Calibration of multi-camera systems with refractive interfaces

A method for performing bundle adjustment–based calibration of a multi-camera setup with refractive interfaces in the optical path is presented. The method contributes to volumetric multi-camera fluid experiments, where it is desirable to avoid tedious alignment of calibration grids in multiple locations and where a premium is placed on accurately locating world points. Cameras are calibrated from image point correspondences of unknown world points, and the location of the refractive interface need not be accurately known a priori. Physical models for two practically relevant imaging configurations are presented; the first is a planar wall separating cameras and a liquid, and the second is a liquid-containing cylindrical tank with finite wall thickness. Each model allows the cameras to be in general location and orientation relative to the interface. A thorough numerical study demonstrates the ability of the calibration method to accurately estimate camera parameters, interface orientation, and world point locations. The numerical study explores the convergence, accuracy, and sensitivity of the calibration method as a function of initialization, camera configuration, volume size, and interface type. The technique is applied to real calibration data where the algorithm is supplied with errant initial parameter estimates and shown to provide accurate results. The ease of implementation and accuracy of the refractive calibration method make the approach attractive for three-dimensional multi-camera fluid measurement methods.