A-central model for the geometric calibration of hyper-hemispherical lenses

Hyper-hemispherical lenses are optical objective lenses with an ultra-wide field of view. Due to their extreme field of view, the geometric calibration introduces several setup difficulties. Various methods have been developed for simplifying the geometric calibration of a camera in the close-range field by defining intrinsic and extrinsic calibration parameters in a limited ambience of a clean room and taking advantage of simple calibration chessboards. A well-known example in this regard is Zhang's approach for pinhole cameras. A similar approach was pursued by Scaramuzza to model more extensive cameras that include fisheye and panoramic lenses. However, despite this toolbox's efficiency, it is ineffectual in the case of a hyper-hemispherical lens because of model limitations in the approximation of the corresponding projection system. In this study, we define and validate what we believe to be a novel a-central model extension (AME) for the description of hyper-hemispherical lenses that is able to overcome these limitations and to describe more accurately the physical behavior introduced by the design of these lenses. For this apparently new a-central model, we obtain significantly improved calibration results for one of the cameras designed in our laboratory and planned to become a planetary payload of an ESA mission.