Hubert W. Schreier

Image Correlation for Shape, Motion and Deformation Measurements

Image Correlation for Shape, Motion and Deformation Measurements provides a comprehensive overview of data extraction through image analysis. Readers will find and in-depth look into various single- and multi-camera models (2D-DIC and 3D-DIC), two- and three-dimensional computer vision, and volumetric digital image correlation (VDIC). Fundamentals of accurate image matching are described, along with presentations of both new methods for quantitative error estimates in correlation-based motion measurements, and the effect of out-of-plane motion on 2D measurements. Thorough appendices offer descriptions of continuum mechanics formulations, methods for local surface strain estimation and non-linear optimization, as well as terminology in statistics and probability. With equal treatment of computer vision fundamentals and techniques for practical applications, this volume is both a reference for academic and industry-based researchers and engineers, as well as a valuable companion text for appropriate vision-based educational offerings.

Systematic errors in digital image correlation caused by intensity interpolation

Recently, digital image correlation as a tool for surface defor- mation measurements has found widespread use and acceptance in the field of experimental mechanics. The method is known to reconstruct displacements with subpixel accuracy that depends on various factors such as image quality, noise, and the correlation algorithm chosen. How- ever, the systematic errors of the method have not been studied in detail. We address the systematic errors of the iterative spatial domain cross- correlation algorithm caused by gray-value interpolation. We investigate the position-dependent bias in a numerical study and show that it can lead to apparent strains of the order of 40% of the actual strain level. Furthermore, we present methods to reduce this bias to acceptable lev- els.

Systematic errors in digital image correlation due to undermatched subset shape functions

Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains.In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.

Advances in light microscope stereo vision

The increasing research focus on small-scale mechanical systems has generated a need for deformation and strain measurement systems for microscale applications. Optical measurement systems, such as digital image correlation, present an obvious choice due to their non-contacting nature. However, the transfer of measurement technology developed for macroscale applications to the microscale presents unique challenges due to the differences in the required highmagnification optics. In this paper we illustrate the problems involved in calibrating a stereo microscope using traditional techniques and present a novel methodology for acquiring accurate, three-dimensional surface shape and deformation data on small-scale specimens.Experimental results demonstrate that stereo microscope systems can be accurately and reliably calibrated using a priori distortion estimation techniques in combination with traditional bundle-adjustment. The unique feature of the present methodology is that it does not require a precision calibration target but relies solely on point correspondences obtained by image correlation. A variety of experiments illustrate the measurement performance of a stereo microscope system. It is shown that the surface strains obtained from the full-field, three-dimensional measurements on tensile specimens undergoing large rigid-body motions are within ±50 microstrain of strain gage measurements for strains ranging from 0 to 2000 microstrain.

Metrology in a scanning electron microscope: theoretical developments and experimental validation

A novel approach for correcting both spatial and drift distortions that are present in scanning electron microscope (SEM) images is described. Spatial distortion removal is performed using a methodology that employs a series of in-plane rigid body motions and a generated warping function. Drift distortion removal is performed using multiple, time-spaced images to extract the time-varying relative displacement field throughout the experiment. Results from numerical simulations clearly demonstrate that the correction procedures successfully remove both spatial and drift distortions. Specifically, in the absence of intensity noise the distortion removal methods consistently give excellent results with errors on the order of +/- 0.01 pixels. Results from the rigid body motion and tensile loading experiments at 200 x indicate that, after correction for distortions, (a) the displacements have nearly random variability with a standard deviation of 0.02 pixels; (b) the measured strain fields are unbiased and in excellent agreement with previous full-field experimental data obtained with optical illumination; (c) the strain field variability is on the order of 60 microstrain in all components with a spatial resolution on the order of 25 pixels. Taken together, the analytical, computational and experimental studies clearly show that the correction procedures successfully remove both spatial and drift distortions while retaining excellent spatial resolution, confirming that the SEM-based method can be used for both micromaterial and nanomaterial characterization in either the elastic or elastic-plastic deformation regimes.

On Error Assessment in Stereo-based Deformation Measurements

Using the basic equations for stereo-vision with established procedures for camera calibration, the error propagation equations for determining both bias and variability in a general 3D position are provided. The results use recent theoretical developments that quantified the bias and variance in image plane positions introduced during image plane correspondence identification for a common 3D point (e.g., pattern matching during measurement process) as a basis for preliminary application of the developments for estimation of 3D position bias and variability. Extensive numerical simulations and theoretical analyses have been performed for selected stereo system configurations amenable to closed-form solution. Results clearly demonstrate that the general formulae provide a robust framework for quantifying the effect of various stereo-vision parameters and image-plane matching procedures on both the bias and variance in an estimated 3D object position.

