误差补偿技术在相位偏移干涉测量中的应用

在研究泰曼—格林相位偏移干涉仪测量原理基础上，分析了位移驱动器移相误差对五幅移相计算结果的影响，一阶线性误差和二阶非线性误差是相位偏移干涉测量技术中产生相位误差的主要因素；提出了五幅算法移相误差补偿技术，该方法直接从相位偏移干涉图中计算移相过程中存在的一阶及二阶移相误差，对五幅算法结果进行误差修正；采用玻璃平晶为测试对象，建立了泰曼一格林干涉仪移相误差补偿原理试验系统。试验结果表明在同时存在一阶移相误差及二阶移相误差情况下，采用提出的移相误差补偿方法可以将位移测量精度提高6倍，相当于采用氦氖激光器的倍程干涉仪中位移精度达到1．0nm。     

Wavelength-modulation Fourier interferometry with elimination of DC phase error

Wavelength-modulation Fourier interferometry has been employed to measure the thickness of a glass plate. However, nonlinear phase-modulation error causes a DC error in the evaluated phase distribution. In this study, a 5 N–2 phase-extraction algorithm was derived for the simultaneous measurement of the thickness and surface shape of a glass plate with eliminating the DC phase error. First, the condition for the error elimination on a complex plane was derived and a new algorithm polynomial was proposed to satisfy this condition. Next, using this condition and 5 N–4 algorithm, 5 N–2 algorithm was derived. The newly developed 5 N–2 algorithm was visualized in the frequency domain using the Fourier transform method. The DC error elimination ability of the 5 N–2 algorithm was confirmed through numerical error analysis. Finally, the surface shape and thickness of the glass plate were simultaneously measured using a large-aperture Fizeau interferometer and the 5 N–2 algorithm. The standard deviations of the thickness and surface shape profiling were 3.113 nm and 10.689 nm, respectively, which were smaller than those obtained using other phase-extraction algorithms.     

可实现误差估计的移相量计算方法

针对移相干涉仪中移相器的标定,提出了一种基于干涉图计算移相量的迭代方法。该方法分为两步:首先假设移相量已知,构建三元最小二乘方程计算位相;然后假设位相已知,构建二元最小二乘方程计算移相量,同时依据三角函数关系和遍历原则,建立估算移相量计算误差的参数。利用计算机仿真和实验验证了提出方法的有效性。计算机仿真显示:提出的方法比已有算法计算精度更高,而且误差估计值与实际计算误差偏离小于15%。在Fizeau干涉仪上开展了验证实验,利用两个电容位移传感器测量了镜架的位移。计算结果与电容传感器测量结果非常吻合,最大偏差仅为0.7nm。另外,利用本文方法得到的误差估计值为0.52nm,显示测量结果和计算结果的偏差在误差估计值范围内。所提出的方法可以高精度地提取移相量,且能给出移相量计算误差,是一种简单可靠的移相器标定方法。     

Measurement of highly reflective surface shape using wavelength tuning Fizeau interferometer and polynomial window function

In this study, a 5N − 4 phase shifting algorithm comprising a polynomial window function and a discrete Fourier transform is developed to measure interferometrically the surface shape of a silicon wafer, with suppression of the coupling errors between the higher harmonics and the phase shift error. A new polynomial window function is derived on the basis of the characteristic polynomial theory by locating five multiple roots on the characteristic diagram. The characteristics of the 5N − 4 algorithm are estimated with respect to the Fourier representation in the frequency domain. The phase error of the measurements performed using the 5N − 4 algorithm is discussed and compared with those of measurements obtained using other conventional phase shifting algorithms. Finally, the surface shape of a 4-in. silicon wafer is measured using the 5N − 4 algorithm and a wavelength tuning Fizeau interferometer. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated by other algorithms. The uncertainty of the entire measurement was 34 nm, better than that of any other conventional phase shifting algorithms.     

