Surface profile measurement in white-light scanning interferometry using a three-chip color CCD

White-light scanning interferometry (WLSI) is a useful technique to measure surface profile when a test object contains discontinuous structures or microstructures. A black and white CCD camera is usually utilized to capture interferograms, and a series of corresponding algorithms is used to achieve the profile measurement. However, the color information in the interferograms is lost. A novel profile measurement method that uses phase information in different color channels (red-green-blue) of an interferogram obtained using a three-chip color CCD in WLSI is proposed. The phase values are extracted by a windowed Fourier transform algorithm. Simulation and experimental results are presented to demonstrate the validity of the proposed method.     

Determination of fringe order in white-light interference microscopy

Combining phase and coherence information for improved precision in white-light interference microscopy requires a robust strategy for dealing with the inconsistencies between these two types of information. We correct for these inconsistencies on every measurement by direct analysis of the difference map between the coherence and the phase profiles. The algorithm adapts to surface texture and noise level and dynamically compensates for optical aberrations, distortions, diffraction, and dispersion that would otherwise lead to incorrect fringe order. The same analysis also provides the absolute height data that are essential to relational measurements between disconnected surfaces.     

Fringe modulation skewing effect in white-light vertical scanning interferometry

An interference fringe modulation skewing effect in white-light vertical scanning interferometry that can produce a batwings artifact in a step height measurement is described. The skewing occurs at a position on or close to the edge of a step in the sample under measurement when the step height is less than the coherence length of the light source used. A diffraction model is used to explain the effect.     

High-speed noncontact profiler based on scanning white-light interferometry

We describe a system for fast three-dimensional profilometry, of both optically smooth and optically rough surfaces, based on scanning white-light techniques. The system utilizes an efficient algorithm to extract and save only the region of interference, substantially reducing both the acquisition and the analysis times. Rough and discontinuous surfaces can be profiled without the phase-ambiguity problems associated with conventional phase-shifting techniques. The system measures steps to 100 μm, scans a 10μLm range in 5 s, and has a smooth surface repeatability of 0.5 nm.     

孔径径向扫描白光散斑干涉法的研究

提出了一种用于动态研究的新方法-孔径径向扫描白光散斑干涉法,介绍了两孔和直三孔径向扫描器.该方法是一种非接触式的用于动态测量的白光散斑法.分析了孔径径向扫描白光散斑干涉法的基本原理,给出了白光散斑全场滤波分析的平均光强解析式和实验结果.该方法的优点是利用散斑的调频技术能在一张白光散斑图上记录物体的连续动态变形的信息,在全场滤波分时,能将物体动态变形的信息方便地提取出来,得到清晰的全场白光散斑条纹图.直三孔径向扫描法能得到物体在x方向、y方向和45°方向上的变形信息.在实时全场滤波分析观察时,将滤波孔连续地沿径向扫描,可观察到物体连续动态变形的全过程,从而为物体的动态研究提供了一种新方法.     

Theoretical limits of scanning white-light interferometry signal evaluation algorithms

Scanning white-light interferometry is widely used for the microstructure analysis of technical and biological specimens. For each pixel in the focal plane of the apparatus a white-light interferogram is acquired and evaluated by means of an algorithm. We discuss some properties of mathematically optimal evaluation methods and the best possible achievable resolution derived therefrom depending on the setup parameters. A comparison of the results to one of the algorithms described in the literature is given.     

Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry

White-light scanning interferometry is increasingly used for precision profile metrology of engineering surfaces, but its current applications are limited primarily to opaque surfaces with relatively simple optical reflection behavior. A new attempt is made to extend the interferometric method to the thickness-profile measurement of transparent thin-film layers. An extensive frequency-domain analysis of multiple reflection is performed to allow both the top and the bottom interfaces of a thin-film layer to be measured independently at the same time by the nonlinear least-squares technique. This rigorous approach provides not only point-by-point thickness probing but also complete volumetric film profiles digitized in three dimensions.     

Sensitivity analysis of thin-film thickness measurement by vertical scanning white-light interferometry

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.     

Determination of the instrument function of a grating spectrometer by using white-light interferometry

We determined the instrument function or the response function of a grating spectrometer with finite slit widths in conditions of partial coherent illumination, by using a spectral-interference technique with white light. A Michelson interferometer of variable path delay is used to produce the spectral-interference fringes of required spacing. By deconvolution of the spectral visibility data for various exit and entrance slit widths, we have determined the exact form and frequency width of the instrument function for the spectrometer as well as the working region of the spectrometer for the least distorted output spectrum.     

Vibration-compensated interferometry system using phase-modulating interference fringe subdivision technology

An innovative vibration-compensation method, with phase-modulating interference fringe subdivision technology, is described. It simulates fringe movement by the phase difference of signals and can detect the fringe movement with an accuracy of 1/400 fringe spacing using this subdivision technology. A closed-loop vibration-compensation system is built, and the measurement of an interference fringe movement and a vibration-compensation test are successfully demonstrated. Because of this new method and a new feedback algorithm that was introduced, interference fringes can be stabilized at any preset phase position in real time. Compared with known methods, this method is simple and inexpensive, as well as effective.     

