Theoretical analysis of systematic errors in Gaussian weighted digital image correlation due to undermatched shape functions

In recent years, the measurement accuracy of digital image correlation (DIC) has garnered significant attention. Among various advancements, Gaussian weighted DIC (GW-DIC), characterized by the incorporation of Gaussian weights into correlation coefficients, stands out for its remarkable enhancement of metrological performance, especially in complex deformation fields. Herein, we establish a mathematical model to quantify systematic errors caused by undermatched shape functions in GW-DIC. This model formulates the retrieved displacement as a function of weight radius, shape function order, and the underlying displacement field. Through the model, we derive the transfer function of GW-DIC, theoretically demonstrating that GW-DIC can eliminate oscillations in the frequency domain. Moreover, we present closed-form formulas for measured displacement and peak attenuation in Gaussian displacement fields. To our knowledge, this is the first theoretical model for the measurement accuracy of GW-DIC, offering significant potential for applications in metrological performance estimation, calculation parameter optimization, and error compensation.