Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter

Parallel two-step phase-shifting interferometry for microscopy is presented, and the recording condition for generalized two-step phase-shifting interferometry is discussed. A 45° tilted cube beamsplitter enables to replicate the orthogonally linear polarized object and reference waves into two parallel beams, respectively. As a consequence, two interferograms with quadrature phase shift are obtained along the two beams, and phase reconstructed with an improved algorithm. To reconstruct the phase distribution from the two-step phase-shifting interferograms, a certain recording condition should be satisfied. However, the recording condition has not ever been discussed before. In this paper, the recording condition for the two-step phase-shifting interferometry is derived and that is: the intensity of reference wave should be no less than two times object wave intensity.     

3-D surface profilometry using simultaneous phase-shifting interferometry

Urgent needs for high-speed, non-contact and on-line measurement with high accuracy and repeatability are of great interest for automatic optical inspection (AOI) industries. Therefore, optical phase-shifting interferometry for precision 3-D surface profilometry has become an important metrological method due to its non-contact and high measurement accuracy. Traditional phase-shifting interferometry is very sensitive to vibrations because image acquisition in various phase-shifting sequences could easily introduce measurement errors from environmental influences, such as air disturbance and system structure vibrations. In this paper, we introduce a new simultaneous phase-shifting interferometer for 3-D surface profilometry which employs a single glass plate to generate simultaneous phase-shifted interferograms. Phase reconstruction is performed by using a developed phase-shifting algorithm which uses a three-step phase-shifting method with phase differences of 90°, 180°, and 270° for three interferograms. To verify measurement accuracy and repeatability, the system was employed to measure surface profiles of surface of a flat mirror and set of Mitutoyo gauge blocks. The experiment result shows that the method is proven to be capable of performing one-shot interferometric measurement and minimizing influences from environmental disturbances with measurement repeatability down to 10 nm or less.     

空域移相偏振点衍射波前检测技术

点衍射干涉仪结构简单、共光路、测量精度高, 空域移相干涉仪抗振性能优越, 两者在波前检测领域获得了广泛的应用. 本文采用激光打孔技术, 通过在金属纳米线栅偏振片上制备小孔, 制作了偏振点衍射板; 结合分光结构的空域移相技术, 搭建了空域移相偏振点衍射干涉仪, 并对一焦距为550 mm, F_#10的平行光管准直物镜透射波前进行测量, 与法国Phasics公司生产的商业化波前传感器SID4的测量结果相比较, 两者峰谷值相差0.09λ, 均方根值相差0.012λ ; 利用35项Zernike多项式拟合两者的测量结果, 将拟合得到的系数在同一坐标轴下绘制成两条曲线, 两者基本重合, 从而验证了所搭建的空域移相偏振点衍射波前检测装置的测试精度. 从而在传统点衍射干涉仪的基础上引入了空域移相技术, 实现了波前的高分辨率、高精度、实时检测, 并且提高了对振动、气流等环境因素的抗干扰能力.     

移相式干涉仪在锥体棱镜角度测试中的应用

为了实时、高精度地测试光学零件，对移相式数字波面干涉仪在锥体棱镜角度测试中的应用进行了研究。通过锥体棱镜二面角偏差计算方法得到了二面角偏差和干涉波面之间的关系，分析了干涉波面的形状与锥体棱镜综合误差的关系，编写了锥体棱镜角度和综合误差测试程序，并且在移相式数字波面干涉仪和ZYGO干涉仪上分别对锥体棱镜进行测试，给出了2者的比较测试结果。结果表明，移相式数字波面干涉仪测量锥体棱镜二面角偏差的误差在0.3″范围内，RMS值的测量误差在λ/50内；提出的方法可实现检测过程的自动化。     

Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer

A Fizeau interferometer based set up for measurement of surface forms of plane optical surfaces has been discussed. Phase shifting interferometry has been applied using polarization phase shifter. A linearly polarized (632.8 nm) He–Ne laser has been used as the source. Light reflected from the object and the reference/master surfaces are made circularly polarized in opposite senses by means of two properly oriented quarter wave retardation plates placed at appropriate positions, one inside and other outside the interference cavity of the interferometer, and phase shifts are introduced between the object and the reference/master waves by varying angular orientation of a polarizer/analyzer. Final result is made free from any residual wave-front aberrations introduced by the (intra-cavity) wave plate by subtracting phase values obtained by PSI technique between a high optical quality master surface and the reference surface from that obtained for the test object surface with respect to the same reference surface for each point of the interference field. Results are shown for a plane surface.Advantages of the technique presented are linearity and high accuracy in phase stepping, no perturbation of the interference cavity during the phase shifting and possibility of real time or dynamic interferometry.     

