Investigation of in-plane stresses on bolted flange joints using digital speckle pattern interferometry

Digital Speckle Pattern Interferometry (DSPI) is a promising field for a wide range of applications such as measurement of displacements/deformations, contouring, nondestructive testing, etc. It has holographic sensitivity and circumvents delays in photographic processing/filtering. Speckle correlation interferometry can be made sensitive to only one of the components of in-plane displacement by illuminating the object with two beams symmetric about the viewing axis and imaging along this axis using a viction. This configuration allows measurement of in-plane displacements independent of out-of-plane displacements.

In this paper, the in-plane deformation/stress distribution has been studied for a typical bolted flange joint of a pressure vessel using two beam illumination DSPI. The information obtained can be very useful in predicting the leakage behaviour of such joints employed in pressure vessels. Experimental investigations along with theoretical predictions are presented.     

A novel approach to high-sensitivity grating interferometry

The authors propose a new approach for obtaining information about in-plane and out-of-plane displacements of an object tested using high-sensitivity grating interferometry. The interferences of each of the specimen grating diffraction orders with a reference beam are recorded separately. Computer addition and subtraction of the phase functions calculated from the interferograms give the in-plane and out-of-plane displacement values, respectively. The authors present their experimental work, and then compare their results with those obtained using a conventional grating interferometry approach.     

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.     

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.     

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.     

Sandwich-speckle hologram: A combined method for local displacement analysis

Sandwich hologram interferometry and sandwich speckle photography tend to complement each other as displacement measuring methods; a sandwich hologram is best suited for out-of-plane movements, while speckle photography is used to determine in-plane components. The two techniques can be combined and both holographic and speckle photographic data can be stored on the same sandwich pair. Fringes caused by in-plane rigid body motion can be compensated for and local displacement evaluated.     

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.     

Holography and electronic speckle pattern interferometry in geophysics

Geophysical applications of holography and ESPI are reviewed. First, laboratory experiments of rock deformation and failure with holographic interferometry and holographic in situ stressmeters are briefly summarized. Then, holographic measurements of tunnel deformations made in Japan are described. The holographic recording system, consisting of an He---Ne gas laser and associated optical elements, was installed in a tunnel at the Amagase Crustal Movement Observatory, Japan in 1984. Tunnel deformations caused by tidal and tectonic forces have been precisely determined using the ‘real-time’ technique of holographic interferometry. Finally, some attempts to apply ESPI to geophysical measurements are introduced.     

Picosecond three-color holographic digital interferometry

The possibilities of multicolor digital holographic interferometry are experimentally studied upon measuring displacements of a surface in radiation of a picosecond Nd:YAG laser with the radiation frequency conversion into harmonics (λ₁ = 1.06 μm, λ₂ = 0.53 μm, and λ₃ = 0.35 μm). It is shown that three-color digital holographic interferometry makes it possible to increase the measurement accuracy of displacements. The peculiarities of multicolor digital holographic interferometry by picosecond pulses are discussed.     

Multiple modes in the vibration of cantilevered shells

The term multiple modes describes pairs of modes which are similar in shape but occur at different frequencies. This phenomenon has been observed in holographic vibration test results for a turbine blade. Pairs of modes were found, such as two modes which both resembled first torsional modes. In this investigation holographic interferometry was used to verify the earlier results for the turbine blade and to investigate three shell segments simulating blades. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5·6. The blade geometry is characterized by a circumferential angle of 142° and a ratio of length to inner radii arc length near 1·0. In addition, a NASTRAN finite element analysis was performed on these simulated blades. Both mode shapes and frequencies were found to be in good agreement with the results from the experiment. The multiple mode phenomenon was found to be an artifact of the holographic experiment. Pairs of modes were found in the NASTRAN results for the simulated blades in which the out-of-plane displacements (those seen in the hologram) were very similar, but for which the displacements in the plane of the hologram differed significantly. Thus, the two modes which appeared in the experimental results as first torsional modes were seen to include quite different in-plane displacements. The two modes are therefore quite different and do not contradict the normal result, which may be justified from such elementary considerations as a Rayleigh quotient, that similar modes must produce similar frequencies.     

The optical measurement station for complex testing of microelements

The paper presents a concept of optical measurement station for complex testing of microelements including MEMS, MOEMS and electronic components and assemblies. The wide selection of examples proves that the specific measurement requirements are fulfilled by alternative usage of combined conventional and grating interferometers CI/GI (reflective surfaces), in-plane and out-of-plane ESPI (scattering surfaces) and digital holographic interferometry DHI (mixed surfaces) supported by thermovision. All these methods are realized by integrated microinterferometer (IWaM) based on a glass waveguide or air cavity waveguide arrangements. The air cavity IWaM allows to form a thermal output for combined thermovision CI/GI or ESPI measurements.IWaM has a compact design insensitive to mechanical vibrations and may be easily rearranged to work with the selected measurement techniques. It is also fully integrated with an optical microscope and it is designed to work both in laboratories and in production environments.     

