The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

A modified moiré interferometer for three-dimensional displacement measurement

This paper presents a new optical interferometric system, MMI-T/G, composed of a modified four-beam moire interferometer and a Twyman/Green interferometer. The MMI-T/G system can measure threedimensional displacement fringe patterns with a single loading on the specimen, and the in-plane and out-of-plane displacement fields can be measured independently and defined clearly. The optical setup has the advantages of structural novelty, flexibility, and high fringe contrast. Moreover, the in-plane displacement sensitivity is twice of that of the normal moire interferometer. The measuring techniques to obtain the fringe patterns and displacement fields using the MMI-T/G system axe described. The experimental results of thermal displacement of an electronic device are shown.     

用于多参数同时测量的散斑干涉仪

本文描述了一种新的散斑干涉仪,它可以同时对表面应变物体的面内位移、离面位移、位移梯度和莫尔曲率进行测量;由于利用了取向滤波方法,在滤波系统输出平面同时得到了与这些参数对应的散斑条纹.还利用散斑空间运动规律较好地解释了散斑干涉与散斑剪切干涉之间的关系.     

Influence of in-plane displacement and strain components on slope fringe distributions in double-aperture speckle wedge-shearing interferometry

The influence of in-plane displacement and strain components on slope (first-order derivative of out-of-plane displacement component) fringe distributions in double-aperture speckle wedge-shearing interferometry is discussed in detail. The research results show that only the in-plane displacement component parallel to the centre line of double apertures has an influence on the slope fringe distributions. It is also shown that the in-plane strain components have no influence on the slope fringe distributions when utilising normal illumination and an axisymmetric system. A theoretical analysis and an experimental demonstration are given. The experimental results are in good agreement with the quantitative analysis.     

Measurement of three-dimensional rigid body motion by multiple exposure speckle photography: use of uncollimated beam illumination in free space geometry

A theoretical and experimental analysis is carried out showing the effect of multiple exposures on fringes in the case of three-dimensional motion of a diffuse object illuminated by a diverging beam from a laser point source. Experimental conditions are such that the speckle patterns remain fully correlated in spite of the object moving in three-dimensional space in a direction that makes an angle with the optical axis. Owing to the in-plane component of the three-dimensional displacement the point of null-speckle displacement shifts either in the direction of the in-plane component of the motion or in the opposite direction depending upon the direction of the out-of-plane displacement component. This modifies the fringe profile as compared with the case of pure out-of-plane motion. The intensity distribution at the Fresnel plane of a specklegram is investigated after filtering by a converging beam for double exposure and multiple exposures. Good agreement is found between the theoretical and experimental results.     

Improved 3D displacement measurements method and calibration of a combined fringe projection and 2D-DIC system

An improved measurement method and an automatic calibration procedure are proposed for a combined 2D Digital Image Correlation and Fringe Projection system that allows measuring in- and out-of-plane displacement maps with only one image at each deformation stage of a specimen. The proposed method increases the accuracy and range of the out-of-plane displacements by taking into account the divergences of both the projected fringes (uncollimated) and the camera (with non-zero FOV). The calibration is performed automatically by acquiring a sequence of images of a reference plane by displacing perpendicular to it the camera and fringe projector with a motorized translation stage. The acquired images are then used to obtain a fringe function for each pixel and the necessary parameters required for the correction of the in-plane displacements. Furthermore, a closed form expression is obtained that relates the out-of-plane displacements with the shifted phase at each pixel for a given experimental set-up. This expression is in good agreement with the fringe function obtained by fitting a simple 2nd order polynomial to the experimental obtained calibration data. Finally, the polynomial approach is proposed as a fringe function because it avoids the errors in the determination of the required parameters of the theoretical expression as well as some small misalignment or aberration effects.     

Simultaneous quantitative evaluation of in-plane and out-of-plane deformation by use of a carrier method of large image-shearing shearography

A carrier method for separating out-of-plane displacement from in-plane components based on large imageshearing shearography is presented. A reference surface is fixed on the side of a test object. They are illuminated by two expanded symmetric illuminations respectively. The carrier is introduced by rotating the reference surface to modulate the displacement of an object. By using Fourier transform to demodulate the modulated fringe pattern, two phase maps, which include out-of-plane and in-plane displacements, can be obtained. Then the out-of-plane displacement can be easily separated from in-plane displacement by subtraction and addition of the two unwrapped phase distributions. The principle of the method is presented and proved by a typical three-point-bending experiment. Experimental results show that the method enjoys high visibility of carrier fringes. The system does not need a special beam as a reference light and has simple optical setup.     