双球面法标定立式参考球面的精度分析

采用双球面法对立式Fizeau干涉仪的参考球面进行标定以确定由重力、安装夹持力等导致的面形形变量,提高立式光学系统中光学元件的面形检测精度.首先,推导了双球面法标定算法;进而,理论分析和模拟计算了影响检测精度的环境、重力、安装夹持力等因素;最后,利用双球面法对立式Fizeau干涉仪的参考球面进行标定,并利用误差合成理论分析实验结果.实验结果显示,利用双球面法标定F/1.5的立式Fizeau干涉仪参考面的精度为2.3 nm.其中,算法本身以及实验操作引起的测量重复性不大于0.7 nm,包含环境误差时的重复性低于1.2 nm;重力导致的面形形变约为0.9 nm,标准镜安装导致的面形形变约为1.7 nm.结果论证了双球面法具有很高的标定精度;环境对检测精度的影响与干涉腔长度有关,长度增加时影响很明显;立式工作时,重力、安装等因素导致的标准镜参考球面的面形形变很大,在高精度使用前必须进行标定.     

Simultaneous interferometric measurement of the absolute thickness and surface shape of a transparent plate using wavelength tuning Fourier analysis and phase shifting

The absolute optical thickness and surface shape of optical devices are considered as the fundamental characteristics when designing optical equipment. The thickness and surface shape should be measured simultaneously to reduce cost. In this research, the absolute optical thickness and surface shape of a 6–mm-thick fused silica transparent plate of diameter 100 mm was measured simultaneously by a three-surface Fizeau interferometer. A measurement method combining the wavelength tuning Fourier and phase shifting technique was proposed. The absolute optical thickness that corresponds to the group refractive index was determined by wavelength tuning Fourier analysis. At the beginning and end of the wavelength tuning, the fractional phases of the interference fringes were measured by the phase shifting technique and optical thickness deviations with respect to the ordinary refractive index and surface shape were determined. These two kinds of optical thicknesses were synthesized using the Sellmeier equation for the refractive index of fused silica glass, and the least square fitting method was used to determine the final absolute optical thickness distribution. The experimental results indicate that the all the measurement uncertainties for the absolute optical thickness and surface shape were approximately 3 nm and 35 nm, respectively.     

加权多步波长移相算法研究

波长移相干涉技术通过改变光源的波长实现移相,可以克服硬件移相引入的误差,同时原理上可以实现多组干涉信号的分离。主要应用于大尺寸干涉仪及需要分离多表面干涉信号的系统中。加权多步波长移相算法是其主要的算法,中心思想是通过时域加入合适的窗函数,抑制寄生信号,提出包含轮廓或厚度信息的有用信号。文中介绍其设计思想,进行算法设计,并对一光学件进行了测试和比对。     

相移器平移误差与倾斜误差不敏感相移新算法

相移器的相移误差包括平移误差与倾斜误差,使同一幅干涉图诸像素点的相移量并不相等,但仍然在同一平面上.据此,本文提出了消除相移器位移误差与倾斜误差的最小二乘迭代算法.通过对相移平面的最小二乘拟合,即可以消除相移器平移误差与倾斜误差对位相分布求解结果的影响.并通过数值模拟,验证了这种算法在消除相移器位移误差与倾斜影响上的有效性.     

Calibration method to characterize the accuracy of phase-shifting point diffraction interferometer

Characterization of measurement accuracy of the phase-shifting point diffraction interferometer (PS∕PDI) is usually performed by two-pinhole null test. In this procedure, the geometrical coma and detector tilt astigmatism systematic errors are almost one or two magnitude higher than the desired accuracy of PS∕PDI. These errors must be accurately removed from the null test result to achieve high accuracy. Published calibration methods, which can remove the geometrical coma error successfully, have some limitations in calibrating the astigmatism error. In this paper, we propose a method to simultaneously calibrate the geometrical coma and detector tilt astigmatism errors in PS∕PDI null test. Based on the measurement results obtained from two pinhole pairs in orthogonal directions, the method utilizes the orthogonal and rotational symmetry properties of Zernike polynomials over unit circle to calculate the systematic errors introduced in null test of PS∕PDI. The experiment using PS∕PDI operated at visible light is performed to verify the method. The results show that the method is effective in isolating the systematic errors of PS∕PDI and the measurement accuracy of the calibrated PS∕PDI is 0.0088λ rms (λ = 632.8 nm).     