The holographic-hole drilling method for residual stress determination

Holographic-hole drilling is a method developed for the rapid determination of residual stresses from an optical interference fringe pattern. A small diameter blind hole is drilled into a part containing residual stresses, and the displacements caused by localized stress relief are registered by real-time holographic interferometry. The resulting fringe pattern is evaluated to calculate residual stresses, using a simple ‘fringe counting’ method described here. Results of applying the method in laboratory tests to a variety of uniform biaxial states-of-stress from equibiaxial compression to pure shear are shown. Two sample applications of the method, the evaluation of residual stresses at a cold-worked hole and at a weld bead, are also given. Extensions of the method to evaluate stresses non-uniform in depth and/or along the surface are discussed.     

Measurement of the a.c. impedance of aluminium samples by holographic interferometry

In the present investigation, holographic interferometry was utilized for the first time to measure the alternating current (a.c.) impedance of aluminium samples during the initial stage of anodization processes in aqueous solution without any physical contact. The anodization process (oxidation) of the aluminium samples was carried out chemically in different sulphuric acid concentrations (0.5–3.125% H₂SO₄) at room temperature. In the mean time, a method of holographic interferometric was used to measure the thickness of anodization (oxide film) of the aluminium samples in aqueous solutions. Along with the holographic measurement, a mathematical model was derived in order to correlate the a.c. impedance of the aluminium samples in solutions to the thickness of the oxide film of the aluminium samples which forms due to the chemical oxidation. The thickness of the oxide film of the aluminium samples was measured by the real-time holographic interferometry. Consequently, holographic interferometry is found very useful for surface finish industries especially for monitoring the early stage of anodization processes of metals, in which the thickness of the anodized film as well as the a.c. impedance of the aluminium samples can be determined in situ. In addition, a comparison was made between the a.c. impedance values obtained from the holographic interferometry measurements and from measurements of electrochemical impedance spectroscopy. The comparison indicates that there is good agreement between the data from both techniques.     

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.     

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.     

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.     

A semi-automatic method for measuring interferometry fringes: prototype design and first results

A device for automatically obtaining the information contained in holographic interferometry fringes is proposed. The method may be applied to any kind of interferometric fringes. Accuracy has been demonstrated by contrasting the results obtained with our prototype system and those with the single-beam speckle interferometry technique for the measurement of displacements in a plane. The results show good correlation between the two series of measurements.     

Dynamic time responses of a flexible spinning disk misaligned with the axis of rotation

Using the finite element method, this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry. The misalignment between the axes of symmetry and rotation is one of major vibration sources in optical disk drives such as CD-ROM, CD-R, CD-RW and DVD drives. Based upon the Kirchhoff plate theory and the von Karman strain theory, three coupled equations of motion for the misaligned disk are obtained: two of the equations are for the in-plane motion while the other is for the out-of-plane motion. After transforming these equations into two weak forms for the in-plane and out-of-plane motions, the weak forms are discretized by using newly defined annular sector finite elements. Applying the generalized-α time integration method to the discretized equations, the time responses and the displacement distributions are computed and then the effects of misalignment on the responses and the distributions are analyzed. The computation results show that the misalignment has an influence on the magnitudes of the in-plane displacements. It is also found that the misalignment results in the amplitude modulation or the beat phenomenon in the time responses of the out-of-plane displacement.     

Interferometric 3-D displacement measurement using wavefront analysis

We propose and demonstrate a novel interferometric technique for 3-D displacement measurement. The method is based on the analysis of the phase difference distribution measured when two coherent curved wavefronts originating from different locations interfere. Both the in-plane and out-of-plane displacements are found simultaneously from a single phase difference distribution. We find that our system could measure with an accuracy better than 1.5 μm for in-plane displacements and 36 μm for out-of-plane displacements over 1 mm range. This accuracy was limited by the output lens performance. Theoretical analysis reveals that sub-micron accuracy may be possible with more careful calibration.     

Separation of 3-D displacement components in the white light speckle method

Measurement of in-plane and out-of-plane displacement components using the white light speckle method is considered for three different cases. The first is applicable when in-plane components are small and stresses are directly related to the second differential of the out-of-plane component. The other cases involve components of the same order of magnitude but require recording of either one or two specklegrams. Evidence of experimental demonstration of each case is given.