Towards the standardization of in vitro load transfer investigations of hip prostheses

The effect of optical refraction at an interface between optically dissimilar media is modelled in order to apply the principles of three-dimensional digital image correlation (DIC) to measure deformations on submerged objects accurately. Using an analytical formulation for refraction at an interface, a non-linear solution approach is developed to perform stereo calibration. The proposed method incorporates a simplified parametric representation for the orientation and position of an interface(s), accounting explicitly for the effects of refraction at all such interfaces in the path of each stereo camera. Separating the calibration process into two parts, a modified bundle adjustment process with an updated Levenburg–Marquardt (LM) non-linear optimization algorithm is employed to determine (a) intrinsic and extrinsic stereo camera parameters without interface refraction and (b) orientation and position of each planar interface. Detailed simulations demonstrate the efficiency, accuracy, and stability of the methodology when using multiple images of a grid pattern undergoing general rigid body motion, even in the presence of Gaussian noise in the sensor plane measurements, providing a robust framework for practical implementation of the methodology for submerged object measurements.