Quasi-distributed strain sensing with white-light interferometry: a novel approach

An optical fiber ring is used to generate multiple reference waves in a multiplexed fiber-optic Michelson-type sensor array. The array consists of N sensing segments connected in series along a single optical fiber path and is interrogated with a white-light interferometric technique. Experimental results with a two-sensor array are presented.     

白光扫描干涉测量算法综述

白光扫描干涉测量是光学测量中一种非常重要的方法。在干涉仪的结构、光源的光谱宽度以及扫描步长一定的情况下,选择合适的算法对干涉信号进行处理能够达到更高的测量精度。对重心法、移相法、包络曲线拟合法以及空间频域算法分别加以介绍和比较,为白光干涉信号的算法选取提供了一份详尽的参考。     

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.     

Application of least-square estimation in white-light scanning interferometry

White-light scanning interferometry (WLSI) is a powerful tool for investigating the profile of a test object that contains sharp steps. Due to the light source used in WLSI system, it is able to overcome phase ambiguity problem, which is often encountered in monochromatic interferometry. In this paper, a new algorithm based on least-square estimation using short-time Fourier transform (STFT) is proposed to measure the profile of a test object. STFT is used to extract the peak position of the coherence envelope of a white-light interference signal and retrieve the corresponding phase values simultaneously at first. A complex phasor (CP) method is introduced to further reduce the phase noise. Then, the phase values at several positions around are utilized to achieve a more accurate peak position based on least-square line fitting. Both simulated and experimental results show that the proposed algorithm is able to accurately measure the profile of a test object.     

扫描白光干涉测量技术的算法比较

干涉条纹零光程差位置的确定是扫描白光干涉测量的关键技术之一。介绍了扫描白光干涉法测量物体轮廓的原理,讨论了确定白光干涉条纹零级条纹位置的几种方法,并对随机生成的表面进行了大量的数字模拟测量和分析比较,得出了各种算法对测量准确度的影响。研究结果对白光干涉的应用研究提供了可靠的理论根据。     

Wavelet transform as a processing tool in white-light interferometry

Results of the application of wavelet transform for signal processing in white-light interferometry are reported. The mother wavelet frequency is chosen to be the light-source correlogram 1's, and accurate phase measurements are obtained from simple correlation computations. The fringe envelope is also addressed and permits a complete analysis of coherence-limited fringe patterns. Miscalibrations of phase shift and mean wavelength are also considered.     

Multiplexed fiber Fabry-Perot temperature sensor system using white-light interferometry

A novel monitoring system for a fiber Fabry-Perot interferometer (FFPI) temperature sensor has yielded a resolution of 0.013 degrees C (0.0025 fringe). Light from a broadband source passes through a scanned Michelson interferometer and is reflected from a FFPI to produce a fringe pattern, the temporal position of which is proportional to a change in the optical length of the fiber interferometer. A second Michelson interferometer with a distributed-feedback laser source is used to correct for variations in the translation rate of the motor-driven scanning mirror. Coherence multiplexing of three such sensors has also been demonstrated.     

Testing micro devices with fringe projection and white-light interferometry

Optical sensors are very suitable for the analysis of microscopic structures and micro devices. We compare two very promising methods: the white-light interferometry and the fringe projection technique for the application to this task. The fringe projection is very useful for fast measurement of objects with vertical dimensions of some μm. White-light interferometry is especially useful for highly resolved 3-D measurements. Furthermore, we present a new technique, the scanning fringe projection (SFP), which enables absolute 3-D measurements with one single grating period.     

Grating coupled interferometry for optical sensing

An interferometric sensor based on gratings on a planar waveguide is introduced. The device combines the advantages of known interference-based waveguide sensors with the simplicity of grating couplers. In the presented configuration, two parallel and coherent light beams, laterally separated in the direction of mode propagation, are coupled into a planar waveguide through a grating. One of the coupled beams is phase modulated using a periodically relaxing liquid crystal modulator, resulting in a time varying intensity signal at the end face of the waveguide. Refractive index changes within the waveguide section between the two coupling regions are monitored by observing characteristic changes in the intensity signal.     

