Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging with a spectral interferometric microscope

A noncontact, nonmechanical scanning, wide-field spectral interference microscope is developed for simultaneous measurement of three-dimensional step-height of discontinuous objects and tomographic imaging. A superluminescent diode (SLD) is used as a broadband light source and a liquid-crystal Fabry-Perot interferometer (LC-FPI) as a frequency-scanning device. By means of changing the injection current to the SLD, the spectral profile of the SLD is equalized, and a constant light input to the interferometer is achieved over the entire frequency-scan range. The Fourier-transform technique is used to determine both the amplitude and the phase of spectral fringe signals. Three-dimensional height distribution of a discontinuous object is obtained from the phase information, whereas optically sectioned images of the object are obtained either from the amplitude information alone or from the combination of both the amplitude and phase information. Experimental results with submicrometer resolution are presented for both step-height measurement and tomographic sectioning.     

Two-wavelength Talbot effect and its application for three-dimensional step-height measurement

The phenomenon of Talbot self-image shift by changing the wavelength of the illuminating light is described and demonstrated experimentally. A periodic grating is illuminated by light with wavelengths lambda1 and lambda2 generated by two lasers, and the Talbot self-images are recorded along the longitudinal direction at individual wavelengths. The Talbot self-image shift due to the change in the wavelength of light is implemented for the measurement of the three-dimensional step height of a large discontinuous object without any phase ambiguity problem. Fourier-transform fringe analysis was used to determine the maximum contrast of the high-visibility bands for the measurement of the step height of the object. The main advantages of the proposed system are nonmechanical scanning, high stability because of its common path geometry, compactness, and a wide range of measurement as compared to interferometric three- dimensional profilers.     

基于光纤干涉仪的振动测量技术

本文介绍了基于光纤Mach-Zchndcr干涉仪的振动测量系统,用线阵CCD测量条纹动态位移,实现了光纤干涉条纹图像的连续采集.针对干涉条纹图像噪声的特点完成了低通滤波器的设计、图像的平滑处理,消除了干涉条纹中心的定位误差.文章绘制了干涉条纹位移曲线并对其进行了离散傅里叶变换,给出了所测振动的频谱特性.最后讨论了测量系统的灵敏度以及影响测量精度的因素,为了能够辨别条纹的移动方向,指出了条纹最大允许的移动速度限制,给出了实验结果.     

Analysis of low-coherence interference fringes by the Kalman filtering method

Interferometers with low-coherence illumination allow noncontact measurement of rough-surface relief with a wide range of measurement definition by locating the visibility maxima of interference fringes. The problem is light scattering by the surface to be measured, which can cause distortion of low-coherence interferometric signals. We propose to use a stochastic fringe model and a Kalman filtering method for processing noisy low-coherence fringes dynamically. Prediction of the fringe's signal value at each discretization step is based on all the information available before this step; the prediction error is used for dynamic correction of the estimates of the fringe envelope and phase. The advantages of the Kalman filtering method consist in its immunity to noise, optimal fringe evaluation, and data-processing speed.     

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.     

Discontinuous surface measurement by wavelength-tuning interferometry with the excess fraction method correcting scanning nonlinearity

Wavelength-tuning interferometry can measure surface shapes with discontinuous steps using a unit of synthetic wavelength that is usually larger than the step height. However, measurement resolution decreases for large step heights since the synthetic wavelength becomes much larger than the source wavelength. The excess fraction method with a piezoelectric transducer phase shifting is applied to two-dimensional surface shape measurements. Systematic errors caused by nonlinearity in source frequency scanning are fully corrected by a correlation analysis between the observed and calculated interference fringes. Experiment results demonstrate that the determination of absolute interference order gives the profile of a surface with a step height of 1?mm with an accuracy of 12?nm.     

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.     

一种可溯源原子力探针显微镜

研制了一种基于白光干涉的可溯源原子力探针扫描显微镜,提出了一种稳健的白光干涉零级条纹定位算法,建立了一套高分辨激光干涉位移测量系统。在此基础上提出了一种探针标定方法,实现微纳表面可溯源测量。通过对台阶高度为(21.4±1.5)nm的标准光栅进行10次重复测量,其结果的平均值为21.56 nm,标准差为0.51 nm;同时对高度为150 nm的三维特征样件进行了三维测量,验证了所研制仪器测量的准确性和稳定性。     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

基于白光相移干涉术的微结构几何尺寸表征

将Carré等步长相移法与白光垂直扫描相结合形成了一种白光等步长相移算法,该方法快速、准确、非接触,垂直分辨力可达亚纳米级.测量系统集成了Mirau显微干涉物镜,并通过高精度压电陶瓷纳米定位器带动物镜进行垂直扫描.分析了Carré法应用于白光干涉信号的相位提取的精度,对不同扫描步距以及不同信噪比情况下的测量进行了计算机仿真,确定了测量参数.结合重心法将相位计算的数据范围直接定位于干涉信号的零级条纹,从而省去了相位解包裹过程.通过对微谐振器和标准台阶的测量说明了该方法的有效性,并使用白光相移干涉、白光垂直扫描和单色光相移干涉对44 nm标准台阶进行了测量,并对测量结果进行了比较.     