Development and assessment of a single-image fringe projection method for dynamic applications

A single-image fringe projection profiling method suitable for dynamic applications was developed by combining an accurate camera calibration procedure and improved phase extraction procedures. The improved phase extraction process used a modified Hilbert transform with Laplacian pyramid algorithms to improve measurement accuracy. The camera calibration method used an accurate pinhole camera model and pixel-by-pixel calibration of the phase-height relationship. Numerical simulations and controlled baseline experiments were performed to quantify key error sources in the measurement process and verify the accuracy of the approach. Results from numerical simulations indicate that the resulting phase error can be reduced to less than 0.02 radians provided that parameters such as fringe spacing, random measured intensity noise, fringe contrast and frequency of spatial intensity noise are carefully controlled. Experimental results show that the effects of random temporal and spatial noise in typical CCD cameras for single fringe images limits the accuracy of the method to 0.04 radians in most applications. Quantitative results from application of the fringe projection method are in very good agreement with numerical predictions, demonstrating that it is possible to design both a fringe projection system and a measurement process to achieve a prespecified accuracy and resolution in the point-to-point measurement of the spatial (X, Y, Z) positions.

Experimental Study of Measurement Errors in 3D-DIC Due to Out-of-Plane Specimen Rotation

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out of plane specimen motions, three-dimensional digital image correlation (3D-DIC) oftentimes is employed. The 3D-DIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out of plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using 3D-DIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. This paper presents experimental results regarding the effect of out-of-plane rotation on strain measurement using 3D-DIC. Specifically, full-field deformation results are obtained during rigid body, out-of-plane rotation in the range −40° ≤ θ ≤40° using a two-camera stereovision system. Results indicate that (a) the measured normal strain in the foreshortened direction increases in a non-linear manner with rotation angle, (b) the normal strain along the direction of the rotation axis is essentially zero for all rotation angles and (c) the in-plane shear strain is small but increases linearly with rotation angle. Results also indicate that the magnitude of the errors in the strain are a strong function of how the calibration process is performed, with measurement errors exceeding ±1400 μe for what would normally be considered “small angle” calibration processes.

Experimental Investigation on Material Dynamic Behaviors Using Ultra-high-speed Cameras

The full-field dynamic response of a material undergoing impact loading, especially the early stage of a single impact pulse event, is difficult to measure considering short time duration of the pulse and lack of measurement methods capable of acquiring data at sufficiently high rate. In this study, the investigators employed a recently developed ultra-high-speed HPV-X camera with framing rates up to 5,000,000 fps and a 400 × 250 pixel array to acquire whole field image data, including deformations, velocities, accelerations, strains and strain rates, which occur in the first 100 μs of initial impact of a three-point bend copper beam specimen subjected to centerline impact by a high strength aluminum bar. In addition to 2D image data, strain gauges and load cells are used to (a) provide offset trigger to the flash unit and the camera to ensure uniform illumination and (b) record the time history of force reactions at the two supports for a three-point bend specimen, respectively. Results clearly show that it is possible to quantify the full-field mechanical response of the specimen for framing rates from 1,000,000 to 5,000,000 over a range of input impact amplitudes, providing essential early-stage data that can be used to determine various properties of interest.

Curvilinear Fatigue Crack Growth Under Out-of-Phase Loading Conditions

Methods for predictive modeling and simulation of crack branching and curvilinear crack paths under cyclic out-of-phase loading conditions have been developed and implemented in a custom finite element code CRACK3D. 3D mixed-mode stress intensity factors (SIFs) for fatigue crack growth simulations with curved crack paths and curved crack fronts are determined using the 3D virtual crack closure technique (3D VCCT) and a locally structured re-meshing approach in which the local region immediately surrounding a moving crack front is automatically re-meshed with a structured mesh pattern to facilitate the 3D VCCT and maintain its accuracy. The prediction of the crack growth direction is achieved using the maximum circumferential stress criterion. Fatigue crack growth events under out-of-phase loading conditions in cruciform aluminum specimens with a central hole and an edge crack at the hole are simulated. Simulation predictions of crack branching angles and the curvilinear paths of the branched cracks agree well with experimental measurements.