Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods

The measurement of dynamic displacements by use of speckle pattern interferometry and temporal phase unwrapping allows for the evaluation of large-object displacement fields without the propagation of spatial unwrapping errors. If a temporal carrier is introduced in one of the beams of the interferometer, phase data for whole-object displacement can be retrieved by use of a temporal phase-shifting method or a temporal Fourier transformation approach. We present a comparison between both methods of temporal phase measurement in terms of precision and execution speed. We performed the analysis by using computer-simulated speckle interferograms, an approach that allowed us to know precisely the original phase distribution and also to determine the spatial rms phase error as a function of the phase change introduced between two consecutive speckle interferograms. The performance of both methods to process experimental data is also illustrated by use of the results from a high-speed speckle interferometry study of a carbon fiber panel.     

Three-dimensional shape measurement beyond the diffraction limit of lens using speckle interferometry

Speckle interferometry is generally known as a method for measuring the deformation of an object with rough surfaces. In this paper, a three-dimensional (3D) shape measurement method is proposed for superfine structures beyond the diffraction limit using the basic property of speckle interferometry. Since the differential coefficient distribution of the shape of such an object can be detected in speckle interferometry by imparting a known lateral shift to the measured object, the shape can be reconstructed by integrating the differential coefficient distribution. Based on experimental results obtained using diffraction gratings as measured objects, it is confirmed that the proposed method can measure 3D shapes that are beyond the diffraction limit of the lens.     

Time-resolved vibration measurement with temporal speckle pattern interferometry

Temporal speckle pattern interferometry (TSPI) is an optical measurement procedurefor measuring the displacement of rough technical surfaces. The time-dependent speckle modulation due to optical path difference changes is tracked during the whole displacement of the surface and then evaluated pointwise without referring to neighboring pixels. This feature allows for its use as independent point sensors. This aspect of incremental phase tracking enables TSPI to be used to measure time-resolved mechanical vibrations. It also reduces the deteriorating effect of the decorrelation. Therefore large displacements can be measured. A concept for an inexpensive fiber-optical point sensor was developed and the theoretical accuracy for vibration measurement was investigated. The TSPI measurement of a loudspeaker membrane is compared with a high-precision vibrometer measurement. The first results show good agreement.     

Optimal re-referencing rate for in-plane dynamic speckle interferometry

We investigate experimentally the optimal rate at which the reference speckle pattern should be updated when dynamic speckle interferometry is used to measure transient in-plane displacement fields. Images are captured with a high-speed camera and phase shifting and phase unwrapping are done temporally. For a wide range of in-plane velocities, up to a maximum of 40% of the Nyquist limit, the random errors in the calculated displacement field are minimized by updating the reference speckle pattern after a speckle displacement of 1/10 of the pixel spacing. The technique is applied to measurements of microscale deformation fields within an adhesive joint in a carbon-fiber epoxy composite.     

ESPI and Digital Speckle Correlation Applied to Inspection of Crevice Corrosion on Aging Aircraft

A recent advance in the nondestructive inspection of crevice corrosion is reported. Crevice corrosion is one of the most hazardous defects that threaten the integrity of aging aircraft. Two optical techniques, electronic speckle pattern interferometry (ESPI) and digital speckle correlation (DSC), are employed to reveal the existence of crevice corrosion, which is usually undetectable from outside by visual inspection. The ESPI is configured to measure out-of-plane displacement. Both thermal loading and vacuum loading are used. The anomaly of fringe patterns reveals the existence of crevice corrosion hidden between two metallic plates. Not only the location of defects, but also the approximate size can be estimated. The digital speckle correlation technique takes advantage of laser speckle properties. The speckle decorrelation due to out-of-plane displacement in the region with crevice corrosion is larger than the region without defects. This difference is calculated by a digital correlation algorithm, which reveals the crevice corrosion. These two techniques can be used alternatively for field inspection of aircraft. While digital speckle correlation offers a simple, rapid approach to qualitatively detect defects, ESPI can be used as a supplementary tool if a more sensitive and quantitative evaluation is required.     

