Single-shot two-dimensional surface measurement based on spectrally resolved white-light interferometry

By analyzing the spectral domain's phase information, one can use spectrally resolved white-light interferometry (SRWLI) to obtain the profile with a single frame of an interferogram. We present here a two-dimensional (2D) SRWLI method that can be applied to measure narrow rectangle areas. A frequency comb is produced by using a Fabry-Perot (F-P) etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2D profile with a small width. The experimental details of measurement on a step sample are discussed in this paper.     

Chromium-doped forsterite: dispersion measurement with white-light interferometry

Using a Michelson white-light interferometer, we measure the group-delay dispersion and third-order dispersion coefficients, d2(phi)/d(omega)2 and d3(phi)/d(omega)3, of chromium-doped forsterite (Cr:Mg2SiO4) over wavelengths of 1050-1600 nm for light polarized along both the c and b crystal axes. In this interval, the second-order dispersion for the c axis ranges from 35 fs2/mm to -14 fs2/mm, and the third-order dispersion ranges from 36 fs3/mm to 142 fs3/mm. For the b axis the second-order dispersion ranges from 35 fs2/mm to -15 fs2/mm and the third-order from 73 fs3/mm to 185 fs3/mm. Our data are relevant for the development of optimized dispersion compensation tools for Cr:Mg2SiO4 femtosecond lasers. These measurements help to clarify previously published results and show some significant discrepancies that existed, especially in the third-order dispersion. Our results should furthermore be useful to build up an analytic expression for the index of refraction of chromium forsterite.     

Theoretical measurement uncertainty of white-light interferometry on rough surfaces

A great advantage of the white-light interferometry is that it can be used for profile objects with a rough surface. A speckle pattern that arises in the image plane allows one to observethe interference; however, this pattern is also the source of the measurement uncertainty. We derive the theoretical limits of the longitudinal uncertainty by virtue of the first-order statistics of thespeckle pattern. It is shown that this uncertainty depends on the surface roughness of the measured object only; it does not depend on the setup parameters.     

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.     

High-precision shape measurement by white-light interferometry with real-time scanner error correction

White-light interferometric techniques allow high-precision shape measurement of objects with discontinuous structures by detecting the peak of the coherence envelope. These techniques assume a specific change in the optical path difference (OPD) between the interfering beams; however, the scanning device effecting that change often introduces OPD errors that are carried over to the measurements. We present a technique for measuring OPD changes from the collected interference fringes during each measurement. Information about the scan is directly fed into the algorithm, which compensates for the errors, resulting in improved measurement accuracy. The method corrects not only the scanner errors but also slowly varying vibrations. In addition, this technique can be easily adapted to any existing low-coherence interferometer because no large data storage or postprocessing is required.     

基于视觉和最大长度序列的旋转角度测量系统

针对现有基于视觉的旋转角度测量方法需要在物体旋转轴线方向放置摄像头来获取图像的问题,提出一种基于单目视觉和最大长度序列的旋转角度测量系统.该系统利用摄像头从侧面拍摄柱状旋转体周向的靶标图像实现角位移的测量.首先,该文在介绍最大长度序列的基础上详细描述基于视觉和最大长度序列的平面位移测量方法,包括图像处理、相位检测、序列...     

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.     

Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry

Dispersion properties of novel, tapered, air-silica microstructure fibers are measured between 1.3 and 1.65 microm by white-light interferometry. Dispersion values (beta2) of -181 and -152 ps2/km were obtained for 2.2- and 3-microm core sizes, respectively, at lambda = 1.55 microm.     

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.     

Spectrally resolved white-light interferometry for measurement of ocular dispersion.

Spectrally resolved white-light interferometry was used to measure the wavelength dependence of refractive index (i.e., dispersion) for various ocular components. Verification of the technique's efficacy was substantiated by accurate measurement of the dispersive properties of water and fused silica, which have both been well-characterized in the past by single-wavelength measurement of the refractive index. The dispersion of bovine and rabbit aqueous and vitreous humors was measured from 400 to 1100 nm. In addition, the dispersion was measured from 400 to 700 nm for aqueous and vitreous humors extracted from goat and rhesus monkey eyes. An unsuccessful attempt was also made to use the technique for dispersion measurement of bovine cornea and lens. The principles of white-light interferometry, including image analysis, measurement accuracy, and limitations of the technique, are discussed. In addition, alternate techniques and previous measurements of ocular dispersion are reviewed.     

Direct measurement of refractive-index dispersion of transparent media by white-light interferometry

We report on a technique for measuring the refractive indices of nonabsorbing media over a broad spectral range from 0.5 to 5 microm. White-light interferometry based on a double-interferometer system consisting of a fixed Mach-Zehnder interferometer and a Fourier-transform spectrometer is used for direct measurement of the absolute rotation-dependent phase shift induced by an optical element. Refractive index n(lambda) over the whole investigated spectral range is thus obtained directly to an accuracy of 10(-4) without the need for any specific assumption about dispersion. Results for synthetic fused silica are presented and discussed.     

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.     

Dispersion measurements of water with white-light interferometry

We measure the second- and third-order dispersion coefficients, d(2)k/domega(2) and d(3)k/domega(3), of water for wavelengths from 0.45 to 1.3 mum using a Michelson white-light interferometer. In this interval, the second-order dispersion ranges from 0.068 to -0.1 fs(2)/mum, and the third-order dispersion ranges from 0.048 to 1.18 fs(3)/mum. We observe an oscillation in d(2)k/domega(2) near 1.1 mum that is due to water absorption features near that wavelength. From the dispersion coefficients, derivatives of the index of refraction of water are calculated and compared with available equations. These measured values of d(2)n/dlambda(2) and d(3)n/dlambda(3) should be useful in the evaluation and improvement of existing equations for n(lambda) in water.     

Object illumination angle measurement in speckle interferometry

Errors in measurement of the object illumination angle affect fringe interpretation accuracies in speckle interferometry. To measure the object illumination angle we propose a method based on the moiré effect. The technique is easy to implement and was found to yield fast and accurate measurements.     

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.     

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.     

Fast surface profiler by white-light interferometry by use of a new algorithm based on sampling theory

We propose a fast surface-profiling algorithm based on white-light interferometry by use of sampling theory. We first provide a generalized sampling theorem that reconstructs the squared-envelope function of the white-light interferogram from sampled values of the interferogram and then propose the new algorithm based on the theorem. The algorithm extends the sampling interval to 1.425 microm when an optical filter with a center wavelength of 600 nm and a bandwidth of 60 nm is used. The sampling interval is 6-14 times wider than those used in conventional systems. The algorithm has been installed in a commercial system that achieved the world's fastest scanning speed of 80 microm/s. The height resolution of the system is of the order of 10 nm for a measurement range of greater than 100 microm.     

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.     

Computerization of white-light contact interferometers based on optical image processing

A technique of computerization of white-light contact interferometers intended for calibration of reference end gauges and other objects in the range 0.1–1000 mm with resolution 0.001 μm is considered. Results are presented from studies of contact interferometers based on digital processing of interference images with the use of corresponding mathematical software. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 35–38, July, 2006.