Investigation of two and three-dimensional image correlation techniques with applications in experimental mechanics.

摘要

The digital image correlation method has become a widely used tool for non-contacting deformation measurement applications. In this work, both two and three-dimensional image correlation techniques and algorithms are investigated with a strong focus on systematic errors. Particular emphasis is placed on the investigation of bias in the iterative spatial-domain image matching algorithm. Wherever possible, analytical expressions are derived, and numerical simulations are used extensively throughout this work.; For the case of two-dimensional image correlation, it is shown that interpolation filters used for the calculation of gray values between samples lead to substantial systematic bias. A method for virtually eliminating this bias is presented. For the bias arising from the finite size of the image neighborhoods employed for matching, a direct error prediction based on Savitzky-Golay filters is derived for different shape functions and verified in numerical studies.; The calibration problem for three-dimensional image correlation is investigated. A bundle-adjustment algorithm for camera and stereo system calibration is implemented and shown to be free of bias for input data contaminated by Gaussian random noise. To obtain bias-free calibration data, the bias in extracting elliptical features is mathematically derived and a correction method for the bias is presented.; Two different approaches to solving the stereo correlation problem are investigated. One algorithm is based on a physical model of the object and implicitly enforces the epipolarity constraint, while the other approach is based on unconstrained matching and optimal triangulation. The constrained correlation algorithm is shown to inherently suffer from bias in displacement estimates even for zero motion. The unconstrained method is shown to not suffer from this bias and additional advantages of the method, such as the possibility to correct for relative camera motion caused by vibration, are presented.; Finally, several application examples demonstrate the capabilities of the digital image correlation method. A comparison between strain gage data and strains measured with image correlation shows excellent agreement. Another example demonstrates the method's capability to measure large strains in excess of 500%.