Fringe formation in multiaperture speckle shear interferometry

Multiaperture speckle shear interferometry exhibits sensitivity to in-plane displacement components. The response of the interferometer to in-plane displacement, however, depends on the location of the shear element on an aperture in front of the imaging lens. Two configurations with three apertures, with the shear element positioned at two different locations, are examined theoretically and experimentally.     

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.     

Measurement of nanometric displacements by correlating two speckle interferograms

This paper presents a method to measure nanometric displacement fields using digital speckle pattern interferometry, which can be applied when the generated correlation fringes show less than one complete fringe. The method is based on the evaluation of the correlation between the two speckle interferograms generated by both deformation states of the object. The performance of the proposed method is analyzed using computer-simulated speckle interferograms. A comparison with the performance given by a phase-shifting technique is also presented, and the advantages and limitations of the proposed method are discussed. Finally, the performance of the proposed method to process real data is illustrated.     

Disk-growing algorithm for phase-map unwrapping: application to speckle interferograms

Interferometric techniques combined with phase shifting allow computation of the phase that is linked to the displacement of the object under study. The phases before and after displacement are computed from three or more interferograms (called specklegrams when speckle is used as the information carrier). Subtraction of these two phase patterns leads to a raw phase map. Phase unwrapping restores the 2π discontinuities and gives a continuous phase map. The disk-growing algorithm presented allows the inner and the outer propagation of the unwrapping from a growing disk and so avoids the main problem of anisotropic error propagation for noisy phase maps. It works successfully in speckle interferometry.     

Effects of Window Size on Accuracy and Spatial Resolution in Windowed Phase‐Shifting Digital Holographic Interferometry1

Abstract: Phase‐shifting digital holographic interferometry is a new method to measure displacement distribution on the surface of an object. Usually holography has speckle noise, which leads to a large error in the analysis of displacement and strain distributions. We previously proposed windowed phase‐shifting digital holographic interferometry (windowed PSDHI). The use of this method leads to accurate displacement analysis, decreasing the effect of speckle patterns. However, noise reduction involves a defect, which renders the spatial resolution low. In this paper, by comparing the conventional noise reduction method using spatial averaging with the windowed PSDHI on spatial resolution, the effectiveness of noise reduction is discussed.     

High-speed dynamic speckle interferometry: phase errors due to intensity, velocity, and speckle decorrelation

The recently developed technique of high-speed phase-shifting speckle interferometry combined with temporal phase unwrapping allows dynamic displacement fields to be measured, even for objects containing global discontinuities such as cracks or boundaries. However, when local speckle averaging is included, small phase errors introduced at each time step are accumulated along the time axis, yielding total phase values that depend strongly on the speckle rereference rate. We present an analysis of the errors introduced in the phase evaluation by three sources: intensity errors, velocity errors, and speckle decorrelation. These errors are analyzed when they act both independently and together, for the most commonly used phase-shifting algorithms, with computer-generated speckle patterns. It is shown that, in a controlled out-of-plane geometry, errors in the unwrapped phase map that are due to speckle decorrelation rise as the time between rereferencing events is increased, whereas those due to intensity and velocity errors are reduced. It is also shown that speckle decorrelation errors are typically more important than the intensity and velocity errors. These results provide guidance as to the optimal speckle rereferencing rate in practical applications of the technique.     

ESPI Measurements of Strain on a CFRP‐Reinforced Bending Beam1

Abstract: This paper presents 3D electronic speckle pattern interferometry (ESPI) measurement results of strain components at the end of a carbon‐fibre reinforced polymer (CFRP) plate adhesively bonded to a reinforced concrete beam. To minimise speckle decorrelation because of the inevitable rigid‐body motion of the measured specimen, the load was increased in small increments. Two evaluation schemes are compared: the step‐by‐step addition of the measured displacement components and regain of the correlation by image shifting. Strain is evaluated by interpolating the in‐plane displacement measurements along selected lines, and is compared with results from finite element analysis (FEA). An uncertainty estimate is given.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis

