On noise reduction in strain maps obtained with the grid method by averaging images affected by vibrations

Any image-based contactless measurement system has a limited resolution because of sensor noise. If the sensor is rigorously static with respect to the imaged object, a possibility is to reduce noise by averaging images acquired at different times. This paper discusses images of a pseudo-periodic grid used in experimental solid mechanics to give estimations of in-plane displacement and strain components of a deformed flat specimen. Because of the magnification factor which is employed, the grid images are often affected by residual vibrations, thereby invalidating the assumption that the sensor is static. The averaged grid image is thus a biased estimator of the unknown noise-free image. In spite of this, we prove that the retrieved displacement and strain components still benefit from noise reduction by time-averaging. A theoretical model is discussed, and experiments on real and synthetic data sets are provided.