Shape measurements of mirror surfaces with a lateral-shearing interferometer during machine running

A common path lateral-shearing interferometer with a minimum number of optical components has been developed. Because the interferometer is little affected by mechanical vibrations and air turbulence, it can be mounted on an ultraprecision lathe and can be used to measure the shapes of workpieces. A plane parallel glass plate is used to shear the wavefront under test in the interferometer. To analyze the interference fringes obtained by the interferometer precisely, a fringe-scanning method using a slight tilt of the glass plate is used. Zone plates that are computer-generated holograms are used to measure spherical and aspherical surfaces with the interferometer. A spherical and a parabolic concave mirror were measured with the interferometer. The spherical mirror was also measured by a Fizeau interferometer to compare the error with that measured by the lateral-shearing interferometer. The experimental results agreed well with those measured by the lateral-shearing interferometer.     

A NEW ALGORITHM FOR ELIMINATING PHASE-SHIFT ERROR IN PHASE SHIFTING INTERFEROMETRY

The effect of phase-shift error in phase shifting interferometry is investigated. A new algorithm with two sets of 4 samples for eliminating phase-shift error is presented. The computer simulation and experiment result show that the phase-shift offset should be π when the algorithm is used, and this algorithm has gotten better result than the original 4-sample algorithm.     

被测件随机移相干涉面形测量方法

针对光学元件的面形测量,提出了一种被测件随机移相干涉面形测量法,用于降低移相干涉仪的成本,避免移相器老化产生的移相误差对面形检测精度的影响。该方法利用微位移驱动器驱动被测件在摩擦气浮复合导轨上移动进行随机移相并用相机采集若干幅干涉图;然后利用最小二乘迭代算法处理干涉图数据进而迭代出被测表面相位分布;最后进行一系列数据处理求解出被测件的面形结果。为了验证该方法的可行性,在实验室搭建了改进的斐索移相干涉系统,并选用一个凹面镜和一个平面镜作为被测件在搭建的系统上进行了实验测试,同时与同台仪器上的传统移相方法得到的测量结果进行了比对。结果表明:在激光光源波长λ为632.8nm的情况下,凹球面镜面形PV值和RMS值与传统移相方式测量结果相差0.001λ,和0.002λ;平面镜面形PV值和RMS值与传统移相方式的测量结果相差0.002λ和0.003λ,面形数据基本一致。该方法避免了移相器老化引入移相误差,降低了仪器成本,测量精度高。     

金刚石复合片与硬质合金的钎焊研究

通过聚晶金刚石复合片与YG8硬质合金的高频感应钎焊试验,研究了不同钎料钎剂搭配对高频感应钎焊接头抗剪强度、焊缝厚度的影响,并用扫描电镜和电子探针观察、分析了焊缝的微观结构。结果表明,690℃钎焊温度下含Mn的1号钎料和活性温度较高的QJ102钎剂是最佳搭配方案。探讨了聚晶金刚石复合片的特殊钎焊工艺,认为采用复焊方法可以大幅提高钎焊接头的抗剪强度。     

The Design and Characteristics of a 630-mm Phase-Shifting Interferometer

A large-aperture Fizeau interferometer has been developed for measuring the characteristics of optical elements with flat surfaces. The interferometer has two fields of view with dimensions of 630 and 100 mm and with transverse resolutions of 0.63 and 0.1 mm/pixel, respectively. Due to the calibration of the reference plates, the absolute measurement accuracy of the interferometer is λ/1000 RMS (λ = 632.8 nm) on a 630-mm field of view.     

基于光强实时反馈控制和同步校准的波长调谐移相干涉系统

波长调谐移相干涉技术是通过改变光波长来计算相位的。为了减少可调谐激光器在变波长进行移相时光功率的随机变化对相位计算产生的误差,本文提出了一套光强实时反馈控制系统和同步校准方案。首先分析了光强在某一范围内的随机变化产生测量误差,并选用合适的光电检测设备搭建了一套光强控制系统。该系统能够将光信号转化为电信号,并通过PID来实现对光强的控制。实验结果表明,本系统能够将光强的变化范围控制在±0.002 mW以内,其响应速度达到600 kHz,已远远超过干涉仪CCD的取图速度。最后,对口径为50 mm的光学元件进行表面形貌检测,加入本控制系统后,面形精度的测量指标PV值和RMS值分别提高了1.53×10^-2λ和2.43×10^-3λ,表明本系统在高精度的光学元件检测领域具有重要的实用价值。     

Phase-shifting interferometer using a frequency-tunable diode laser calibrated by an optical frequency comb

We present a phase-shifting interferometer based on a frequency-tunable diode laser calibrated by an optical frequency comb and the Carre? algorithm. By use of the frequency control strategies of locking the diode laser to different comb modes and scanning the repetition rate, an arbitrary single optical frequency synthesizer is obtained. The relative laser frequency uncertainty is 5.7 × 10(-12) for 1 s averaging time with tracing to an Rb clock and accurate phase steps are achieved by optical frequency tuning. The surface topography of a standard sphere is measured by this phase-shifting interferometer based on a flat reference. The phase measurement repeatability is λ∕200. With this technique, phase measurement uncertainties from the laser frequency and phase steps are negligible.     

