Measurement of small rotation angles by using a parallel interference pattern

We propose a method for measuring rotation angles by using a parallel interference pattern. At two points on a parallel interference pattern reflected by an object, we detect phase changes in the reflected parallel interference pattern caused by rotations of the object. A high sensitivity, or a high ratio of the phase change to the rotation angle, 17 mrad/arcsec, can be achieved by determining the positions of two detection points. A high spatial resolution of ~0.5 mm is also obtained. We analyze the measurement error caused by the alignment of the parallel interference pattern and a random measurement error caused by the phase detection. The theoretical analyses and the experimental results make the characteristics of the method clear and show that the method has an accuracy of 0.2 arcsec for small rotation angles.     

干涉条纹快速预处理的新方法

介绍一种基于数学形态学的新方法以实现干涉条纹的快速预处理（去噪声、细化条纹等），该方法所采用的光学系统结构简单，具有图像处理的快速并行性。用它处理了三种干涉条纹，获得了很好的处理效果。     

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.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

运用ASAP光学软件模拟单轴晶体的锥光干涉

为了模拟不同光轴取向、光束发散角、晶体厚度或入射波长等参数下的单轴晶体锥光干涉,在 ASAP中定义起偏器、晶体、检偏器和接收屏的几何形状和光学特性,产生一组锥状高斯光束并设置其相干性和波动性,进行光线追迹、计算并显示接收屏上的干涉场能量分布。所得模拟结果表明,光轴与晶体表面垂直时,干涉条纹是 1组以光轴为圆心且被十字分割的内疏外密、明暗相间的同心圆环;平行时,是 2组分别以光轴的平行和垂直方向为对称轴的、内疏外密、明暗相间的双曲线;既不垂直也不平行时,条纹特征因光轴取向而异;当增大发散角、晶体厚度或减小波长时,干涉条纹都向内移动且条纹数增多,反之亦然;起、检偏器正交时的干涉条纹都和它们平行时的条纹互补。     

A modification of the moireA fringes technique for the analysis of moments and deflexions in a laterally loaded plate

This paper describes an adaptation of the moire fringes method for the analysis of uniformly laterally loaded plates with various edge conditions. In this technique the deflected specimen is composed of two parallel transparent sheets forming walls of a sealed water–filled cell. Under pressure, the cell acts as a lens and interference fringes are produced by photographing a ruled screen through it. A method of analysis using thin lens theory is presented and experimental results are compared with figures obtained by a finite differences solution. Good agreement is found between the result of the two alternative analyses.     

Interference of Three Electron Waves and Its Application to Direct Visualization of Electric Fields

We present a method for the interference of three electron waves and its application to direct visualization of pure-phase objects such as electromagnetic microfields. Using a transmission electron microscope equipped with a field-emission electron gun and two electron biprisms, an object wave and two reference waves at either side of the object wave are superposed to produce a new type of interference pattern. In this pattern, equal-phase lines of the object wave are directly displayed as intensity modulation of periodic interference fringes. An electric field around a latex particle, induced by electron-beam irradiation, has been observed. The electric charge of the particle is estimated, from an observed phase shift, to be 6.4 × 10⁻¹⁷C, which is equal to about 400 electrons. A change of the electric field around charged alumina particles at high temperatures has been observed dynamically.     

Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes

We propose a novel approach to retrieving the phase map coded by a single closed-fringe pattern in digital speckle pattern interferometry, which is based on the estimation of the local sign of the quadrature component. We obtain the estimate by calculating the local orientation of the fringes that have previously been denoised by a weighted smoothing spline method. We carry out the procedure of sign estimation by determining the local abrupt jumps of size pi in the orientation field of the fringes and by segmenting the regions defined by these jumps. The segmentation method is based on the application of two-dimensional active contours (snakes), with which one can also estimate absent jumps, i.e., those that cannot be detected from the local orientation of the fringes. The performance of the proposed phase-retrieval technique is evaluated for synthetic and experimental fringes and compared with the results obtained with the spiral-phase- and Fourier-transform methods.     