基于径向剪切干涉仪的三维位移测量技术

本文提出一种基于双圆光栅径向剪切干涉仪的三维位移测量方法,其测量原理是径向剪切干涉仪所形成的莫尔条纹不仅由二维平面内位移决定,轴向位移会在+1和–1级莫尔条纹之间产生一个特定的相移.首先,基于标量衍射理论对双圆光栅径向剪切干涉仪的+1和–1级莫尔条纹强度分布进行推导,建立了三维位移量与莫尔条纹强度分布的精确解析关系;其次,在频谱分析的基础上,利用半圆环滤波器进行空间滤波,实现+1和–1级莫尔条纹的同时成像;然后,提出了从莫尔条纹图中定量提取三维位移的算法,并通过数值模拟进行验证;最后,实验结果验证了该方法测量平面内位移的最大绝对误差为4.8×10^–3 mm,平均误差为2.0×10^–4 mm,轴向位移的最大绝对误差为0.25 mm,平均误差为8.6×10^–3 mm.该方法具有装置简单、测量精度高、非接触、瞬时测量等特点,可实现三维位移的同时测量.     

Optical modulation and digital demodulation of an in-plane moiré carrier

A rotational mismatch of gratings is used to generate a fringe carrier of an in-plane moiré pattern so that specimen deformation shows itself in the form of modulation of the carrier frequency. As both the unmodulated and modulated carriers are the patterns without fringe-loop or fringe-connection, they are automatically numbered with monotonical increasing orders by a digital image processing system without any ambiguity. The orders at every pixel of the image are determined by interpolation of the orders of the tracked fringes to establish two grey image files, from the difference of which, the orders of the in-plane displacement moiré are displayed with grey-level variation.     

Measuring Microscopic Deformations with Digital Image Correlation

This paper describes a feasibility study of a high magnification full field deformation measurement system. The system consists of an image acquiring and analysis system and an optical metallurgical microscope. It can be used to determine in-plane surface deformations at magnifications up to 2000 pixels/mm. Images from an optical microscope are acquired by using a CCD camera and a digitizing board, and stored in a microcomputer. The surface displacement field is determined by using the digital image correlation method. Displacement gradients on the surface are computed after smoothing the displacement data. By performing a number of experiments and analyzing them, sources of errors in the system and their magnitudes are determined. Methods to minimize these errors are also discussed. It is realized that the system has every potential of quantifying in-plane surface displacement fields and the strains on the surfaces of specimens used in the research areas of micromechanics of solids. © 1997 Elsevier Science Ltd. All rights reserved.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

Experimental and numerical investigations of resonant vibration characteristics for piezoceramic plates.

Electronic speckle pattern interferometry (ESPI) is a full field, non-contact technique for measuring the surface displacement of a structure subjected to static loading or, especially, to dynamic vibration. In this article we employ an optical system called the amplitude-fluctuation ESPI with out-of-plane and in-plane measurements to investigate the vibration characteristics of piezoceramic plates. Two different configurations of piezoceramic plates, namely the rectangular and the circular plates, are discussed in detail. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes is demonstrated. The resonant frequencies of the piezoceramic plates are also measured by the conventional impedance analysis. From experimental results, we find that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by the impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extensional) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes.     

The effect of out-of-plane motion on 2D and 3D digital image correlation measurements

The effect of out-of-plane motion (including out-of-plane translation and rotation) on two-dimensional (2D) and three-dimensional (3D) digital image correlation measurements is demonstrated using basic theoretical pinhole image equations and experimentally through synchronized, multi-system measurements. Full-field results obtained during rigid body, out-of-plane motion using a single-camera vision system with (a-1) a standard f55mm Nikon lens and (a-2) a single Schneider–Kreuznach Xenoplan telecentric lens are compared with data obtained using a two-camera stereovision system with standard f55mm Nikon lenses.Results confirm that the theoretical equations are in excellent agreement with experimental measurements. Specifically, results show that (a) a single-camera, 2D imaging system is sensitive to out-of-plane motion, with in-plane strain errors (a-1) due to out-of-plane translation being proportional to ΔZ/Z, where Z is the distance from the object to the pin hole and ΔZ the out-of-plane translation displacement, and (a-2) due to out-of-plane rotation are shown to be a function of both rotation angle and the image distance Z; (b) the telecentric lens has an effective object distance, Z_eff, that is 50× larger than the 55 mm standard lens, with a corresponding reduction in strain errors from 1250 μs/mm of out-of-plane motion to 25 μs/mm; and (c) a stereovision system measures all components of displacement without introducing measurable, full-field, strain errors, even though an object may undergo appreciable out-of-plane translation and rotation.     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

Moiré interferometry for deformation measurement

Moiré interferometry utilizes high frequency gratings to contour displacement components with a sensitivity of the order of 0·5 μ. This paper briefly reviews the technique for in-plane deformation measurement and its current applications to analyze adhesive bonded joints and composite deformation. The modified set-up for out-of-plane displacement measurement is described and used for fracture mechanics studies and vibration analysis. Finally, a set-up for simultaneous measurement of all three displacement components is described.     