A novel interferometric method named statistical interferometry is proposed and studied. In the method, in contrast to the conventional deterministic interferometry, the complete randomness of the two interfering light fields, i.e., the random interference of the fully developed speckle fields, plays an essential role and is used as a standard of phase in a statistical sense. Preliminary experiments were conducted to verify the validity of the method, followed by a computer simulation. As an experimental result, the accuracy of the measurements of an out-of-plane displacement was confirmed up to lambda/800 by comparison with the heterodyne interferometer. The method has the advantage of simplicity of the optical system required, while at the same time providing high accuracy.     

Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. II: Finite element modeling

In holography and speckle interferometry the measurement range is generally limited by the greatest number of fringes that can be resolved in a single image. As a result these techniques have been generally confined to small displacement measurement applications. In the case of out-of-plane measurements one can overcome this limitation by simply adding incremental measurements at individual detector pixels. In the case of in-plane measurements, however, summing incremental measurements is not a straightforward procedure since the interference pattern moves laterally across the detector as the material deforms. We describe a modeling technique based on finite elements which solves this problem. In combination with a full field method such as holography or speckle interferometry, it provides a very sensitive measurement technique with dense spatial sampling and large dynamic range. Experimental results of speckle interferometry operating in transmission to measure in-plane displacements of biological membranes are presented, where total material displacements are of the order of millimeters. The results also demonstrate how the finite strain tensor is calculated analytically from the data at any point on the material.     

NDI of interfaces in coating systems using digital interferometry

This paper describes a new application of two laser interferometry techniques to the non-destructive inspection (NDI) of coated surfaces. The purpose is to detect interfacial disbond between the coating and the substrate. Debonding is detected by properly exciting the surface of the object under inspection in such a way that the interference fringe pattern is modified rendering the disbond readily visible. The fringe patterns resulting from the associated images were captured using electronic speckle pattern interferometry (ESPI) and shearography. Image processing techniques are applied to enhance the detection and better definition of the debonded layer. Some results and discussions are presented to illustrate the applicability of these two optical techniques to thermal barrier coatings.     

Use of electronic speckle pattern interferometry in the detection of fatigue failure in high strength steels

The fatigue behaviour of next generation high strength steels (σ_UTS = 950–1000 MPa) has been studied. Specifically, this study is focused on the initiation stage of fatigue microcracks. With this purpose, high cycle fatigue tests under uniaxial loading have been performed. During these tests, the deformation history of the specimen has been tracked by means of speckle interferometry. This technique allows monitoring the evolution of the displacement field and its derivatives on the specimen surface, so that it can be used as a tool for detecting microcracks in the first stages of crack initiation. The observation of the fracture surfaces provides complementary information about the localization of the initiation of failure thus, a correlation between the observations made by interferometry and the actual location of the fatigue nucleus and the evolution of the crack during its propagation can be established. Results appoint speckle interferometry as a promising technique for the detection of fatigue failures.     

Wavelet analysis of speckle patterns with a temporal carrier

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer. The intensity variation of each pixel on recorded images is then analyzed along the time axis by a robust mathematical tool, i.e., a complex Morlet wavelet transform. After the temporal carrier is removed, the absolute displacement of a vibrating object is obtained without the need for temporal or spatial phase unwrapping. The results obtained by a wavelet transform are compared with those from a temporal Fourier transform.     

Application of dynamic phase shifting with wavelet analysis to electronic speckle contouring

Dynamic phase shifting is a temporal phase unwrapping method, i.e., a method in which a sequence of speckle patterns is analyzed along the time axis. Each pixel can thus be considered as an independent detector, which is of particular interest for the study of complex surfaces. I report the application of this technique, which is based on a wavelet analysis, to contouring measurements with a dual-beam illumination electronic speckle pattern interferometry setup. I present a new, more general geometric model of the setup. I also investigate the possibility of enhancing the accuracy by using the intermediate phase values. Tests are performed on a simply described object and compared with coordinate measuring machine measurements.