关键词: 齐明点, 球面透镜, 等光程面, 透镜组合

Abstract: Spherical aberration in spherical lenses limits the precision of optical instruments, but using aplanatic points one can effectively eliminate both spherical aberration and coma. While standard textbooks derive the formulas for aplanatic points, they lack intuitive descriptions of the actual ray propagations from these points. This study analyzes the imaging process at a single refractive spherical surface using geometric ray tracing. It first demonstrates that the optical path length from any point on the spherical surface to the two aplanatic points is constant, establishing these points as lying on a surface of constant optical path length. Furthermore, it reveals that when the incidence angle satisfies certain conditions, the reflective point varies, which shows that the two aplanatic points is not the conjugate points of all rays, therefore establishing the correct picture of ray propagation between aplanatic points. The study systematically categorizes two types of aplanatic lens designs. Additionally, it proposes three lens combination schemes: converging lens groups with parallel orientation; oppositely oriented lens groups; and combinations combining diverging and converging lenses. This combination schemes provide a theoretical basis and practical concepts for optical system design.

Key words: Aplanatic point, spherical lens, equivalent optical path surface, lens combination