Uso de programación lineal para conocer los parámetros geométricos de superficies cónicas convexas

Abstract

In this paper we proposed a method to obtain the analytic shape of an optical convex surface starting from the coordinates of some points measured on the surface. In other words, we want to find the analytic shape of the surface that best fits a distribution of points measured on a surface (in particular, we want to apply the method to the secondary mirror of the Large Millimeter Telescope; this mirror is a convex surface of 2.57 m diameter, conic constant K= -1, and f/0.4). The method consists of solving the adjustment problem as a problem of polynomial approximation in uniform norm and it is solved by means of linear programming. Finally, we present the result obtained when we evaluate some conical surfaces with the proposed method.