift interferometer

In order to implement the null test of aspheric surfaces as simply as that of spherical ones in a commercial digital phase-shift interferometer, computer generated holograms (CGHs) that are composed of a main CGH, which produces the ideal aspheric wavefront, and an alignment CGH, which aids in calibration, were utilized. The principle of testing aspheric surface in an interferometer with CGHs is explained and critical aspects in designing, fabricating and calibrating CGHs are discussed in detail. Error analysis of the experimental results demonstrated that the uncertainty of the testing system is better than λ/10 (λ=0.6328 μm).     

提高二元计算全息图设计精度的新途径

用于非球面光学元件检测的计算全息图的设计与制作精度对实现非球面的高精度检测是至关重要的。为了提高计算全息图的设计精度,采用Householder变换把矛盾方程组的系数矩阵正交三角化,直接求解波面拟合系数,避免了法方程组的构造。全息图的设计是直接利用MATLAB的内部函数编程来实现的。对具有旋转对称性和非旋转对称性的物波进行了波面拟合,并设计了相应的计算全息图。结果表明,物波函数的拟合精度和全息图的绘制精度均有明显的提高,且计算速度快。     

用二元光学技术制作计算全息波面变换元件

基于计算全息原理与二元光学技术设计制作了应用于机载平视显示器（HUD）中的计算全息波面变换元件,该元件具有较高的衍射效率,一块二元相位型计算全息元件的衍射效率比一般计算全息图的衍射效率提高了四倍,并能产生传统光学元件不能实现的光学波面,如非球面,环状面和锥面等,制作工艺简单,复制简便。     

计算机产生全息图对补偿器检测的技术研究

用一种计算全息板代替补偿器零检验光路中理想的大型非球面,实现对补偿器的定量检验.用于检测补偿器旋转对称的二元反射式全息板根据非球面方程设计,并确定其光程差,再由激光直写(精度可达0.6μm)来制作完成,合成相当于理想非球面反射波前.其检测精度小于λ/10.补偿器的参量由抛物面和三级球差理论确定.     

Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test

An off-axis Ronchi test based on the phase-shifting technique is presented to measure the aspheric mirror quantitatively. In this paper, slopes of deviations from the mirror's ideal aspheric shape are derived when an off-axis point source is used. By integrating these slopes, the deviations of the shape are obtained and then the tested shape can be reconstructed. Compared with the coaxial Ronchi test, the measurement error caused by combination fringes can be avoided, and this system is more flexible. In the experiment, a marked point is used to guide the phase unwrapping procedure, which improves the accuracy of extracting corresponding phase points. In addition, the method has strong anti-noise ability. The validity of the method has been verified by both computer simulations and a preliminary experiment.     

Fabricating of aspheric micro-lens array by excimer laser micromachining

This work presents a unique method for fabricating aspheric micro-lens array based on a KrF 248 nm excimer laser micromachining with precise surface profile control. Based on a planetary contour scanning laser machining method along with a shading metal mask and sample movable stage, an array of micro-lenses with precisely controlled surface profiles can be fabricated. Each lens surface profile can be aspheric and pre-designed. Experiments have been carried out and the machining accuracy of each lens surface profile is examined. Good surface roughness and profile accuracy are observed.     

一种三次非旋转对称的相位板的检测系统设计

作为零位干涉检测方法中非常有前途的一种方法.计算全息可以用于非旋转对称的非球面的检测.以三次相位板为例,阐述了利用计算全息图检测非旋转对称的非球面的基本原理.分析并推导了三次相位传播过程引入的高阶波像差的理论公式,给出了三次相位板的检测系统的没计结果.详细讨论了计算全息图衍射级次的分离以及计算全息图的二元化,给出了振幅型的计算全息图的图样.计算全息图的刻线最小问隔是40μm,计算全息图的制作精度对检测结果的波前误差的影响仅仅为0.005λ.对检测系统作了详细的公差分析,结果表明所有调整公差对整个检测系统的影响和方根值为83.954 nm.     

傅里叶变换条纹相位分析法测量非球面镜

本文将傅里叶变换(FFT)条纹位相测量方法用于非球面镜的检测。叙述了波面位相偏差测量原理。提出用最小二乘拟合波象差代替计算全息图(CGH)补偿非球面波象差,并分析了测量误差。     

中小口径双非球面数控抛光技术研究

针对口径Φ62 mm双凸非球面透镜,进行了数控研磨和抛光技术研究.提出了规范性的加工工艺流程,实现了中小口径双非球面元件的高效、快速抛光.根据计算机控制光学表面成型技术,采用全口径抛光和小抛头修抛的两步抛光法,在抛光中对其面形误差进行多次反馈补偿,使被加工零件表面的面形精度逐步收敛.最终两面的面形精度均小于0.5 μm,中心偏差小于0.01 mm,满足了光学系统中对非球面元件的精度要求,并且在保证有较高面形精度和较好表面光洁度的同时,解决了双非球面中心偏差和中心厚度难以控制的加工技术难题.     

大数值孔径、高次非球面透镜的加工与检验

通过一空间相机光学系统中某透镜的高次非球面表面加工过程,提出了一种基于小磨头数控光学表面成型技术(CCOS,Computercontrolopticalsurfacing)和非球面轮廓检验、零位补偿检验技术的中等口径高次非球面光学表面的加工、检测方法,并且给出了补偿器实际光学设计结果。文中采用这种方法加工的高次非球面表面,最终精度优于1λP V(λ=632.8nm),满足了设计要求。对这种技术的适用范围进行了简明的讨论。     

使用环形子孔径拼接检测大口径非球面镜

针对高精度大口径非球面镜通常存在定量检验方法(补偿器法、全息法、自准直法)所需要的辅助元件制造困难、成本高这两个主要难点,利用不同曲率半径的参考球面波前来匹配被测非球面表面不同的环带区域,使它们之间的偏离量减小到在小口径干涉仪的测量范围内,每次测量仅是被测表面的一部分,通过算法"拼接"可得到全孔径的面形信息。给出了其拼接数学模型、参量求解方法及其精度评定判据。仿真分析表明,该技术是切实可行的,算法具有较高的拼接精度。该方法无需辅助光学元件就可实现对大口径、大相对口径非球面的直接测量,且具有很宽的适用范围。