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.     

Examination of the upper measurement limit in displacement measurement using fringe compensation in digital holography

Digital holography is a widely used method for displacement measurement in coherent optical metrology. An obvious limit of the method is that too large displacements result in dense fringes, so the fringes are practically invisible. The maximum number of contour fringes in displacement measurement is limited, because the cameras are discrete devices and sampling theory plays an important role. Because of the limited measurement range, compensation methods are promising tools for practical measurements. It can be shown that the practical measurement range can be extended above the Nyquist sampling limit. Compensation methods can be digital, because digital holographic interferometry operates with images recorded with a digital camera. In our research work the upper measurement range of fringe compensation method was examined. Our goal was to perform automatic compensation even if the displacement is higher than the measurement range of the basic method. The operation of the automatic fringe compensation method was based on the combination of two types of out-of-plane displacement measurements with different sensitivities.     

A windowing technique for the automated analysis of holo-interferograms

A systematic method for measuring surface deformations is described which includes the use of real-time holographic interferometry, the incorporation of a carrier fringe pattern to achieve fringe linearization, and the application of image digitization and automated computer analysis for rapid quantitative interpretation. In this method, regions of interest can be selected by the use of a windowing technique in which the operator specifies the desired subregion. The problem of correctly numbering fringes which originate or vanish at the boundary where the scanning begins is solved by an algorithm which ensures correct identification of the fringe orders. The output includes a perspective plot of the out-of-plane deformation field.This method is demonstrated by its application to a measurement of the out-of-plane deformation of a hermetically sealed plastic housing loaded by internal pressurization.     

Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry

An optical system for lensless Fourier transformed holographic interferometry is constructed to enable the measurement of minute displacements from nanometers to micrometers scale and to obtain corresponding strain distributions using a CCD camera with poor spatial resolution. Since a Fourier spectrum of an object beam is recorded on a hologram in this technique, the image reconstruction is easily performed with a single pass of 2-D fast Fourier transformation. Then, the map of the phase difference over the whole field is obtained by comparing two images before and after deformation. A suitable and effective unwrapping process is, however, inevitably required since the phase difference distribution is wrapped from −π to π in this technique. For phase unwrapping, the maximum spanning tree method is adopted here, which seeks a spanning tree that maximizes overall edge weights given by the cross amplitude. In-plane and out-of-plane displacements are obtained separately from the phase difference distributions at one's request. Moreover, in-plain strain is easily calculated from the in-plane displacement distribution.     

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.     

Comparison of double-pulse digital holography and HPFEM measurements

Pulsed digital holographic interferometry is a widely used technique for measurement of surface deformations. The results are displayed as high-quality images containing the surface deformation represented as a continuous function with high-precision and good resolution. On the theoretical side, the high precision finite-elements method (HPFEM) can be used to compute whole deformation maps of elastic continua, with a resolution comparable to that obtained with digital holographic interferometry. To prove the latter a series of resonant modes from a flat rectangular metal plate obtained with digital holographic interferometry will be compared to the same modes obtained under the same conditions with HPFEM. A very useful measurement concept is reached by combining both methods since they can be performed in parallel and within the same working area.     

Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems

Gray-level data pages enhance the storage capacity of holographic data storage systems. A balanced three gray-scale data page in phase mode produces a homogenized Fourier spectrum which is regarded to be necessary for suitable exploitation of the holographic recording medium. A commercially available transmission type twisted nematic liquid crystal display has been characterized for use as a phase spatial light modulator with phase modulation in the range 0–3π/2 at 532 nm wavelength, such that it may be used for holographic data storage with binary as well as three gray-level phase-modulated data pages. Experimental results of the phase and amplitude modulation characteristics of the SLM, Fourier plane homogeneity, and recording of phase-modulated binary, three gray-level data pages and their reconstruction with a real-time holographic interferometric method are presented.     

