一种非旋转对称"花瓣形"相位板的检测系统设计

提出了利用计算全息图检测非旋转对称的"花瓣"形位相板.分析并推导了光线经过"花瓣"形相位板传播中的高阶像差的理论公式,并以此为指导进行了"花瓣形"相位板的检测系统的设计,给出了设计的结果.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间隔是20 μm,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103.187 nm.     

一种非旋转对称“花瓣形”相位板的检测系统设计

提出了利用计算全息图检测非旋转对称的“花瓣”形位相板.分析并推导了光线经过“花瓣”形相位板传播中的高阶像差的理论公式,并以此为指导进行了“花瓣形”相位板的检测系统的设计,给出了设计的结果.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间隔是20 μｍ,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103.187 nm.     

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。     

计算全息图案位置误差致波前误差的标定方法

通过对计算全息图检测非球面的误差进行分析,提出了一种用于计算全息图检测非球面过程中图案位置误差引入的波前误差的标定方法。该方法先设计检测过程中所需要的辅助波前和检测波前在计算全息基板上所对应的相位分布,再通过光场叠加的方式得到复合相位。辅助波前用于计算实际位置与设计位置的偏差,进而计算出位置畸变引起的检测误差,并将其从系统中消除。检测波前用于得到与非球面匹配的波前,进而对非球面面形进行检测,并提出了图案位置误差引入的非球面波前差的计算方法。为评估该方法的可行性,将复合相位所对应的计算全息图导入衍射计算软件中进行仿真,同时得到了平面、球面和非球面各个级次的衍射光斑,证明了该方法的正确性。     

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。     

用双计算全息图检测凹非球面

为实现对凹非球面的高精度检测,提出并设计了一种二元纯相位型双计算全息图.设计的双计算全息图由主全息和对准全息两部分组成,分别用于检测非球面和精确定位主全息.介绍了双计算全息图的工作原理及其设计方法,并给出了一个检测Φ140、F/2抛物面反射镜的双计算全息图设计实例,实验得到的均方根(RMS)误差为0.062λ.通过分析对准全息的误差,推导出主全息的条纹位置畸变误差,最后计算出其综合误差为0.06A.为验证实验结果的可靠性,将其与平面镜自准直检测结果(ERMS=0.062A)比较,结果二者吻合良好.     

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.     

计算全息检测离轴非球面的离散相位拟合

为了计算补偿用计算全息图的刻线位置,需要对光线追迹得到的离散相位数据进行拟合。为此详细推导了均匀三次B样条和非均匀三次B样条的基函数,介绍了各自对应的曲面拟合方法。以一块抛物型离轴非球面数据为例,对其非对称的离散相位分布进行了三次B样条曲面拟合。拟合结果表明,三次B样条曲面拟合能使拟合面经过所有数据点,保证拟合精度,且得到的连续的相位补偿函数表达式结构简单（最高次数只有3次）, 还能根据实际情况优化采样点数量,控制计算量。     

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。     

提高计算全息检测非球面量程的新技术

本文分析了宽条纹干涉型计算全息图的特点.提出了用宽条纹计算全息三级波面检测非球面的一项新技术.三级波面检测技术使全息图的条纹数减少约62%.实验结果证实了该技术的有效性和潜力.     

Using computer-generated holograms to test cubic surface

Computer-generated holograms (CGH) have been widely used to evaluate symmetrical aspherical surfaces in combination with Fizeau interferometers. Because the CGH can create any wavefront shape, it can also be used in unsymmetrical aspherical surfaces testing. Taking the cubic surface as an example, this paper gives a thinking of testing unsymmetrical surfaces. First we deduce the expression of the aberration for the cubic phase when propagating and the CGH null lens design has been carried out while taking into consideration the higher order aberrations. The separation of the diffraction orders of the CGH is discussed. We fabricated the CGH using e-beam photography and tested a 13-mm diameter cubic surface.     

计算全息法检测离轴凸非球面照明镜组初始结构设计

设计一种特殊的应用于计算全息法(CGH)高精度检测离轴凸非球面系统的照明系统。该照明系统一方面用作参考系统,另一方面将检测光近似垂直投射到待检测镜面上,使得检测系统为近似共光路系统,降低照明系统的制造精度。分析了照明系统的几何光路模型,将复杂的两用途系统简化,得到照明系统工作距离、照明系统焦距以及参考面曲率半径三个特征参量之间的关系。设计时,通过控制这几个特征参量,得到满足检测要求的系统初始结构。设计结果表明,该方法可以满足系统使用要求。     

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).     

Zone Plate Common Path Interferometer for Testing Aspherical Mirror with Large Aperture

A new CGH (computer generated hologram) common path interferometer, which can be used for testing an aspherical mirror with large aperture, is proposed. This interferometer does not have a circle of least confusion, and a spatial filter can be used effectively to stop extraneous lights so that interferograms with good contrast can be obtained. The phase shifting technique can be easily applied to the interferometer. The method of designing and making the CGH zone-plate is described.     

Problems on fabrication of computer-generated holograms for testing aspheric surfaces

Interferometric optical testing using computer-generated hologram （CGH） can give highly accurate measurement of aspheric surfaces has been proved. After the system is designed, a phase function is obtained according to the CGH＇s surface plane. For the requirement of accuracy, an optimization algorithm that transfers the phase function into a certain mask pattern file is presented in this letter, based on the relationship between the pattern error of CGH and the output wavefront accuracy. Then the writing machine is able to fabricate such a mask with this kind of file. With that mask, an improved procedure on fabrication of phase type CGH is also presented. Interferometrie test results of an aspherie surface show that the whole test system obtains the demanded accuracy.     

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.     

Computer generated hologram null compensator for optical metrology of a freeform surface

A computer-generated hologram (CGH) null compensator has been designed for optical metrology of a freeform surface (FFS) with positive base radius. The CGH is being employed in the freeform testing for the first time. The basic concept of the optical metrology and the testing procedure are explained explicitly. The design results of the CGH null compensator are presented in this article. Moreover, the design method and its results are discussed in detail.