Fringe visibility analysis with different scale apertures in speckle photography

Abstract

The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.     

Lau Effect in Reflection

Abstract

The interference phenomenon known as the Lau effect is usually produced when two transmission gratings are located in tandem and are illuminated incoherently. This paper extends the study on this effect by analysing the optical arrangement in which the second transmission grating is replaced by a reflection grating. The interference fringes produced under incoherent illumination in this new reflection Lau geometry are, in certain respect, similar to those in the usual transmission geometry. The new set of fringes, however, become changeable in their profile when one of the gratings is subjected to an in-plane translatory motion in the direction perpendicular to the grating lines. The characteristics of the fringe formation phenomenon are examined quantitatively from the viewpoint of the incoherent superposition of multi-diffraction patterns of the gratings. We present a theoretical analysis and a supporting experimental verification of this phenomenon.     

Fringe Variation and Visibility in Speckle-shearing Interferometry

Abstract

Frequency spectra are analysed for two typical speckle-shearing interference recording methods; using a single aperture speckle-shearing camera (SASSC) and a double-aperture speckle-shearing camera (DASSC) to show the fringe variation due to the displacement involved in differentiation. Speckle statistics are then made for the filtering system to show the fringe-contrast variation resulting from the object deformation and the aperture of the filtering-image system.     

Analysis of mutually incoherent symmetrical illumination for electronic speckle pattern shearing interferometry

A speckle shearing interferometer has been designed using symmetrical mutually incoherent illumination, in an effort to provide measurements of in-plane strain. An analysis of the sensitivity to displacement and strain of this interferometer is presented, together with analysis of the optical phase extraction of the resultant fringe pattern. This interferometer is an improvement on previous designs as it provides information on the in-plane strain separated from components of the displacement. Experimental results provide qualitative data in the form of fringe patterns in support of the theoretical analysis.     

FATIGUE CRACK TIP STRAINS IN 7075-T6 ALUMINUM ALLOY

Abstract— The plastic enclave surrounding a fatigue crack in a 7075-T6 aluminum alloy specimen is studied using moiré interferometry. Two distinct plastic zones are identified from inspection of moiré interferometric fringe patterns. The sizes and shapes of the monotonic and the cyclic plastic zones are correlated with previous theoretical and experimental results. Live load strain distributions in the plastic enclave are computed from high sensitivity (0.417 micron per fringe) full-field in-plane displacement contour maps. Comparison with theoretical and experimental strain distributions are included.     

Optical configuration in speckle shear interferometry for slope change contouring with a twofold increase in sensitivity

We present a novel optical configuration that yields a fringe pattern that represents the slope changes of a three-dimensional object with a twofold increase in sensitivity. The method offers controllable sensitivity over a wide range. We accomplish it by modifying the in-plane displacement sensitive configuration of speckle interferometry. The detailed theory and the experimental results are presented with a brief discussion on the limiting aspects of the configuration.     

Method for fringe enhancement in holographic interferometry for measurement of in-plane displacements

Theoretical background along with experimental results are given for a simple method for in-plane fringe enhancement in dual-beam illumination holographic interferometry. In this method, the fringes representing in-plane displacements arise as a moirépattern between two interferograms. To distinguish the in-plane displacement, a sequence of images is recorded while the reference mirror is continuously tilted at random. The in-plane fringes arethen found as the maximum contrast of the out-of-plane fringes in the image sequence. The resulting fringe quality is close to the quality of the out-of-plane fringes.     

Biaxial alignment in sputter deposited thin films

Biaxially aligned thin films have not only a preferential crystallographic out-of-plane orientation, but also have an alignment along a certain reference direction parallel to the substrate plane. This type of film has been obtained by unbalanced reactive magnetron sputter deposition on both amorphous glass and randomly textured polycrystalline substrates tilted with respect to the incoming material flux.First, we focus on the development of microstructure and crystallographic out-of-plane orientation. The results are summarized in an extended structure zone model. Based on experimental results, a mechanism for the in-plane alignment is proposed which shows that an in-plane alignment can only be obtained when an overgrowth mechanism drives the microstructural evolution of the thin film. The quality of the in-plane alignment can be evaluated from X-ray diffraction pole figures. The influence of several deposition parameters (target-substrate distance, target-substrate angle, deposition pressure, and substrate bias) on the degree of in-plane alignment is discussed. The influence of these parameters can be traced to the influence of two main properties, i.e. the mobility of the adatoms at the growing surface and the angular spread of the incoming material flux. Finally, since impurities are hard to exclude during deposition, their influence on the microstructure, the preferential out-of-plane orientation, and the in-plane alignment is reported.     

Analysis of coherent symmetrical illumination for electronic speckle pattern shearing interferometry

In an effort to find a non-contact technique capable of providing measurements of in-plane strain, a speckle shearing interferometer was designed using symmetrical coherent illumination. This paper presents an analysis of the sensitivity to displacement and strain of this interferometer, together with an analysis of the phase-stepping of the resultant fringe patterns. New notation is introduced alongside this analysis to define the interference components in speckle shearing interferometers using multiple illumination beams. Experimental results show fringe patterns and phase stepping in support of the theoretical analysis.     

