This paper develops a set of digital volume correlation (DVC) algorithms to address 3-D deformation measurements of soft gels with the aid of laser-scanning confocal microscopy. As an extension of the well-developed digital image correlation (DIC) method, the present DVC approach adopts a three-dimensional zero-normalized cross-correlation criterion (3-D ZNCC) to perform volume correlation calculations. Based on a 3-D sum-table scheme and the fast Fourier transform technique, a fast algorithm is first proposed to accelerate the integer-voxel correlation computations. Subsequently, two kinds of sub-voxel registration algorithms, i.e., 3-D gradient-based algorithm and 3-D Newton–Raphson algorithm, are presented to obtain the sub-voxel displacement and strain fields of volume images before and after deformation. Both a series of computer-simulated digital volume images and an actual agarose gel sample randomly embedded with fluorescent particles are employed to verify the 3-D deformation measurement capability of the proposed DVC algorithms, which indicates that they are competent to acquire 3-D displacement and strain fields of soft gels.
RETRACTED: Development of a fiber Bragg grating sensing beam for internal deformation measurement in asphalt pavement
