Automated fringe analysis techniques in Japan

Research efforts for interferometric fringe analysis techniques and their applications in Japan are reviewed with an emphasis on recent developments. Digital fringe analysis techniques and theoretical approaches to phase measuring interferometry are described. Automatic fringe analysis of speckle interferometry are also presented.     

New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor

White-light phase shifting interferometry (WLPSI) is frequently used for the precision measurement of 3D patterns in various fields. Phase error is one of the most dominant errors in WLPSI, and it is mainly generated by the scanner positioning error and mechanical vibrations. In this paper, phase error detection method by image analysis is proposed, and the numerical correction method for minimizing the phase error is also proposed. The image reconstruction method (IRM), iterative IRM (IIRM) as pre-processors, partial IRM (PIRM), least squares method (LSM) as a main processor, and surface compensation method (SCM) as a post-processor were developed for correcting phase errors. The five methods are implemented and simulated, and the pros and cons of each method are explained.Mirau type interferometry and the phase error generator using a PZT stage were used, and the measurements by WLPSI were done under various vibration conditions. The captured images were analyzed by the five correction methods, and the results were compared. Phase error was effectively minimized by the correction methods, and repeatability of 0.2 nm was obtained in the case of the specimen of 500 nm in height. Repeatability of 10 nm was obtained by conventional WLPSI algorithms for the same specimen.     

移相干涉测量中的抗振技术

移相干涉测量技术是一种众所周知的非接触式的高精密测量方法,具有广泛的应用范围。环境振动是移相干涉仪测量误差的主要来源之一,国际上一些从事干涉测量的工作人员提出了许多抗振的方法,大体上分为主动技术和被动技术。主动抗振技术主要是系统自身探测振动并通过反馈回路对振动进行补偿,被动抗振技术则是通过各种技术措施尽量减小干涉仪对环境振动和气流影响的敏感度。从这两方面对干涉仪的抗振技术研究的进展做简单介绍,并介绍了作者所在课题组在这两个方面所进行的研究工作。     

Comparison between instantaneous and integral intensities in dynamic speckle pattern interferometry

A new speckle measurement technique called temporal speckle pattern interferometry or time sequential speckle pattern interferometry has been developed recently. Its principle is that by capturing the temporal speckle patterns related to the object deformation or displacement, the whole-field displacement, the amplitude of the vibrating object and the shape of the tested object can be calculated through speckle intensity fluctuation scanning technique or Fourier-transforming method. In this paper, we combine the analytical and numerical methods to simulate the properties of the time demodulation in temporal speckle patterns interferometry techniques. The performance of three kinds of temporal phase sequences, power, exponential and harmonic phase sequences, are studied with the parameters of temporal speckle intensity fluctuation, the value of the spatial phase term, optical integral time of the recording camera and the initial phase of the temporal speckle intensities. The results indicate that the normalized value and period change of the instantaneous intensity are nearly coincident with that of the integral intensity for the harmonic temporal phase sequences and are different for the power and exponential temporal phase sequences.     

Lau phase interferometry with a vibrating object

In this paper, we have demonstrated experimentally the vibration analysis of a reflecting object in a time-averaged mode using Lau phase interferometry. Experimental results provide information about the tilt at every point of a vibrating plate. The Lau phase interferometry is robust and simple. Experimental results are compared with conventional shadow-moiré method.     

Analysis of measuring features of interferometric methods for studying “weak” optical inhomogeneity with a small transverse size

Comparative analysis of interference methods, which are most promising for studying optical inhomogeneities with a small transverse size, is carried out. It is shown based on analysis of interference fringes for the two most widely used interferometric methods (two-beam interferometry with a reference wave and lateral-shear interferometry) that in the case of a lateral shift exceeding the geometrical size, lateral-shear interferometry shows twice as high sensitivity as that of double-beam interferometry with a reference wave and is more promising for estimating the size of “weak” optical inhomogeneities.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

Iterative Fourier transform method for phase map recovery in electronic speckle-shearing pattern interferometry

Increasing phase values at the edges of objects under analysis in electronic speckle shearing interferometry (ESSPI) cause errors in the actual recovering methods to obtain the spatially integrated phase. An iterative least minimum squares method is proposed here to recover the phase map from the approximated ESSPI derivatives when the displacement phase is increasing near the object edges. It is based in an iterative Fourier transform method derived from a least-squares phase map recovery algorithm. Experimental results from a rotating cylindrical bar show the validity of our approach.     