采用标记拼接的相位测量轮廓术

提出一种采用标记拼接的新的光学三维传感方法。在采用结构照明的光学三维传感中,阴影及条纹错位关系到被测量物体三维面形重建的质量。在处理阴影时,传统方法是采用插值方法,在处理条纹错位时,通常采用增大条纹周期或采用几组条纹周期不同的光波进行投影,这样通常降低了测量精度。为了提高测量精度,本文提出一种在同一参考面内,采用单组相移正弦条纹进行投影,通过旋转被测物体,并对旋转前后两次重建物体在信息可靠区域内进行标记拼接,恢复物体表面完整三维信息的方法。实验证实了此方法的有效性及实用性。     

White-light Phase-stepping Interferometry for Surface Profiling

Abstract

Interferometric profilers suffer from phase ambiguities if the measurement range involves a change in the optical path difference greater than a wavelength. This limitation has been overcome by using white light and scanning the object in height. We show how an achromatic phase shifter operating on the geometric phase can be used to evaluate the fringe contrast directly and to locate the position of the zero-order white-light fringe along the scanning axis.     

Wrapped statistics-based phase retrieval from interference fringes

We propose a wrapped statistics-based approach for phase estimation from noisy reconstructed interference fringes in digital holographic interferometry. The state space model required here is formed by Taylor series expansion of the phase function as state model and the wrapped dynamical system as measurement model. Prediction of the state using Kalman filter is straightforward since the state model is linear. However, the non-linearity issue induced due to the wrapping of the measurements is handled by changing the innovation correction step, which accounts for the probability of wrappings. Through the simulation and experimental study, we have shown that the proposed approach is robust to both, noise in fringe pattern as well as the dynamic range of the phase pattern, simultaneously. Moreover, it outperforms when compared with the other state-of-the-art phase retrieval approaches.     

气流场ESPI载频条纹图的消噪处理与相位提取方法

为拓展ESPI方法在流动可视化测量技术中的应用,对气流场ESPI载频条纹图进行了傅立叶变换、数字全低通滤波,和傅立叶逆变换的处理以消除散斑噪声,并直接将其替换为原散斑相关条纹图,进而成为保留了流场信息的高对比度、低噪声的灰度条纹图,便于提取原散斑图中流动相位信息。根据模拟数据确定了由这两种条纹图互换所引起的空间相移量和相应流场测量中的修正量。提出了用灰度扫描法对互换后的条纹图进行一维灰度扫描,由灰度计算得出气流扰动的一维相位差分布和流场一维温度分布;同时也用FTP法对该图进行了二维相位展开和温度分布计算,亦可对多帧条纹图进行时间轴上的逐点相位提取以计算其他流场参数。结果表明,计算数据与实测符合,方法简单易行,为在气流场参数测量中应用动态ESPI方法提供了一种实用有效的方法。     

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.     

Phase extraction from electronic speckle pattern interferometry addition fringes

Addition fringes are obtained in real time from electronic speckle pattern interferometry (ESPI) by use of a twin-pulsed laser when two pulses are fired during a single field of a CCD camera. This enables object deformations to be studied in harsh environmental conditions. However, the fringe patterns have poor visibility because optical noise is additive. To our knowledge automatic phase extraction from addition fringes has not previously been achieved: Low-pass filtering to suppress random speckle noise also eliminates the fringes because of their low visibility. Two phase-stepping algorithms that calculate phase from ESPI fringes without the need for a preprocessing filter are presented. In the first ESPI subtraction fringes are considered, for which an improvement in accuracy is seen, and in the second ESPI addition fringes are considered, which, we believe, has enabled the phase to be extracted for the first time. The algorithms are demonstrated with theoretical data and with experimental ESPI fringepatterns recorded with a cw laser. As presented, they form the first step toward a procedure that can beused with twin-pulsed ESPI.     

Generation of carrier fringes in holography and shearography

Double-exposure holography and double-exposure shearography are often used together with the carrier fringe technique, which requires additional shifting of the light source in a prescribed manner between exposures. In the holographic carrier fringe technique, difficulty in prescribing a suitable movement of the light source may be alleviated through visualization of the moiré fringes that are reconstructed by slight displacement of two overlaid families of ellipsoids in a holodiagram. Because shearography is the first differential of holography, it is often impractical to perform two successive optical differentiations on the ellipsoids to visualize the shearographic carrier fringes. A simple method of discerning holographic and shearographic carrier fringes is described. The method is based on the hyperboloids in a holodiagram that represent Young's (interference) fringes produced by the interference of two point sources. The hyperboloids are analogous to holographic carrier fringes, whereas the moiré patterns reconstructed from two overlaid hyperboloids are analogous to shearographic carrier fringes. Use of this method for explaining the formation of deformation fringes in plate bending, as well as the effect of light-source movement on the deformation fringes, is also illustrated.