The Effects of Motion on Dynamic Moiré Interferometry

Experimental techniques (e.g. laser interferometry, photoelasticity) that generate fringe data are currently being utilized for analyzing full-field surface deformations in a variety of dynamic problems in experimental mechanics. As opposed to static problems, the transience of surface deformations in dynamic problems poses a unique problem in accurately resolving the fringe data that is acquired. Neumann determined that for time-lapse, double-exposure holographic interferometry the fringe contrast depends on the data acquisition time, wavelength of the light source, and transience of the dynamic phenomena. Dally performed a similar analysis for dynamic photoelasticity, where the dependence was on the stress gradients instead of the wavelength of the light source. This paper attempts to extend the analysis of Neumann and Dally to the analysis of transient fringe intensity data obtained from using dynamic moiré interferometry. It is found that the fringe contrast can depend on the frequency of the fringe field rather than the wavelength of the light source or stress gradients, and the fringe contrast will decay more rapidly for Gaussian light sources than constant intensity light sources. © 1997 Elsevier Science Ltd. All rights reserved.     

Mechanical characterization of unplasticised polyvinylchloride thick pipes by optical methods

In this work a number of techniques (electronic speckle pattern interferometry, holographic interferometry, strain gauge and finite element method) are brought to bear in order to establish consistency in the results of strain measurement. This is necessary if optical non-destructive testing methods, such as those used here, are to gain acceptance for routine industrial use. The FE model provides a useful check. Furthermore, ESPI fringe data facilitates the extension of FE models, an approach that is of growing importance in component testing.

The use of in-plane and out-of-plane sensitive electronic speckle pattern interferometry (ESPI) for non-destructive material characterization of thick unplasticised polyvinylchloride (uPVC) pipes is presented. A test rig has been designed for stressing pipes by internal pressure. ESPI gives a complete mapping of the displacement field over the area imaged by the video camera. The results for the strain of uPVC obtained from ESPI data and from strain gauges are in good agreement. The value of Young's modulus has been obtained from the fringe data and compared with results obtained using holographic interferometry and from strain gauge measurements. The FE model also produces fringe data that is consistent with the ESPI results.     

The governing equations of Moiré interferometry II. Gratings at ±45° to the measurement axes

The effects of tilting of the grating plane on moiré interferometric fringe patterns are studied using the method of Livnat and Post (Experimental Mechanics, 25(4) (1985) 6–360). Tilting may result either from rigid-body rotations or from out-of-plane displacement gradients. Tilting may introduce a significant error if it is assumed that the fringes represent contours of in-plane displacement, particularly if the in-plane deformation is small compared with the out-of-plane displacement gradient. Knowledge of the surface slope appears to be sufficient to correct the error. It is also shown that the fringe patterns do not capture the added displacement caused by rigid-body rotations exactly. The implications of these effects are briefly discussed for an experiment measuring the deformation at the tip of a crack in a ductile steel, in which the out-of-plane displacement gradients are relatively large.     

A digital phase-measurement system for real-time holographic interferometry

While holographic interferometry gives a good picture of the stress distribution over a complex structure, its use in stress-analysis has been limited by the fact that quantitative information on the deformation of the surface is directly available only at points on the fringe maxima or minima, and interpolation between these points is slow and not very accurate. An improved phase-measurement system for real-time holographic interferometry is described. This uses a diode array television camera to view the interference pattern, and digital electronics to calculate and store the phase difference at a 100 × 100 grid of points. This permits measurements of the phase with an accuracy estimated at ±2°.     

Speckle interferometric damage investigation of fibre-reinforced composites

With the aid of the recently reported technique of adding up phase images modulo 2π that correspond to stepwise applied load increments, the fringe density that can be achieved in electronic speckle pattern interferometry (ESPI) has been substantially improved. This technique also allows the measurement of much larger deformations than were hitherto possible with ESPI. The analytical power of the method is demonstrated in the measurement of high local displacement gradients in carbon fibre-reinforced plastics (CFRPs). In-plane and out-of-plane displacement field measurements, performed with one single optical instrument, are compared with finite-element models. This paper reports how the technique is used to detect and quantify damage in fatigued CFRP laminates via its effect on the surface displacement field. Moreover, the measured displacement fields are used to validate a finite-element damage model. The correctness of the delamination measurement is verified with the aid of ultrasonic C-scan reference results.     

