Refractive geometry for underwater domes

Mengkun She,David Nakath,Yifan Song,Kevin Köser

doi:10.1016/j.isprsjprs.2021.11.006

Abstract

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows for a large field of view, and avoids refraction 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, both in 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 perform the alignment. Consequently, such systems are prone to being decentered by some offset, leading to challenging refraction patterns at the sphere that invalidate the pinhole camera model. We show that the overall camera system becomes an axial camera, even for thick domes as used for deep sea exploration and provide a non-iterative way to compute the center of refraction without requiring knowledge of exact air, glass or water properties. We also analyze the refractive geometry at the sphere, looking at effects such as forward- vs. backward decentering, iso-refraction curves and obtain a 6th-degree polynomial equation for forward projection of 3D points in thin domes. We then propose a pure underwater calibration procedure to estimate the decentering from multiple images. This estimate can either be used during adjustment to guide the mechanical position of the lens, or can be considered in photogrammetric underwater applications.

Highlights

More than two-thirds of Earth’s surface is covered by water – or – by the oceans
Here evaluation becomes very indirect, as it is very hard to obtain ground truth information, and experiments are sensitive to deformation of the tank due to the weight of the water, calibration uncertainties, inaccurate physical measurements of distances and many other effects. While all this will occur in complex systems and real world applications, we think it is important to isolate and understand the refraction effects
If we can directly compute a homography between an underwater image and the chessboard pattern, and the residual error for the homography is below the corner detector noise, this means that the center of refraction is effectively not observable in this calibration image, i.e. refraction effects are drowned in noise

Summary

Introduction

More than two-thirds of Earth’s surface is covered by water – or – by the oceans. For professional photographers, so-called dome port systems have become popular that rely on a spherical window to avoid view limitations They are mechanically more stable and relatively thin spherical glass can resist extremely high pressure at several kilometers of depth. Current practical solutions adopt standard pinhole calibration parameters to compensate the remaining refraction for an approximately centered lens, which allows to achieve high accuracy and has been widely applied in shallow water survey tasks [5, 6, 7, 8] This solution is usually performed at an ideal working distance with a well designed control network, which is difficult to achieve in less controllable scenarios such as robotic mapping applications in the deep ocean

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