Digital Image Correlation (DIC) has been established as a flexible and effective technique to measure the displacements on specimen surface by matching the reference subsets in the undeformed image with the target subsets in the deformed image. With the existing DIC techniques, the user must rely on experience and intuition to manually define the size of the reference subset, which is found to be critical to the accuracy of measured displacements. In this paper, the problem of subset size selection in the DIC technique is investigated. Based on the Sum of Squared Differences (SSD) correlation criterion as well as the assumption that the gray intensity gradients of image noise are much lower than that of speckle image, a theoretical model of the displacement measurement accuracy of DIC is derived. The theoretical model indicates that the displacement measurement accuracy of DIC can be accurately predicted based on the variance of image noise and Sum of Square of Subset Intensity Gradients (SSSIG). The model further leads to a simple criterion for choosing a proper subset size for the DIC analysis. Numerical experiments have been performed to validate the proposed concepts, and the calculated results show good agreements with the theoretical predictions.

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.

In digital image correlation (DIC), to obtain the displacements of each point of interest, a correlation criterion must be predefined to evaluate the similarity between the reference subset and the target subset. The correlation criterion is of fundamental importance in DIC, and various correlation criteria have been designed and used in literature. However, little research has been carried out to investigate their relations. In this paper, we first provide a comprehensive overview of various correlation criteria used in DIC. Then we focus on three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion, and a parametric sum of squared difference (${\mathrm{PSSD}}_{ab}$) criterion with two additional unknown parameters, since they are insensitive to the scale and offset changes of the target subset intensity and have been highly recommended for practical use in literature. The three correlation criteria are analyzed to establish their transversal relationships, and the theoretical analyses clearly indicate that the three correlation criteria are actually equivalent, which elegantly unifies these correlation criteria for pattern matching. Finally, the equivalence of these correlation criteria is further validated by numerical simulation and actual experiment.

Fringe-projection profilometry is one of the most commonly used noncontact methods for acquiring the three- dimensional (3D) shape information of objects. In practice, the luminance nonlinearity caused by the gamma effect of a digital projector and a digital camera yields undesired fringe intensity changes, which substantially reduce the measurement accuracy. In this Letter, we present a robust and simple scheme to eliminate the intensity nonlinearity induced by the gamma effect by combining a universal phase-shifting algorithm with a gamma correction method. First, by using three-step and large-step phase-shifting techniques, the gamma value involved in the measurement system can be detected. Then, a gamma pre-encoding process is applied to the system for actual 3D shape measurements. With the proposed technique, high accuracy of measurement can be achieved with the conventional small-step phase-shifting algorithm. The validity of the technique is verified by experiments.

A mathematical description of the absolute out-of-plane height distribution in 3D shape measurement with an arbitrarily arranged fringe projection profilometry system is presented, and a corresponding algorithm is proposed to determine the parameters required for accurate 3D shape determination in practical applications. The proposed technique requires neither a specific and precise experimental setup nor a manual measurement of geometric parameters, and it yields high measurement accuracies while allowing the system components to be arbitrarily set and positioned. Computer simulations and a real experiment have been conducted to verify the validity of the technique.