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Underwater cameras are typically placed behind glass windows to protect themfrom the water. Spherical glass, a dome port, is well suited for high waterpressures at great depth, allows for a large field of view, and avoidsrefraction if a pinhole camera is positioned exactly at the sphere's center.Adjusting a real lens perfectly to the dome center is a challenging task, bothin terms of how to actually guide the centering process (e.g. visual servoing)and how to measure the alignment quality, but also, how to mechanically performthe alignment. Consequently, such systems are prone to being decentered by someoffset, leading to challenging refraction patterns at the sphere thatinvalidate the pinhole camera model. We show that the overall camera systembecomes an axial camera, even for thick domes as used for deep sea explorationand provide a non-iterative way to compute the center of refraction withoutrequiring knowledge of exact air, glass or water properties. We also analyzethe refractive geometry at the sphere, looking at effects such as forward- vs.backward decentering, iso-refraction curves and obtain a 6th-degree polynomialequation for forward projection of 3D points in thin domes. We then propose apure underwater calibration procedure to estimate the decentering from multipleimages. This estimate can either be used during adjustment to guide themechanical position of the lens, or can be considered in photogrammetricunderwater applications.

Refractive Geometry for Underwater Domes