An efficient solution to ray tracing problems for hemispherical refractive interfaces

Refraction effects, their description and modeling are important aspects of underwater and multimedia photogrammetry. For hemispherical interfaces, the usual approach to refraction is to rely on standard pinhole representations, e.g. by employing the Brown model. This is strictly only possible if entrance pupil of the lens and dome center coincide which is not trivial to achieve. However, simulations and other authors show that systematic residual errors occur with these approaches up to considerable margins if offsets of some millimeters are present. Hence, we propose a novel efficient, yet strict optimization algorithm to account for offsets between dome port centers and entrance pupil. It is about two orders of magnitude faster than standard ray tracing implementations that account for refraction while providing similar or equal results. The algorithm is employed for analysis on a simulation and two real data sets and performance of additionally estimating the dome center is investigated. Our method is capable of improving accuracy in one data set at a maximum of 30% but even so cannot provide improvements for the second data sets. An explicit calibration model is hence to be chosen carefully and most likely relies on the offset’s margins and each individual application.