两步广义相移干涉术的光学实验验证

提出了一种基于两步广义相移干涉术的波前再现技术以及基于衍射场统计特性的未知相移值提取算法,并且进行了光学实验验证.该方法中可仅利用两幅干涉图及一次不需精确预设的未知相移,参照物光光强和参考光光强,即可通过计算提取真实的相移量,进而恢复出物波波前复振幅,而无需借助傅里叶谱分析或数字滤波等操作.在光学实验中,对借助于空间光调制器（SLM）的间接输入和三维漫反射物体直接输入两种情况进行了详细地研究,得到的光学实验结果验证了所提方案的有效性和可行性. 关键词： 信息光学 相移干涉术 波前再现 数字图像处理     

菲索干涉仪中精确移相的实现

为了实现移相式菲索干涉仪对光学元件面形的高精度测量,建立了干涉仪同步采集移相系统,并对精确移相方法进行了研究。介绍了移相系统的构成和工作原理,计算了测量过程中移相器的速度。针对PZT移相器在移相过程中会引入离焦误差,并存在加速段和减速段的问题,详细设计了移相器的行进过程。最后,对移相器的性能进行了标定。在改造后的干涉仪上开展了重复性验证实验,结果表明：干涉仪可以获得λ/11 340的RMS测量重复性。对改造后干涉仪与Zygo公司生产的Verifire XP/D干涉仪的测量精度做了比对实验,结果显示：相同元件下两者测量结果的面形RMS之差约为0.9 nm,表明提出的移相系统及移相方法在重复性和准确度方面都能满足纳米级面形测量的要求,为研制高精度移相干涉仪奠定了基础。     

一种机械扫描式精密相移测长方法

以相移干涉测长为应用背景,提出了一种基于“机械扫描”的相移测长方法。利用超高弹性石英材料研制出了干涉测长所需的单体3路相移装置,并利用该相移装置建成了相移测长装置,成功地将位移传感器的量值在线溯源到光学频率标准,从而实现了对3路相移的准确测量。介绍了一种引入步长控制误差的“新五幅相移”实现相位解算方法,算法准确度达到0.01%。对不确定度的定量分析结果表明,基于该机械扫描式相移技术构建的绝对长度测量系统准确度可达0.5 nm。     

两步相移数字全息物光重建误差分析与校正

系统研究了两步相移数字全息干涉术中相移误差引起的波前再现误差的计算和校正方法. 基于衍射物光相位分布的随机性和振幅相位的相互独立性原理,介绍了相移数字全息中物光波前再现误差的表达形式,推导出步长为π/2的两步算法中物光重建误差的表达式. 通过进一步分析这一重建误差的结构和特点,结合物光表达式,给出了自动校正相移误差引起的波前重建误差的校正方法. 该方法无需增加测量,在未知相移误差大小的情况下,只对标准两步相移算法恢复的物光复振幅进行处理就可以实现对物光振幅和相位的同时校正. 计算机模拟结果表明,校正后可将 关键词： 相移干涉术 数字全息 物光重建 误差校正     

由三个压电陶瓷堆组成的干涉仪移相器的校正与标定

根据傅里叶变换原理 ,提出了一种对由三个压电陶瓷堆 (PZT)组成的干涉仪移相器进行非线性及平行性校正与标定的方法。在对各个压电陶瓷堆进行非线性校正的基础上 ,利用干涉图像自动分析系统 ,综合分析各个压电陶瓷堆之间的牵制作用 ,从而得到对整体干涉仪移相器平行性校正的补偿依据。组建了一套卧式数字平面干涉仪 ,在干涉仪移相器承重 6kg的情况下进行实验 ,非线性误差由 12 %校正至 0 3 %。由于干涉仪相移器承重而引起的移相过程中的条纹旋转降至 2° ,条纹间距变化小于 2 %。     

基于相移干涉术的光学信息隐藏系统的软件实现

结合双随机相位编码技术与相移干涉术,提出了一种信息隐藏系统,待隐藏信息被加密到多幅干涉图数据中后。通过选取合适的权重因子,它们可以被嵌入到宿主图像中;利用特定的相移再现公式和逆菲涅耳衍射变换,可以实现隐藏信息的提取及解密．通过基于Matcom的VisualC＋＋与Matlab混合编程,设计和开发了一款信息隐藏系统软件,经过界面测试,该软件可以实现图像读取及显示、基本几何参数输入、信息加密及嵌入、信息提取及解密、鲁棒性测试等主要功能．     

用于相移点衍射干涉仪的加权最小二乘相位提取算法

针对现有的相位提取算法只对某些特定的误差不敏感,不能满足高精度光学检测的要求,本文引入一种等间隔多步移相算法—权重待定的加权最小二乘算法。通过在最小二乘算法中添加待定的权重,分析移相点衍射干涉仪中多种误差源对算法的影响,获得多组约束方程,从而确定权重和新算法。对新算法和标准四步算法、Hariharan五步算法进行比对分析,验证了新算法对PZT线性和二阶非线性移相不准、光强的一阶二阶波动和光源频率一阶二阶波动等误差抑制能力远远优于标准四步算法和Hariharan五步算法;新算法对CCD的量化误差、光强噪声、频率噪声的抑制能力也具有一定优势,且对CCD的二阶响应非线性完全不敏感。     