散斑剪切干涉条纹特性的实验研究

本文通过位移位相存在的真实性实验、小孔滤波的必要性实验、位移梯度的解相关性实验,证实了散斑剪切于涉术的条纹是由物体变形所引起的“位移位相”和“位移微分位相”以及由位移和位移微分共同决定的“附加位相”之和的余弦条纹。实验证实这种余弦条纹的分布,随着滤波孔的位置而变化,它的衬比随着位移和位移梯度的增大而下降。特别是,当在象面上一点相遇的两个物点的象面散斑位移之差的模值大于散斑的直径时,两者相遇的象点上的条纹消失。     

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.     

Application of the holographic carrier fringe and FFT technique for deformation measurement

This paper describes a holographic system based on the use of fibre optics and automatic spatial carrier fringe pattern analysis. Carrier fringes are generated by simply translating the object beam between two exposures. Single-mode optical fibres are used to transfer both the object and reference beams. The fast Fourier transform method is used to process the interferograms: it extracts phase from fringe patterns resulting from the interference of tilted wavefronts. The method is illustrated by measuring the deformation of an arbitrarily clamped, uniformly loaded circular plate. The results are given for the perspective plot of the out-of-plane deformation field, the maps of wrapped and unwrapped phase, and a contour map of the unwrapped phase.     

基于条纹中心线的载波散斑条纹解调方法

针对传统傅里叶变换法在处理含有多突起的载波散斑条纹图时,由于存在频谱展宽会出现严重的解调相位失真,提出了一种基于条纹中心线的载波散斑条纹解调方法.根据载波调制时所采用平行调制方式和倾斜调制方式,分别从理论上对相关的中心线解调法进行数学推导,并进一步采用最小二乘三次曲面拟合法获得被测物面全场的离面位移信息.实验结果表明:利用上述中心线解调法和曲面拟合法能解调出复杂的载波条纹图,并获得具有亚像素定位准确度、连续光滑的全场离面位移信息.     

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.     

Determination of fractional fringe orders in holographic interferometry using polarization phase shifting

A simple method to determine the fringe orders at points between fringes in holographic interferometry is presented. The method is based on the use of two reference beams in the recording and reconstruction of the interferogram. A phase difference is imposed between the reference beams on reconstruction through polarization elements. The interferogram is viewed through a polarizer to recombine the images. The fractional fringe order is obtained from the angle through which the polarizer is rotated to shift the adjacent fringe to the point of interest.     

A new formula for fringe localization in holographic interferometry

Holographic interferometry generally involves the interference of two or more speckle fields reflected from or transmitted through a diffused object. The visibility of the resulting fringes depends on the degree of coherence of the interfering speckle fields. Through a statistical analysis it is found that the degree of coherence of speckle fields is essentially a function of the relative speckle displacement and average speckle size. The analysis leads to a new physical model for holographic interferometry. With this model the problem of fringe formation and localization may be analyzed and formulated in terms of speckle movement. A new formula for ideal fringe localization is then derived from the analysis. Furthermore, a localization factor V_c, i.e. the visibility of the holographic fringes, is introduced to analyze the partial fringe localization in holographic interferometry, which is of practical interest to most researchers.     

Deformation measurements of specularly reflecting objects using holographic interferometry with diffuse illumination

It is demonstrated that, by using diffuse object illumination, deformation measurements with holographic interferometry can be performed on a specularly reflecting object without the use of any additional coating of the object surface. An analytical expression for the secondary fringe formation is found, and the system is demonstrated only to be sensitive to deformations along the surface normal. A method for carrying out topographic measurements on specularly reflecting surfaces is suggested. The fringe visibility is studied for a rigid rotation of the object by using matrix methods. It is found that maximum fringe visibility is obtained if the recording camera is focused on the surface of the object.