Analysis of a low-finesse Fabry-Perot sensing interferometer illuminated by a multimode optical fiber

A model of the reflected fringe system for an ideal plane-parallel, low-finesse Fabry-Perot (FP) cavity illuminated by a multimode optical fiber has been developed and experimentally validated. This showed that the phase dispersion within the cavity arising from the divergent nature of the incident illumination significantly degrades the visibility of the reflected fringes. Departures from the ideal FP cavity are also examined. The effect on fringe visibility when the plane of the FP cavity is tilted with respect to the fiber axis and when the cavity surfaces are no longer perfectly parallel to each other has been explored. The analysis described is relevant to the design and the optimization of multimode optical-fiber sensors that use FP sensing cavities.     

Multiple-reflection effects in photoelastic stress analysis

The interpretation of fringes observed in photoelastic stress measurements made with coherent well-collimated optical radiation such as a laser beam and slab specimens with parallel surfaces is affected by multiple internal reflections of light within the sample, which are usually negligible when incoherent light is used. An analysis of the multiple-reflection effects in photoelastic measurements involving the plane polariscope configuration is presented. The results show that the isochromatic fringes are modified by the interference of multiply reflected waves. The multipass differential phase accumulations that display oscillatory magnitudes as functions of the model thickness and the optical wavelength result in a shifted and altered intensity profile across the isochromatic fringes. It is shown that for large values of reflectivity, as in the case of samples with reflective coating or partial mirrors, the bright fringes split into multiple peaks.     

Effect and suppression of secondary fringes in FATWindII

By considering the instrument as a complex operator on the incident electric field, a model to calculate secondary fringes of the Field-widened, Achromatic, Temperature-compensated Wind Imaging Interferometer (FATWindII) has been built. The distribution of secondary fringes on a charge coupled device detector has been plotted. The effects of secondary fringes on inversion errors of temperature and wind velocity have been presented. The results show that antireflection coating on the air/glass interface cannot meet the accuracy requirement of FATWindII. A theoretical method for calculating the optimal wedge angles of compensating glasses is derived to suppress the secondary fringes while preserving the primary ones. By adopting both methods, coating with antireflection film and shaping wedge compensating glasses, the relative intensity of secondary fringes is reduced to below 2.5% and the inversion errors of temperature and wind velocity introduced by the effects of secondary fringes can be minimized to about 0.05 K and 0.045 ms(-1), respectively.     

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.     

An image-Moiré method for the direct determination of partial slopes in fixed plates

A new image-Moiré method yielding directly the partial slope distribution in bent plates is proposed. The fringes are formed by the interference between the grating on the front face of a transparent plate with its reflected image through it on the other face. In illustration of the applicability of the method, results for a centrally loaded simply supported circular plate are presented.     

一种测量表面膜层厚度的新方法

在近年来迅速发展的微细加工技术中,表面膜层厚度的测量是十分重要的问题。本文提出一种新方法,它利用迈克耳逊干涉光路,通过对膜层前后两表面反射光束和来自另一臂的反射光束产生的两组白光干涉纹黑线间隔的测量,即可得到表面膜层的厚度、这种测量方法迅速、简便、设备简单、精确度高、不损伤膜层表面,适合在实验室和工厂广泛应用。     

Influence of unparallel grating planes in talbot interferometry with cross gratings of different spatial frequencies in two directions

The effects of an arbitrary small inclination between two cross gratings on the moiré fringes in Talbot interferometry are discussed when the frequencies of the grating differ in two perpendicular directions. We show that the small angles, alpha and beta, by which the beam-splitter cross grating is rotated around the two axes parallel to the two perpendicular line directions of the cross grating, have a greater influence on the moiré fringes with cross gratings than that with one-dimensional gratings. A simple and practical detection method for the angles between the two unparallel grating planes in Talbot interferometry is also proposed. The theoretical analyses are proved by experimental results.     