Broadband near-infrared fibers dispersion measurement using white-light spectral interferometry

A new technique for an experimental determination of the effective refractive index, group refractive index and dispersion of fibers in a broad near-infrared spectral range is presented. The method is based on a white-light spectral interference which utilizes an unbalanced Michelson interferometer. The effective refractive index is obtained by a direct fitting the cosine function to the spectral interference pattern recorded by a low resolution spectrometer. The method has been tested in the spectral range of 1000-1700 nm both with standard telecommunication fibers and a sample of a photonic fiber. The accuracy of dispersion measurement () exceeds those from the previously reported near-infrared white-light spectral interference methods.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

Dispersive white-light spectral interferometry including the effect of thin-film for distance measurement

A spectral-domain white-light interferometric technique is used for measuring distances in a Michelson interferometer with a mirror represented by a thin-film structure (TFS) on a substrate. A fibre-optic spectrometer is employed for recording spectral interferograms that include wide wavelength range effects of dispersion in a cube beam splitter and multiple reflection within the TFS. Knowing the effective thickness of the beam splitter, its dispersion and parameters of the TFS and substrate, the positions of the second interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones. We apply the technique to the beam splitter made of BK7 optical glass and to a uniform SiO₂ thin film on a silicon wafer. We compare the results of the processing that include and do not include the effect of the TFS.     

Refractive index distribution measurements by means of spectrally-resolved white-light interferometry

A new procedure to measure the spatial distribution of the refractive index in transparent media is presented. It is based on the spectral analysis of optical interferograms obtained from a wide, continuous-spectrum light source. The method yields fairly high precision (up to 10^-8) in the measurements of local values of differential refractive index, Δn (Δn=n−n_ref), along a line in the sample. By means of a CCD TV-camera linked to a microcomputer, fast recording and automatic data processing are achieved. As an application, we present an experimental study of a thermal gradient in a liquid sample.     

High-precision index measurement in anisotropic crystals using white-light spectral interferometry

White-light spectral interferometry appears an excellent tool for precise determination of indices, and has already been successfully applied to different isotropic or weakly dispersive materials such as glass or rhodamine films. In this paper, we extend the spectral method to the measurement of anisotropic media with strong dispersion. The method is discussed below and allows an accuracy of the order of 10^-5 on the principal indices of a birefringent silver thiogallate (AgGaS₂) crystal.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

Wavelength-scanning white-light interferometry with a 3x3 coupler-based interferometer

A novel white-light interferometry capable of retrieving the absolute optical path difference is presented, in which a 3x3 coupler-based interferometer is employed. The measured phase change is in agreement with that obtained by Fourier transform white-light interferometry. The linear property is also experimentally demonstrated.     

New data-processing technique for measurement of metallic foil thickness with differential white-light interferometry

The thickness of metallic foil was measured by differential white-light interferometry (DWLI). Two tandem Michelson interferometers (MI), in which the reflective surfaces measured are the surfaces of the metallic foil, were used as a basic interferometry system to obtain interference fringes on a spectrometer. Therefore, the interference fringes depend only on the path differences caused by the thickness of the metallic foil. The interference fringes were analyzed using a modified extremum method based on the least root-mean-square (RMS) deviation. Experimental results for thickness measurements are presented. Measurement time is only 100 ms or less for a thickness of 1–80 μm.     

Compensation of phase change on reflection in white-light interferometry for step height measurement

We present a method for compensating for the phase change on reflection in scanning white-light inteferometry that practically permits precise three-dimensional profile mapping of composite target surfaces that comprise multiple, dissimilar materials. The compensation method estimates the variation of phase change with the spectral distribution of the light source through a first-order approximation and then directly compensates for the measurement errors by performing two additional quasi-monochromatic phase-measuring interferometric measurements. Experimental results prove that the proposed compensation method is capable of reducing the measurement error in step height gauging to +/-5 nm or less.     

基于光纤白光干涉测量技术的折射率测量仪

设计了基于光纤白光干涉测量技术的折射率测量仪,用来测量尺寸较小、形状简单的透光材料折射率。与传统折射率检测方法相比较,光纤折射率测量仪具有设备尺寸小、测量精度高、操作简易、便于携带等优点。实验测得某种石英玻璃的折射率值为1.464,与标准值偏差为0.02,误差为1.4%;测得某种普通玻璃的折射率为1.502,与标准值偏差为0.002,误差为0.1%;测得K9玻璃的折射率为1.507,与标准值偏差为0.009,误差为0.6%。     

Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry

White-light scanning interferometry (WLSI) has been widely used in micro-profile measurement such as Micro-Electro-Mechanical Systems (MEMS) and Computer Generated Hologram (CGH) diffractive elements. It does not contain phase ambiguity problem which is often encountered in monochromatic wavelength interferometry. This paper presents an algorithm based on windowed Fourier transform (WFT) to extract the phase of a white-light interferogram and compensates for the difference in zero optical path difference (ZOPD) position in WLSI. With the WFT technique, the center wavelength of a white-light source and the phase of a white-light interferogram could be retrieved simultaneously. The effect of noise, scanning interval of a piezoelectric transducer (PZT) and the window size of WFT are also analyzed. Both simulated and experimental results show that the proposed algorithm has good noise immunity and is able to accurately measure the micro-profile of a specimen.