白光干涉测量法中蝠翼效应的模拟分析

为探索白光干涉仪在测量矩形台阶时的蝠翼效应误差,建立白光干涉虚拟测量模型.在模型中,考虑白光光源带宽和干涉物镜数值孔径以及圆孔衍射模型的影响,分析蝠翼效应与真实台阶高度、光源中心波长之间的关系.模拟结果表明当台阶高度差是λ0/4的奇数倍时会出现蝠翼效应,且越接近λ0/4的奇数倍,蝠翼效应越显著.关于对蝠翼误差的补偿,分...     

Multiperiod fringe projection interferometry using a backpropagation method for surface profile measurement

Interference fringes with different periods are projected on an object surface. There is a constant phase point where the phase of the fringe is kept at a constant value while the period is scanning. Multiple optical fields with different periods on the object surface are made from detected phases of the fringes. The multiple optical fields are backpropagated to the constant phase point of the phase where all of the phases of the multiple backpropagated fields become the same value and the amplitude of the sum of the multiple backpropagated fields becomes maximum. The distance of the backpropagation provides the position of the object surface. Some experiments show that this method can measure an object surface with discontinuities of several millimeters with high accuracy of several micrometers.     

Improved optical profiling using the spectral phase in spectrally resolved white-light interferometry

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Abstract

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.     

Linearization and flattening technique for fringe analysis and its application to holographic interferometry

A simple technique for correcting the nonlinearity of a camera-digitizer system is presented. With this technique cameras that are extremely nonlinear but which enhance fringe contrast can be used. The technique can also reduce the number of phase-shifted interferograms required for quantitative analysis from three to two or (with some restrictions) to one. The last option is important for the interpretation of transient phenomena. The technique is demonstrated for the strain analysis of a pressure vessel by holographic interferometry (HI). The contribution to suitable noise elimination is also described.     

Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function

This letter introduces a new approach for the demodulation of fringe patterns recorded in holographic interferometry using high-order ambiguity function (HAF). The proposed approach is capable of retrieving the phase from a single fringe pattern. The main advantage of this approach is that it directly provides an estimation of the continuous phase distribution and thereby avoids the necessity of using a cumbersome 2D phase unwrapping procedure. This method first computes the discrete-time analytic signal of the recorded fringe pattern. Then, by modelling this analytic signal as a polynomial phase signal embedded in additive complex white Gaussian noise, a parametric estimation procedure based on HAF is employed to directly estimate the unwrapped phase distribution. Numerical simulations and experimental results demonstrate the potential of the proposed approach.     

Direct determination of isochromatic fringe order by use of two wavelengths

A method of direct determination of photoelastic fringe order is proposed. The relations between the integral fringe order for one wavelength and the fractional fringe orders of two wavelengths are derived. The exact fringe order of the whole field is automatically calculated. The usefulness of this method is demonstrated through experimental result.     

Measuring intermodal dispersion in optical fibres using white-light spectral interferometry with the compensated michelson interferometer

Abstract

Employing a low-resolution miniature fibre-optic spectrometer, it is demonstrated that the spectral interference fringes are resolved at the output of a tandem configuration of the compensated (non-dispersive) Michelson interferometer and a two-mode optical fibre only in the vicinity of two different equalization wavelengths. Namely, the overall equalization wavelength at which the optical path difference (OPD) in the interferometer is the same as the group OPD between modes, and the fibre equalization wavelength at which the group OPD between modes is zero. Moreover it is shown that the OPD adjusted in the interferometer and measured as a function of the overall equalization wavelength gives directly the spectral dependence of the intermodal group OPD in an optical fibre. Thus the new technique of white-light spectral interferometry is used to measure intermodal dispersion in two different two-mode optical fibres in the spectral range approximately from 620 to 850 nm.     

White-light interferometry using a channeled spectrum. I. General models and fringe estimation algorithms

Astrometric measurements using stellar interferometry rely on the precise measurement of the central white-light fringe to accurately obtain the optical path-length difference of incoming starlight to the two arms of the interferometer. Because of dispersion in the optical system the optical path-length difference is a function of the wavelength of the light and extracting the proper astrometric signatures requires accommodating these effects. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the path-length delay. Because of throughput considerations these channels are made sufficiently broad so that monochromatic models are inadequate for retrieving the phase/delay information. The presence of dispersion makes the polychromatic modeling problem for phase estimation even more difficult because of its effect on the complex visibility function. We introduce a class of models that rely on just a few spectral and dispersion parameters. A phase-shifting interferometry algorithm is derived that exploits the model structure. Numerical examples are given to illustrate the robustness and precision of the approach.