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Imaging theories of rotating quadric surfaces

Year: 2024
Type: article
Abstract: The spherical refraction and reflection imaging formulas with spherical center and curvature center parameters are basic formulas in optics, which are simple and convenient for application. However, the reflection and refraction formulas for spherical surfaces cannot be conveniently extended to other rotating quadric surfaces of the same type. In this paper, what we believe to be a new method is proposed that introduces focus and focus parameters (semi-positive focal chord length) on studying the imaging problems of rotating quadric surfaces (i.e., rotating paraboloid, ellipsoid, hyperboloid, and spherical surface) and their lenses. First, the general imaging formula, optical power formula, object defense, and image square focal length formula, Gauss formula, and Newton formula are established by introducing focus and focus parameters. Second, the base point and base plane of the rotating quadric surface and its optical system are studied, and the position of the base point and base plane, the focal length formula, and the imaging formula of the object and image sides are given. Third, the optical center of the rotating quadric surface and its optical system are studied, the position of interest is determined, and the imaging formula of the system is established. Fourth, the spherical aberration of the rotating quadric surface and its optical system are studied. It is found that the rotating quadric surface and its optical system can be imaged ideally under paraxial light and that there are aberrations in the imaging under non-paraxial light. The results show that the new imaging formulas and conclusions for the rotational quadric surface and its optical system are simple and general. When the corresponding focus parameters are considered, the imaging formulas and conclusions of the rotating paraboloid, ellipsoid, hyperboloid, spherical surface, and gas surface can be obtained. It is also found that the aspheric rotational quadric surface can eliminate spherical aberration, and the imaging quality of the rotational ellipsoid is the highest, which is better than the best spherical imaging; the imaging quality of thin lenses of rotating paraboloid, ellipsoid, and hyperboloid is better than that of the spherical lens, and the imaging quality of thin lenses of rotating hyperboloid and paraboloid are the highest; This research provides technical support for the development of new optical elements and the updating of optical instruments.
DOI: 10.1364/optcon.542435
Language: English
Open Access status: gold
Estimated APC paid: $1,372
OpenAlex ID: W4404229381
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Cites: 18
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Related to: 10