A method for calculating the wedge spacing of a Fizeau wavelength meter

The wedge spacing of a Fizeau wavelength meter is an important parameter in the conversion of fringe patterns into wavelengths of interfering light. In this paper, computation formulae are derived for calculating the wedge spacing of a Fizeau wavelength meter. The calculated accuracy, which is of the order of 0.1 μm, is discussed. The main advantage of this method is that it calculates an accurate value of the wedge spacing using an estimated value of the spacing and two known wavelengths.     

Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements

A new two-frame interferometric method with a blind phase shift of a reference wave is proposed for the reconstruction of smooth surface relief areas. In this method, a correlation approach based on the determination of correlation coefficient between intensity distributions of two interferograms is applied for the phase shift extraction. An algorithm for this method realization is developed and its performance is verified on test surfaces. An experimental setup containing a Twiman-Green interferometer was used in the reconstruction of smooth surfaces of metal specimens using the developed algorithm. Surface displacement phase fields were generated in case of a CT-notched specimen made of an aluminum alloy by the interactive procedure of element stitching of two surface reliefs and subtracting the surface relief after cyclic loading from the initial one. The received surface displacement fields allow us to determine the studied specimen fatigue process zone (FPZ) and FPZ size.     

移相干涉技术中移相器的自校正方法

移相干涉技术（ＰＳＩ）是８０年代兴起的一门干涉图形自动识别技术，移相器作为移相干涉技术的关键部件其移相误差将直接影响到移相干涉技术的干涉图的识别精度。本文提出了一种移相器的自校正方法，即利用移相干涉仪的自身系统，通过快速傅里叶方法，对移相器进行逐步逼近校正。结合移相式红外干涉仪的研制，给出了一组移相器的自动校正的实验，实验表明，校正后的移相器的非线性误差可由原来的５％降低到０．２％。     

波长调谐干涉测量的相移标定方法

基于菲索干涉的变频相移技术,提出一种分步相移标定方法.生成n组t步相移干涉图,每步相移为π/2;将每步的n组干涉图分别与初始干涉图做相乘和傅里叶变换运算,在此基础上构建每步相移的误差函数;通过求取误差函数极值点来实现对每步相移值的准确标定.结果表明,该标定方法的标定准确度优于传统标定方法,且标定准确度提高了2~3个数量级.该方法不仅避免了传统相移标定中存在的随机误差,也彻底消除了累积误差.     

Determination of displacement with a piezoelectric transducer using phase-shift algorithms

This investigation accurately measures the relationship between applied voltage and the displacement of a piezoelectric transducer device both by analyzing phase shifting interferometry algorithms and using a Twyman-Green interferometer. Simulations are performed to calculate unknown phase shifts, especially around π/2 and 3π/2. It is indicated that the Hariharan algorithm is indeed an effective phase shifting interferometry algorithm.     

抑制高阶谐波误差的随机相移条纹分析算法

高阶谐波和随机相移误差是影响条纹分析精度的主要因素。为了同时解决这两个问题,提出了基于频域滤波的迭代相移算法。该算法采用巴特沃斯低通滤波器,从频域上滤除条纹的高阶谐波分量,再运用最小二乘迭代方法从三帧随机相移条纹图像中提取相位信息。数值模拟和实验结果表明,该算法可有效地抑制由高阶谐波和随机相移引入的波纹误差,误差PV值和RMS值分别为0.368 8 rad和0.025 3 rad,其精度高于传统的三步相移算法和Wang算法。该方法适合于高精度干涉测量和三维物体表面轮廓测量。     

Design and experiments for the waveguide to coaxial cable adapter of a cavity beam position monitor

The waveguide to coaxial cable adapter is very important to the cavity beam position monitor(CBPM)because it determines how much of the energy in the cavity could be coupled outside.In this paper,the waveguide to coaxial cable adapter of a CBPM is designed and experiments are conducted.The curve shapes of experiments and simulations are very similar and the difference in reflection is less than 0.1.This progress provides a reliable method for designing the adapter.     

Design and experiments for the waveguide to coaxial cable adapter of a cavity beam position monitor

The waveguide to coaxial cable adapter is very important to the cavity beam position monitor (CBPM) because it determines how much of the energy in the cavity could be coupled outside. In this paper, the waveguide to coaxial cable adapter of a CBPM is designed and experiments are conducted. The curve shapes of experiments and simulations are very similar and the difference in reflection is less than 0.1. This progress provides a reliable method for designing the adapter.