Maxwell鱼眼微球透镜对有限远物点的成像及其像差

本文在文献［１］的基础上用变折射率介质中的光线理论研究了Ｍａｘｗｅｌｌ鱼眼球透镜对有限远物点成像的可能，导出了它对有限运物点的像距和纵、横向球差的计算公式。数值计算的结果表明该种球透镜不仅可以对有限远物点成像，且其纵、横向球差甚小．若合适选取透镜的参数，其纵、横向球差可比均匀折射率球透镜小两、三个数量级，在短物距时也比自聚焦棒透镜小。从而进一步显示了它在集成光学和微型光学系统中应用的可能性。

The Aberrations of Maxwell Fisheye Sphere Micro-Lens for the Object Points with Finite Distance

Using the theory of ray in gradient index medium the possibility of imaging for the Maxwell fisheye sphere lens to the object points with finite distance is studied on the basis of reference 1]. The formulas to calculate the image distance and the longitudinal and transverse spherical aberrations have been derived.The results of rigorous numerical calculation shows that the Maxwell fisheye sphere micro-lens may notonly image for the object points with finite distance, but also have very small spherical aberrations. In the suitable parametes its spherical aberrations can be smaller than those of the homogeneous index sphere lens by two or three order of magnitude, and for the short object distances its spherical aberrations are even smaller than those of the selfco, so that the sort of spherical symmetric GRIN spherelens is obviously applicable to integrated optics and micro-optical system.