Measurement of Wave-Front Aberrations in Lithography Lenses with an Overlay Inspection Tool

Measurement methods using overlay inspection tools have been established for wave-front aberrations in optical lithography lenses used for integrated circuit manufacturing. Three-beam interferometry and asymmetric two-beam interferometry can transform the wave-front aberrations at selected points on the lens pupil to lateral image shifts for fine grating objects. A technique of overlapped exposures makes the image shifts of inner lines of the grating images optically measurable, even if the images are too fine to be resolved optically. These methods are available in the fields of integrated circuit manufacturing and lithography tool assembling. This paper sums up measurement methods for wave-front aberrations. It is experimentally estimated that the methods are equally matched with the phase measuring interferometry widely used in the tool assemblies respecting accuracy and precision.This paper was originally presented at the 2nd International Conference on Optical Design and Fabrication, ODF2000 which was held on November 15–17, 2000 at the International Conference Center, Tokyo, Waseda University, Japan.     

Visualized measurement of the electric field in large aperture LiNbO3 crystal by digital holographic interferometry

The electric field distribution in Li Nb O3 crystal under different electrode shape is presented by using the digital holographic interferometry. Three configurations of phase modulator including the rectangular electrode type,single-triangle electrode type, and dual-triangle electrode type are performed in this experiment. The nonuniform electric field distribution in these phase modulators are observed and the electric field increases with voltage increasing. The digital holographic interferometry with high electro-optic effect improves the measurement precision. The digital holographic interferometry provides an effective way for studying the electric field distribution. Such in situ quantitative analysis of electric field distribution is a key to optimizing electrode shape.     

移相干涉测量术及其应用

为了对移相式数字干涉仪在光学元件测量中的应用有全面了解，介绍了移相干涉术的基本原理。结合激光数字波面干涉仪，阐述移相干涉术的四步重叠平均算法、压电晶体移相器(PZT)的结构、3 PZT的组合方法、移相器的标定误差和非线性误差的校正方法、波面相位解包的自适应种子算法、波面相位的评价指标等内容。结合移相数字波面干涉仪，叙述了移相干涉测量技术在普通光学元件、红外光学元件、大口径光学元件、非球面光学元件等测量中的应用并指出了应用过程中的注意事项。最后明确指出光干涉技术正沿着高相位分辨率、高空间分辨率、宽波段和瞬态高速测量的方向发展，并将会在瞬态波前测量、微机械的微结构动态分析等方面有着越来越广泛的应用。     

Spectrally-resolved white-light interferometry as a profilometry tool

Phase-shifting interferometry and white-light interferometry are reliable techniques for surface analysis in which the optical path difference has to be changed by some transducer to evaluate the phase. We present here a different procedure in which optical path modulation is completely avoided. This technique is based on the spectral analysis of white-light interferograms. By means of a spectroscopic device, a non-visible interferogram is split into its monochromatic components and absolute, unambiguous values of the phase are obtained along the spectral axis. Only one interferogram is required to obtain the profile of one-dimensional surfaces with nanometric resolution.     

相移全息干涉计量的统计分析

本文从统计光学的角度对相移全息干涉计量原理进行了详细的分析,指明由于变形过程中面内位移引起的散斑消相关效应的存在,使相位测量产生随机误差,误差的大小由面内位移量的大小决定,且这种误差不随相移计量过程中采样次数的增加而减小。提出了几种提高相位测量精度的有效方法,给出了相应的实验结果。     

Four-step spatial phase-shifting shearing interferometry from moiré configuration by triple gratings

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.     

