An Improved Error Evaluation in One-Dimensional Deformation Measurements by Linear Digital Image Correlation

Simple analytical error formulas were derived for one-dimensional deformation parameter estimation by an image correlation analysis with linear subpixel interpolation. A two-parameter deformation function was used in the analysis to account for both rigid-body translation and constant displacement gradient in an image subset. Errors in parameter estimation were found to explicitly relate to the image grayscale error consisting of subpixel approximation, image noise (including quantization error), and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of errors in deformation parameter estimation on the subset size was established when random image noise was dominant and it was confirmed by the numerical results of both nonlinear and linear image correlation analyses of synthetic image pairs. The power-law relationship can be used to guide the selection of suitable image quality, subpixel approximation, subset size, and subset deformation function for the desired measurement precision of deformation parameters.