Nonlinear geometric optics: an analytical function theory of the design of optical lenses

摘要

Abstract: Advanced optical ware needs an advanced design idea. This paper is devoted to study the focus-out distribution law of a spherical lens, which discovered the distribution law of the cross-points of the principal light axis of a lens and the outcoming light of the non-axial incident light after being twice refracted by the lens, i.e. focus-out distribution law, or call focus-out distribution function. An explicit function theory of non-focus-out non-spherical lens surface form is put forward first and it may be of use of lens design. This design is different from the traditional spherical lens, the standard quadratic non- spherical lens, and the computer-designed series expansion high order non-spherical lens. It consists in that it is a strict analytical-form explicit function. We call it as analytical-form non-sphere. The analytical-form non- spherical lens make the focus reach optimum state. This ia an important development in optical lens design.!11