Digital phase stepping speckle interferometry

A variation of electronic speckle pattern interferometry (ESPI) is presented whereby phase fringes are produced in contrast to speckle correlation fringes. Digital phase stepping speckle interferometry uses a phase measurement technique developed for holographic interferometry, which involves phase shifting of the reference beam in a conventional speckle interferometer. Saw-tooth phase fringes are produced by subtracting the phases of the speckle fields before and after object deformation in a digital frame store. This enables the sign of the deformation to be distinguished. After application of a special low-pass digital filter, the phase fringes are of adequate quality to be counted automatically.     

Simultaneous 2D in-plane deformation measurement using electronic speckle pattern interferometry with double phase modulations

Electronic speckle pattern interferometry(ESPI) and digital speckle pattern interferometry are wellestablished non-contact measurement methods. They have been widely used to carry out precise deformation mapping. However, the simultaneous two-dimensional(2D) or three-dimensional(3D) deformation measurements using ESPI with phase shifting usually involve complicated and slow equipment. In this Letter, we solve these issues by proposing a modified ESPI system based on double phase modulations with only one laser and one camera. In-plane normal and shear strains are obtained with good quality. This system can also be developed to measure 3D deformation, and it has the potential to carry out faster measurements with a highspeed camera.     

微探针纳米尺度振动测试的实验研究

微探针是扫描探针显微镜(SPM)的重要组成部件,其共振频率等振动特性直接影响系统的性能。给出了系统微探针共振频率的测试方法,对微探针在压电陶瓷驱动力作用下的受迫振动进行了有限元分析。提出了相位变化0.1°所对应的0.1nm位移分辨率的双频激光外差干涉光学测量系统,对微探针纳米尺度振动特性进行了测试对比实验,并对SPM标定样块进行了比对分析。实验结果验证了双频激光外差干涉测量方法的可行性和其应用价值。     

Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry

If a laser beam illuminates a continual deformation object surface, it will lead to a temporal speckle pattern on the observation plane. Recording this time-dependent speckle pattern the deformation of the surface of an object can be obtained. Two methods, scanning phase method (SPM) and time sequence phase method (TSPM), have been introduced for measuring the displacement caused by the deformation in temporal speckle pattern interferometry (TSPI). Their principle is that by capturing a series of speckle interference patterns related to the object deformations, the fluctuations in the intensity of the interference patterns can be obtained. Through scanning these fluctuations and estimating both the average intensity and modulation of the temporal speckle interference patterns, the phase maps for whole-field displacements are calculated. In this way one is capable of quantitatively measuring continual displacements simply using a conventional electronic speckle pattern interferometry (ESPI) system without phase shifting or a carrier. The elaboration on the new methods is given in this paper and experiments are performed to demonstrate their performance with a conventional ESPI system.     

Monitoring of residual stresses in injection-molded plastics with holographic interferometry

Residual stresses are often trapped in injection-molded plastic parts due to the rapid cooling of the material in this manufacturing process. These stresses are a common source of failure in plastic components in automobiles, appliances and computers and are difficult to measure with conventional residual-stress experimental methods. Real-time holographic interferometry appears to be a viable technique to identify and monitor these stresses in plastic parts. In this investigation, holographic interferometry was used to monitor the relaxation of residual stresses in the plastic-molded actuator arm of a computer hard drive. In the first phase of this study, the relaxation of these residual stresses as a function of temperature was observed. In the second phase, the time to completely relax the residual stresses in the plastic part at an elevated temperature, the annealing temperature, was determined. In the third phase of this investigation, the rate of relaxation of these residual stresses as a function of time at various operating temperatures, was studied. Based on the results of this study, holographic interferometry appears to be a powerful research tool in the study of residual stresses in plastic parts. It also has the potential to be a practical tool for the inspection of manufactured plastic parts for the presence of residual stress.