基于频域分析的抗振移相干涉测量

针对移相干涉测量中振动引起的移相误差和对比度变化,提出了一种从空间载波干涉图频谱中提取移相和对比度信息的方法。该方法通过分析载波干涉图频谱,从基带和边带中提取移相和对比度信息,运用最小二乘法补偿对比度变化并复原波前位相。最后采用构造平滑孔径函数对带有孔径的干涉图进行处理。数值仿真证明:提出的方法可以高精度检测移相量和对比度变化,能够有效补偿因对比度变化引起的位相复原误差。在频率为9Hz、幅度为0.5μm的简谐振动条件下实验验证了本文方法的实用性。结果显示:从受振动干扰的干涉图中复原平晶表面时,其复原误差PV值小于0.015波长。该方法无需硬件改动,有望为移相干涉测量应用于现场测量提供一种低成本的解决方法。     

基于双平行平面相机模型的钢板尺寸视觉测量

提出基于双平行平面相机模型的视觉测量方法,用于测量生产线上运动钢板的尺寸。该方法采用数据驱动的方式计算像点在标定平面上投影点的世界坐标;采用k近邻(k-NN)方法生成目标在标定平面上的无畸变投影图像,并建立投影图像与世界坐标系的直接关联。提出了双平行平面模型下相机光心位置标定算法,利用线结构光进行板材厚度测量;在无畸变的投影图像上利用钢板边缘间的平行和垂直性进行钢板边缘特征提取,通过边缘直线的世界坐标方程求取长宽尺寸。最后,给出了针对大尺寸钢板测量的多相机测量系统框架。提出的方法为单目视觉测量方法,相比于其他方法具有现场安装简单和标定工作量小的特点。通过图像分辨率为640×480的相机对尺寸为80mm×50mm×15mm的标准铝块进行了测量,结果显示:厚度测量误差为0.1mm,长度和宽度的误差在0.2mm以内。实际应用中测量精度远高于加工精度,能够满足产品计量的要求。     

Absolute interferometric test for high numerical-aperture spherical concave surfaces: Gravitational effect

Spherical concave surfaces with high numerical apertures are required in industry for lithography optics at ultraviolet and X-ray wavelengths. Among the systematic errors in these spherical-surface test, the gravitational deformation has not been separated from the other optical aberrations. We utilized a two-surface comparison method to quantify the gravitational deformation in a vertical Fizeau interferometer. Certain aberrations vary with rotation around the optical axis. We averaged the ordinary aberrations and isolated the aberration caused by gravitational deformation. Experimental results show that a 4-in concave surface with an F-number 0.75 reveals to have a gravitational deformation of 7 nm peak-to-valley.     

Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration

This paper performs a comprehensive analysis and calibration on the geometric error of the ultra-precision drum roll lathe with dual-spindle symmetrical structure and cross slider layout. Firstly, the volumetric error model which contains all geometric errors of the dual-spindle ultra-precision drum roll lathe (DSUPDRL) is developed based on the combination of the homogenous transfer matrix (HTM) and multi-body system (MBS) theory. Secondly, sensitivity analysis for the volumetric error model is conducted to identify the sensitive geometric error components of the DSUPDRL using an improved Sobol method based on the quasi-Monte Carlo algorithm. The result of sensitivity analysis laid the foundation for the subsequent geometric error calibration. Then, some sensitive error components along the X and Z directions are calibrated using a laser interferometer and a pair of inductance displacement probes. Besides the volumetric error model, the concentricity error caused by dual-spindle symmetrical structure is proposed and calibrated by the on-machine measurement using a classic reversal method. Finally, a large-scale roller mold with a diameter of 250 mm and a length of 600 mm is machined using the DSUPDRL after calibration. The experimental result shows that 1.4 μm/600 mm generatrix accuracy is obtained, which validate the effectiveness of the geometric error analysis and calibration.