相位扫描法制作变栅距光栅

提出了一种制作变栅距(VLS)光栅的相位扫描方法。该方法的主要装置包括一个用于控制刻划机运动的光栅干涉仪和一个相位扫描机构。如果调整光栅干涉仪,保证接收场中只有两条干涉条纹,然后改变用于对条纹进行计数的光电传感器的位置,就可以刻划出具有变栅距的刻槽。对光电式光栅刻划机的控制系统和结构都做了详细论述。按照上述方法成功刻划出了试验性的VLS光栅,它的最小栅距增量为0.33nm,并对在制作过程中产生的误差进行了讨论。采用测量衍射角的方法进行了栅距检测试验,由变栅距光栅和等栅距光栅作出的拟合曲线表明:相位扫描方法是加工具有亚纳米栅距增量的VLS光栅的有效方法,该方法对超精密定位也具有借鉴作用。     

Interferometry for the evaluation of the dynamical optical and mechanical properties of transparent materials

A theory is developed which leads to an interferometric method for determining the dynamic ratio, Poisson's ratio to the modulus of elasticity, and the dynamic stress-optical coefficients of transparent plates, both during the same set of tests and without attaching mechanical or electrical sensors on the surface of the specimen.

The method requires a monochromatic light source, that is, a parallel beam is directed perpendicularly to the vicinity of a crack tip which exists in the plate specimen under investigation. The rays impinging on the crack tip are transmitted through the plate and reflected by the two parallel surfaces of the plate. At the same time, because of the variation of the optical path (index of refraction and thickness of the plate) in the said area, the rays are refracted in such a way as to form two caustic surfaces, one by the transmitted and one by the reflected rays. These two caustic surfaces, when intercepted with two opaque screens, provide two strongly illuminated curves of a general epicycloid shape called caustics.

The size of the caustics is directly related to the applied load, the material properties and the distance specimen-screen. Their ratio, however, as it is taken at equally distant screens, depends only on the optical and mechanical properties of the material in question.

In addition, an interferogram consisting of fringes, as formed from rays reflected by the two surfaces of the plate, is obtained. The fringe number depends on the wavelength of the light source and the optical path. When the plate specimen is loaded, the optical path changes. This results in a change of the fringe number and consequently to a displacement of fringes with respect to a reference point as they are observed on an opaque screen.

The ratio of the two caustics, taken during a static test, and the number of displaced fringes per applied load, taken during a dynamic test, provide enough information for the determination of the aformentioned mechanical and optical parameters.

Experiments conducted according to the method developed on acrylic plates and for a tensile impulse of total time duration of 600 μsec produced a reduced by 23.5% ratio of Poisson's ratio to modulus of elasticity from the static value and a reduced by 21% stress-optical coefficient from the static value.     

无Talbot效应的莫尔偏折术研究

研究了一种无Ｔａｌｂｏｔ效应的莫尔偏折术，它用干涉直条纹代替光栅，以克服Ｔａｌｂｏｔ距不能连续改变的限制。提出了双光路和型、单光路双曝光和型、积型三种型式的莫尔偏折术。分析了原理，并用实例介绍了特点。     

Deriving wavelength spectra from fringe images from a fixed-gap single-etalon Fabry-Perot spectrometer

A new method is described for inferring wavelength spectra from two-dimensional images of Fabry-Perot interference fringes. This new method addresses the practical difficulties that have been previously encountered in determining the fringe image's center, magnification, and distortions accurately enough to fully exploit the spectral resolution provided by the etalon. The method proceeds in two steps. First, the instrument's mapping of image position to interference order is characterized by use of images of a scene illuminated uniformly by a highly monochromatic laser. Then this information is applied to resample two-dimensional images of unknown radiation sources down to sets of one or more one-dimensional wavelength spectra. Discrete cross-correlation techniques are used at both stages of anal-     

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。