  Traditional lens design is a numerical and forward process based on ray
tracing and aberration theory. This method has limitations because the initial
configuration of the lens has to be specified and the aberrations of the lenses
have to considered. This paper is an initial attempt to investigate an analytic
and inverse lens design method, called Lagrange, to overcome these barriers.
Lagrange method tries to build differential equations in terms of the system
parameters and the system input and output (object and image). The generalized
Snell's law in three dimensional space and the normal of a surface in
fundamental differential geometry are applied. Based on the Lagrange method
equations for a single surface system are derived which can perfectly image a
point object.