Digital speckle pattern interferometry (DSPI) with increased sensitivity: Use of spatial phase shifting

This paper presents a real-time digital speckle pattern interferometry system with twofold increase in sensitivity for the measurement of in-plane displacement and first order derivative of out-of-plane displacement (slope). Spatial phase shifting technique has been used for quantitative fringe analysis. The system employs a double aperture arrangement in front of the imaging system that introduces spatial carrier fringes within the speckle for spatial phase shifting. For in-plane displacement measurement, the scattered fields from the object are collected independently along the direction of illumination beams, and combined at the image plane. For slope measurement, a shear is introduced between the two scattered fields. Experimental results on an edge clamped circular plate subjected to in-plane rotation for in-plane displacement measurement and central loading for slope measurement are presented.     

Digital speckle pattern interferometric (DSPI) and thermo-graphic investigations on the thermal responds in human teeth

Human dentine is a composite material made up of constituents of varying thermal properties, which when subjected to changes in temperature experiences complex thermal effects. In this study, the response of functionally adapted dentine to temperature changes in physiological range is analyzed using a digital speckle pattern interferometer (DSPI) and thermography in conjunction with an advanced digital fringe processing technique. The advanced digital fringe processing is conducted using an asymmetric and central peak Gaussian filter, in order to remove noise and, subsequently, enhance the quality of the images. This investigation demonstrates the responds of functionally adapted dentine to temperature changes in its own plane and out of plane. Distinct pattern of out-of-plane and in-plane displacement was observed on the dentine by the DSPI analysis. The thermo-graphic analysis was used to rationalize the above nature of deformation in the dentine. These analyses showed that the inner, cervical dentine exhibited conspicuous deformation at the maximum temperature rise and equilibrated last during temperature drop.     

Additive-subtractive phase-modulated speckle interferometry: Fringe visibility under partial decorrelation

Additive-subtractive phase modulated speckle interferometry (ASPMSI) is a technique that minimizes the susceptibility of speckle methods to environmental noise while providing fringes of good visibility. The method requires the acquisition of two consecutive video frames of additive-speckle images of the same two deformed states of an object at a rapid enough rate such that ambient noise is not a problem. The additive-speckle images as expected are of very poor visibility due to the presence of the self-interference term. An interframe phase-modulation is introduced and the two additive-speckle images are digitally subtracted to improve the fringe visibility by removing the self-interference term. The ASPM-SI method works with in-plane and out-of-plane deformation sensitive ESPI as well as with displacement-gradient sensitive speckle-shearing interferometry. It is shown that the ASPM-SI scheme has higher visibility than conventional additive-SI and performs consistently better than subtractive-SI schemes in the presence of partial interframe speckle decorrelating optical noise. Furthermore, it is shown that the fringe visibility of the out-of-plane displacement sensitive interferometer which uses a protected reference beam separate from the object beam can be made to be essentially unity even at complete interframe decorrelation.     

Robustness of Objective and Subjective Speckle Patterns in the Speckle Strain Gauge

The robustness to rigid body object motions of three optical systems used in the speckle strain gauge were experimentally investigated and compared with analytical results of the correlation. It was found that an out-of-plane motion of the object damaged the reliability of the strain measure when recording the objective speckle patterns while subjective speckle patterns were more robust. Besides out-of-plane object motions, the robustness of a free-space geometry and an afocal imaging configuration are approximately the same, while a telecentric imaging system is more robust to rigid body motions but more sensitive to deformation gradients (basically in-plane rotation and tilt). Results from a measurement of the relaxation in a lead-tin alloy used in organ pipes is also presented.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Wako, Saitama, Japan.     

Measuring in-plane and out-of-plane coupled motions of microstructures by stroboscopic microscopic interferometry

A stroboscopic Mirau microscopic interferometer system for measuring in-plane and out-of-plane periodic motions of microstructures is demonstrated. One full cycle of a periodic motion is divided into a number of motion phases. One sequence of interferograms with different phase shifting steps is collected at every motion phase by using stroboscopic imaging. A bright-field image can be extracted from one sequence of interferograms with the same motion phase. In-plane displacements are measured by applying an image matching method to all bright-field images, followed by a compensation for the relative positions of interferograms at the different motion phases, before calculating the phase distribution related to out-of-plane deformation. We demonstrate its capability for measuring a combination of out-of-plane deformation and in-plane displacement in a microresonator.