Digital speckle pattern interferometry for deformation analysis of inner surfaces of cylindrical specimens

Deformation study of curved engineering and technical surfaces, such as pipes and pressure vessels, has gained much importance in the recent past. Speckle interferometric techniques and their electronic and digital analogs, which are whole field techniques, have been effectively applied for practical nondestructive testing applications over the years. However, little work has been done that discusses the speckle fringe formation with a fruitful theoretical formulation to study deformation analysis of curved surfaces. We propose an extended theory for speckle fringe formation on curved surfaces, which can be applied to the study of curved engineering and technical specimens under various loading conditions such as in-plane, out-of-plane, and out-of-plane shear configurations. Simulated contours are generated by use of finite element models with similar loading conditions, and the data are analyzed and compared with the obtained experimental results.     

De-correlation Effects in Speckle-pattern Interferometry

A theoretical analysis of de-correlation effects in plane strain sensitive speckle-pattern interferometry is presented. Experimental results supporting the theoretical model are summarized and it is shown that in-plane translations and out-of-plane rotations typically of order 10² μm and 10^-3 radians respectively may be tolerated before fringe visibility becomes unacceptable. The results also indicate how the interferometer may be optimized. Interferograms which show the strain fields resulting from machining are presented.     

Simple method for simultaneously measuring the magnitude and direction of 2D in-plane displacement in white-light speckle photography

A simple method for simultaneously measuring the magnitude and direction (or argument) of a 2D in-plane displacement vector is presented. The theoretical mechanism for extracting the desired displacement signal from random noises produced by the nonoverlapping area of the recorded specklegrams of the test specimen surface is derived in detail. This procedure is realized by establishing a 1D displacement model in a white-light speckle photographic system using discrete Fourier transform shifting theorem. Results of the computer simulation and experiment show that the present method exhibits advantages such as convenient displacement direction determination, better robustness and wider measurement range than those of the traditional fringe analysis-based method. These characteristics make the proposed method a potential approach in practical applications.     

Experimental measurement and numerical analysis on resonant characteristics of piezoelectric disks with partial electrode designs

Three experimental techniques are used in this study to access the influence of the electrode arrangement on the resonant characteristics of piezoceramic disks. These methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, pointwise displacement, and electric impedance, respectively. In this study, one full electrode design and three nonsymmetrical partial electrode designs of piezoelectric disks are investigated. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time for out-of-plane and in-plane motions. The second experimental method is the impedance analysis, which is used to measure the resonant and antiresonant frequencies. In addition to these experimental methods, LDV-DSA is used to determine the resonant frequencies of the vibration mode with out-of-plane motion. From the experimental results, the dependence of electrode design on the vibration frequencies and mode shapes is addressed. Numerical computations based on the finite element method are presented, and the results are compared with the experimental measurements. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.     

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.     

Analysis of the complex phase error introduced by the application of the Fourier transform method

Abstract

The relation between modulus and phase errors introduced by the application of the Fourier transform method to fringe pattern analysis has been established. The theoretical results obtained are proposed for the reconstructed phase error correction. Numerical verification for a one-dimensional fringe pattern, comparison of corrected and non-corrected results obtained for different basic spatial frequencies and an example of application of the proposed correction for real data are given.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Fringe Formation in an In-Plane Displacement Measurement Configuration with Twofold Increase in Sensitivity: Theory and experiment

A fringe-formation theory for a dual-beam illumination configuration that leads to a twofold increase in sensitivity for the measurement of in-plane displacement is described. Here we have taken into account all four beams simultaneously that are generated at the image plane owing to two-beam illumination and their cross-interference terms for fringe formation. We show that the sensitivity obtainable is the usual interferometric sensitivity when we take into account all four beams simultaneously and doubles only when the retroreflected beams are observed. A detailed theory and an experimental demonstration of the method are presented.     

Finite element visualization of fatigue crack closure in plane stress and plane strain

Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon. Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs. Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction. Finite element analyses indicate that crack closure does occur under pure plane strain conditions. The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction. This in-plane contraction also leads to the generation of complex residual stress fields. The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios. This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain.     

Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs

Three experimental techniques are used in this study to access the resonant characteristics of piezoceramic bimorphs in parallel and series connections. These experimental methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, point-wise displacement, and electric impedance, respectively. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time by the AF-ESPI method. LDV-DSA is used to determine the resonant frequencies of the vibration mode for out-of-plane motion. The impedance analysis is used to measure the resonant and antiresonant frequencies for in-plane motion. Although the out-of-plane mode is the dominant motion of piezoceramic bimorphs, it is found in this study that the amount of displacement for the in-plane motion in parallel connection is large enough to be measured by AF-ESPI and impedance. It is interesting to note that resonant frequencies of the specimen in parallel connection for the out-of-plane motion determined by LDV-DSA are the same as that for the in-plane motion obtained by impedance. Furthermore, both in-plane and out-of-plane mode shapes for the specimen in parallel connection are obtained in the same resonant frequency from the AF-ESPI method. It is concluded in this study that the particle motions of piezoceramic bimorphs for parallel connection in resonance are essentially three-dimensional. However, it is found that only out-of-plane vibration modes can be excited for the specimen in series connection. Numerical computations based on the finite-element method are presented, and the theoretical predicted results are compared with the experimental measurements. Good agreements between the experimental measured data and numerical calculated results are found for resonant frequencies and mode shapes of the piezoceramic bimorph.